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Transcript of Satellite Gravimetry - Earth Online - ESA · Satellite Gravimetry. Reiner Rummel. Institute of...
Satellite
Gravimetry
Reiner RummelInstitute of Advanced
Study
(IAS)
Technische Universitaumlt Muumlnchen
Lecture
Three
5th ESA Earth Observation Summer School
2-13 August 2010 ESA-ESRIN Frascati
Italy
Lecture
ThreeMeasurement
of the
free
fall of a test massInterpretation of the
motion
of a satellite
in its
orbit
as test mass
in free
fallFrom
the
orbit
to the
earthlsquos
gravitational
fieldThe
use
of several
test masses
in free
fallCase
One the
satellite
mission
GRACEMeasurement
of temporal changes
in gravitationCase
Two the
ESA Living
Planet mission
GOCEThe
principle
of gravitational
gradiometryOutlook
plan for
lecture
three
test mass
in free
fall
gravitationthe
story
of the
falling
apple
Reference R Westfall The
life of Isaac NewtonCambridge Univ
Press 1999[Compare
page
51 and 305]
the size of gravity from measuringpositionand time
test mass
in free
fall
0 0x t
1 1x t
2 2x t
Absolute-Gravimeter FG5atTU Hannover
test mass
in free
fall
Absolut-Gravimeter
FG5 (Micro-g
Solutions Inc)
InterferometerTripod
SupportSprings
Superspring
Main Spring
APD
ION PUMPDrive Motor
Dropping
Chamber
Free-FallingCorner Cuber
Drag-FreeChamber
Laser
Internal
ReferenceCorner Cube
Servo
Coil
drop height 02m time 02s
600 000 fringes
per drop
100 drops
per set 25 sets
Mach-Zender
laser
interferometer
time Rubidium atomic
clock
10-10
vacuum 10-4 Pa
residual drag compensation
micro
seismisity super spring
test mass
in free
fall
Absolute-Gravimeter FG5atTU Hannover
position laser interferometry
time atomic clock
air resistance to be eliminated
silence no vibrations
test mass
in free
fall
test mass
in free
fall
terrestrial
absolute gravimetry
in the
mountains
10 0 spherical
Earth10-3 flattening
amp centrifugal
acceleration
10-4 mountains valleys ocean
ridges subduction10-5 density
variations
in crust
and mantle
10-6 salt
domes sediment
basins ores10-7 tides atmospheric
pressure
10-8 temporal variations oceans hydrology10-9 ocean
topography polar motion
10-10 general
relativity
gravity
(in laboratory
at TU Muumlnchen)9807 246 72 ms2
stat
iona
ryva
riabl
etest mass
in free
fall
test mass
in free
fall
map
with
global distribution
of in-situ
measurements
I Newton ldquoDe mundi
systemateldquo
1715
satellites
-
test masses
in free
fall
Newtonlsquos
brilliant
conclusionOrbit motion
of planets
(Kepler) obeys
the
same
law
as a
free
falling
bdquoappleldquo
(Galileo)
satellite orbitCase 1 homogeneous sphere space fixed (Kepler) ellipseCase 2 oblate sphere precessing
ellipse (spiral)Case 3 actual Earth modulation from gravitation
satellites
-
test masses
in free
fall
1957 Sputnik 1
earth
flattening
J2
=108410-6
earth
oblateness
deduced
from
orbit
plane precession
satellites
-
test masses
in free
fall
1957 Sputnik 1
today LAGEOS I and II
test mass
in free
fall
Cox amp Chao Science 297 2002
steady decrease of earth flattening change of trend in recent years
satellites
-
test masses
in free
fall
Dickey Marcus de Viron Fukumori 2002
Temporal changes
of the
Earthlsquos
flattening What
are
the
causes
candidates
ocean
masses
melting
ice
caps
atmospheric
masses
hydrology
satellites
-
test masses
in free
fall
observatories ldquoseerdquo
onlyshort arc segments
satellites
-
test masses
in free
fall
A new
era continuous
tracking
in 3D of low
earth
orbiters
(LEOs) by
navigation
satellites
(GPS GALILEO GLONASShellip)
satellites
-
test masses
in free
fall
Absolut-GravimeterFG5TU Hannover
bull location GPS
bull time synchronized atomic clocks
bull air resistance measured
bull silence no ground vibrations
satellites
-
test masses
in free
fall
atmospheric
pressure
at satellite
altitude
laboratory10-4Pa = 10-6mbar300 km altitude87710-8mbar
satellites
-
test masses
in free
fall
Emiliani
C1992 p272
CHAMP satelliteGeoForschungsZentrum
Potsdam
mission life time 2000 ndash
2010
star
sensorsGPS receiver
accelerometerat centre
of mass
satellites
-
test masses
in free
fall
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
positioning (orbit determination)of CHAMP by GPS
σ
= 3 cm
(Rothacher
amp Svehla 2003)
from
the
orbit
to gravitation
gravitation from
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
2 2x t 0 0x t
1 1x t
from
the
orbit
to gravitation
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
Lecture
ThreeMeasurement
of the
free
fall of a test massInterpretation of the
motion
of a satellite
in its
orbit
as test mass
in free
fallFrom
the
orbit
to the
earthlsquos
gravitational
fieldThe
use
of several
test masses
in free
fallCase
One the
satellite
mission
GRACEMeasurement
of temporal changes
in gravitationCase
Two the
ESA Living
Planet mission
GOCEThe
principle
of gravitational
gradiometryOutlook
plan for
lecture
three
test mass
in free
fall
gravitationthe
story
of the
falling
apple
Reference R Westfall The
life of Isaac NewtonCambridge Univ
Press 1999[Compare
page
51 and 305]
the size of gravity from measuringpositionand time
test mass
in free
fall
0 0x t
1 1x t
2 2x t
Absolute-Gravimeter FG5atTU Hannover
test mass
in free
fall
Absolut-Gravimeter
FG5 (Micro-g
Solutions Inc)
InterferometerTripod
SupportSprings
Superspring
Main Spring
APD
ION PUMPDrive Motor
Dropping
Chamber
Free-FallingCorner Cuber
Drag-FreeChamber
Laser
Internal
ReferenceCorner Cube
Servo
Coil
drop height 02m time 02s
600 000 fringes
per drop
100 drops
per set 25 sets
Mach-Zender
laser
interferometer
time Rubidium atomic
clock
10-10
vacuum 10-4 Pa
residual drag compensation
micro
seismisity super spring
test mass
in free
fall
Absolute-Gravimeter FG5atTU Hannover
position laser interferometry
time atomic clock
air resistance to be eliminated
silence no vibrations
test mass
in free
fall
test mass
in free
fall
terrestrial
absolute gravimetry
in the
mountains
10 0 spherical
Earth10-3 flattening
amp centrifugal
acceleration
10-4 mountains valleys ocean
ridges subduction10-5 density
variations
in crust
and mantle
10-6 salt
domes sediment
basins ores10-7 tides atmospheric
pressure
10-8 temporal variations oceans hydrology10-9 ocean
topography polar motion
10-10 general
relativity
gravity
(in laboratory
at TU Muumlnchen)9807 246 72 ms2
stat
iona
ryva
riabl
etest mass
in free
fall
test mass
in free
fall
map
with
global distribution
of in-situ
measurements
I Newton ldquoDe mundi
systemateldquo
1715
satellites
-
test masses
in free
fall
Newtonlsquos
brilliant
conclusionOrbit motion
of planets
(Kepler) obeys
the
same
law
as a
free
falling
bdquoappleldquo
(Galileo)
satellite orbitCase 1 homogeneous sphere space fixed (Kepler) ellipseCase 2 oblate sphere precessing
ellipse (spiral)Case 3 actual Earth modulation from gravitation
satellites
-
test masses
in free
fall
1957 Sputnik 1
earth
flattening
J2
=108410-6
earth
oblateness
deduced
from
orbit
plane precession
satellites
-
test masses
in free
fall
1957 Sputnik 1
today LAGEOS I and II
test mass
in free
fall
Cox amp Chao Science 297 2002
steady decrease of earth flattening change of trend in recent years
satellites
-
test masses
in free
fall
Dickey Marcus de Viron Fukumori 2002
Temporal changes
of the
Earthlsquos
flattening What
are
the
causes
candidates
ocean
masses
melting
ice
caps
atmospheric
masses
hydrology
satellites
-
test masses
in free
fall
observatories ldquoseerdquo
onlyshort arc segments
satellites
-
test masses
in free
fall
A new
era continuous
tracking
in 3D of low
earth
orbiters
(LEOs) by
navigation
satellites
(GPS GALILEO GLONASShellip)
satellites
-
test masses
in free
fall
Absolut-GravimeterFG5TU Hannover
bull location GPS
bull time synchronized atomic clocks
bull air resistance measured
bull silence no ground vibrations
satellites
-
test masses
in free
fall
atmospheric
pressure
at satellite
altitude
laboratory10-4Pa = 10-6mbar300 km altitude87710-8mbar
satellites
-
test masses
in free
fall
Emiliani
C1992 p272
CHAMP satelliteGeoForschungsZentrum
Potsdam
mission life time 2000 ndash
2010
star
sensorsGPS receiver
accelerometerat centre
of mass
satellites
-
test masses
in free
fall
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
positioning (orbit determination)of CHAMP by GPS
σ
= 3 cm
(Rothacher
amp Svehla 2003)
from
the
orbit
to gravitation
gravitation from
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
2 2x t 0 0x t
1 1x t
from
the
orbit
to gravitation
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
test mass
in free
fall
gravitationthe
story
of the
falling
apple
Reference R Westfall The
life of Isaac NewtonCambridge Univ
Press 1999[Compare
page
51 and 305]
the size of gravity from measuringpositionand time
test mass
in free
fall
0 0x t
1 1x t
2 2x t
Absolute-Gravimeter FG5atTU Hannover
test mass
in free
fall
Absolut-Gravimeter
FG5 (Micro-g
Solutions Inc)
InterferometerTripod
SupportSprings
Superspring
Main Spring
APD
ION PUMPDrive Motor
Dropping
Chamber
Free-FallingCorner Cuber
Drag-FreeChamber
Laser
Internal
ReferenceCorner Cube
Servo
Coil
drop height 02m time 02s
600 000 fringes
per drop
100 drops
per set 25 sets
Mach-Zender
laser
interferometer
time Rubidium atomic
clock
10-10
vacuum 10-4 Pa
residual drag compensation
micro
seismisity super spring
test mass
in free
fall
Absolute-Gravimeter FG5atTU Hannover
position laser interferometry
time atomic clock
air resistance to be eliminated
silence no vibrations
test mass
in free
fall
test mass
in free
fall
terrestrial
absolute gravimetry
in the
mountains
10 0 spherical
Earth10-3 flattening
amp centrifugal
acceleration
10-4 mountains valleys ocean
ridges subduction10-5 density
variations
in crust
and mantle
10-6 salt
domes sediment
basins ores10-7 tides atmospheric
pressure
10-8 temporal variations oceans hydrology10-9 ocean
topography polar motion
10-10 general
relativity
gravity
(in laboratory
at TU Muumlnchen)9807 246 72 ms2
stat
iona
ryva
riabl
etest mass
in free
fall
test mass
in free
fall
map
with
global distribution
of in-situ
measurements
I Newton ldquoDe mundi
systemateldquo
1715
satellites
-
test masses
in free
fall
Newtonlsquos
brilliant
conclusionOrbit motion
of planets
(Kepler) obeys
the
same
law
as a
free
falling
bdquoappleldquo
(Galileo)
satellite orbitCase 1 homogeneous sphere space fixed (Kepler) ellipseCase 2 oblate sphere precessing
ellipse (spiral)Case 3 actual Earth modulation from gravitation
satellites
-
test masses
in free
fall
1957 Sputnik 1
earth
flattening
J2
=108410-6
earth
oblateness
deduced
from
orbit
plane precession
satellites
-
test masses
in free
fall
1957 Sputnik 1
today LAGEOS I and II
test mass
in free
fall
Cox amp Chao Science 297 2002
steady decrease of earth flattening change of trend in recent years
satellites
-
test masses
in free
fall
Dickey Marcus de Viron Fukumori 2002
Temporal changes
of the
Earthlsquos
flattening What
are
the
causes
candidates
ocean
masses
melting
ice
caps
atmospheric
masses
hydrology
satellites
-
test masses
in free
fall
observatories ldquoseerdquo
onlyshort arc segments
satellites
-
test masses
in free
fall
A new
era continuous
tracking
in 3D of low
earth
orbiters
(LEOs) by
navigation
satellites
(GPS GALILEO GLONASShellip)
satellites
-
test masses
in free
fall
Absolut-GravimeterFG5TU Hannover
bull location GPS
bull time synchronized atomic clocks
bull air resistance measured
bull silence no ground vibrations
satellites
-
test masses
in free
fall
atmospheric
pressure
at satellite
altitude
laboratory10-4Pa = 10-6mbar300 km altitude87710-8mbar
satellites
-
test masses
in free
fall
Emiliani
C1992 p272
CHAMP satelliteGeoForschungsZentrum
Potsdam
mission life time 2000 ndash
2010
star
sensorsGPS receiver
accelerometerat centre
of mass
satellites
-
test masses
in free
fall
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
positioning (orbit determination)of CHAMP by GPS
σ
= 3 cm
(Rothacher
amp Svehla 2003)
from
the
orbit
to gravitation
gravitation from
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
2 2x t 0 0x t
1 1x t
from
the
orbit
to gravitation
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
the size of gravity from measuringpositionand time
test mass
in free
fall
0 0x t
1 1x t
2 2x t
Absolute-Gravimeter FG5atTU Hannover
test mass
in free
fall
Absolut-Gravimeter
FG5 (Micro-g
Solutions Inc)
InterferometerTripod
SupportSprings
Superspring
Main Spring
APD
ION PUMPDrive Motor
Dropping
Chamber
Free-FallingCorner Cuber
Drag-FreeChamber
Laser
Internal
ReferenceCorner Cube
Servo
Coil
drop height 02m time 02s
600 000 fringes
per drop
100 drops
per set 25 sets
Mach-Zender
laser
interferometer
time Rubidium atomic
clock
10-10
vacuum 10-4 Pa
residual drag compensation
micro
seismisity super spring
test mass
in free
fall
Absolute-Gravimeter FG5atTU Hannover
position laser interferometry
time atomic clock
air resistance to be eliminated
silence no vibrations
test mass
in free
fall
test mass
in free
fall
terrestrial
absolute gravimetry
in the
mountains
10 0 spherical
Earth10-3 flattening
amp centrifugal
acceleration
10-4 mountains valleys ocean
ridges subduction10-5 density
variations
in crust
and mantle
10-6 salt
domes sediment
basins ores10-7 tides atmospheric
pressure
10-8 temporal variations oceans hydrology10-9 ocean
topography polar motion
10-10 general
relativity
gravity
(in laboratory
at TU Muumlnchen)9807 246 72 ms2
stat
iona
ryva
riabl
etest mass
in free
fall
test mass
in free
fall
map
with
global distribution
of in-situ
measurements
I Newton ldquoDe mundi
systemateldquo
1715
satellites
-
test masses
in free
fall
Newtonlsquos
brilliant
conclusionOrbit motion
of planets
(Kepler) obeys
the
same
law
as a
free
falling
bdquoappleldquo
(Galileo)
satellite orbitCase 1 homogeneous sphere space fixed (Kepler) ellipseCase 2 oblate sphere precessing
ellipse (spiral)Case 3 actual Earth modulation from gravitation
satellites
-
test masses
in free
fall
1957 Sputnik 1
earth
flattening
J2
=108410-6
earth
oblateness
deduced
from
orbit
plane precession
satellites
-
test masses
in free
fall
1957 Sputnik 1
today LAGEOS I and II
test mass
in free
fall
Cox amp Chao Science 297 2002
steady decrease of earth flattening change of trend in recent years
satellites
-
test masses
in free
fall
Dickey Marcus de Viron Fukumori 2002
Temporal changes
of the
Earthlsquos
flattening What
are
the
causes
candidates
ocean
masses
melting
ice
caps
atmospheric
masses
hydrology
satellites
-
test masses
in free
fall
observatories ldquoseerdquo
onlyshort arc segments
satellites
-
test masses
in free
fall
A new
era continuous
tracking
in 3D of low
earth
orbiters
(LEOs) by
navigation
satellites
(GPS GALILEO GLONASShellip)
satellites
-
test masses
in free
fall
Absolut-GravimeterFG5TU Hannover
bull location GPS
bull time synchronized atomic clocks
bull air resistance measured
bull silence no ground vibrations
satellites
-
test masses
in free
fall
atmospheric
pressure
at satellite
altitude
laboratory10-4Pa = 10-6mbar300 km altitude87710-8mbar
satellites
-
test masses
in free
fall
Emiliani
C1992 p272
CHAMP satelliteGeoForschungsZentrum
Potsdam
mission life time 2000 ndash
2010
star
sensorsGPS receiver
accelerometerat centre
of mass
satellites
-
test masses
in free
fall
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
positioning (orbit determination)of CHAMP by GPS
σ
= 3 cm
(Rothacher
amp Svehla 2003)
from
the
orbit
to gravitation
gravitation from
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
2 2x t 0 0x t
1 1x t
from
the
orbit
to gravitation
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
Absolute-Gravimeter FG5atTU Hannover
test mass
in free
fall
Absolut-Gravimeter
FG5 (Micro-g
Solutions Inc)
InterferometerTripod
SupportSprings
Superspring
Main Spring
APD
ION PUMPDrive Motor
Dropping
Chamber
Free-FallingCorner Cuber
Drag-FreeChamber
Laser
Internal
ReferenceCorner Cube
Servo
Coil
drop height 02m time 02s
600 000 fringes
per drop
100 drops
per set 25 sets
Mach-Zender
laser
interferometer
time Rubidium atomic
clock
10-10
vacuum 10-4 Pa
residual drag compensation
micro
seismisity super spring
test mass
in free
fall
Absolute-Gravimeter FG5atTU Hannover
position laser interferometry
time atomic clock
air resistance to be eliminated
silence no vibrations
test mass
in free
fall
test mass
in free
fall
terrestrial
absolute gravimetry
in the
mountains
10 0 spherical
Earth10-3 flattening
amp centrifugal
acceleration
10-4 mountains valleys ocean
ridges subduction10-5 density
variations
in crust
and mantle
10-6 salt
domes sediment
basins ores10-7 tides atmospheric
pressure
10-8 temporal variations oceans hydrology10-9 ocean
topography polar motion
10-10 general
relativity
gravity
(in laboratory
at TU Muumlnchen)9807 246 72 ms2
stat
iona
ryva
riabl
etest mass
in free
fall
test mass
in free
fall
map
with
global distribution
of in-situ
measurements
I Newton ldquoDe mundi
systemateldquo
1715
satellites
-
test masses
in free
fall
Newtonlsquos
brilliant
conclusionOrbit motion
of planets
(Kepler) obeys
the
same
law
as a
free
falling
bdquoappleldquo
(Galileo)
satellite orbitCase 1 homogeneous sphere space fixed (Kepler) ellipseCase 2 oblate sphere precessing
ellipse (spiral)Case 3 actual Earth modulation from gravitation
satellites
-
test masses
in free
fall
1957 Sputnik 1
earth
flattening
J2
=108410-6
earth
oblateness
deduced
from
orbit
plane precession
satellites
-
test masses
in free
fall
1957 Sputnik 1
today LAGEOS I and II
test mass
in free
fall
Cox amp Chao Science 297 2002
steady decrease of earth flattening change of trend in recent years
satellites
-
test masses
in free
fall
Dickey Marcus de Viron Fukumori 2002
Temporal changes
of the
Earthlsquos
flattening What
are
the
causes
candidates
ocean
masses
melting
ice
caps
atmospheric
masses
hydrology
satellites
-
test masses
in free
fall
observatories ldquoseerdquo
onlyshort arc segments
satellites
-
test masses
in free
fall
A new
era continuous
tracking
in 3D of low
earth
orbiters
(LEOs) by
navigation
satellites
(GPS GALILEO GLONASShellip)
satellites
-
test masses
in free
fall
Absolut-GravimeterFG5TU Hannover
bull location GPS
bull time synchronized atomic clocks
bull air resistance measured
bull silence no ground vibrations
satellites
-
test masses
in free
fall
atmospheric
pressure
at satellite
altitude
laboratory10-4Pa = 10-6mbar300 km altitude87710-8mbar
satellites
-
test masses
in free
fall
Emiliani
C1992 p272
CHAMP satelliteGeoForschungsZentrum
Potsdam
mission life time 2000 ndash
2010
star
sensorsGPS receiver
accelerometerat centre
of mass
satellites
-
test masses
in free
fall
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
positioning (orbit determination)of CHAMP by GPS
σ
= 3 cm
(Rothacher
amp Svehla 2003)
from
the
orbit
to gravitation
gravitation from
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
2 2x t 0 0x t
1 1x t
from
the
orbit
to gravitation
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
Absolut-Gravimeter
FG5 (Micro-g
Solutions Inc)
InterferometerTripod
SupportSprings
Superspring
Main Spring
APD
ION PUMPDrive Motor
Dropping
Chamber
Free-FallingCorner Cuber
Drag-FreeChamber
Laser
Internal
ReferenceCorner Cube
Servo
Coil
drop height 02m time 02s
600 000 fringes
per drop
100 drops
per set 25 sets
Mach-Zender
laser
interferometer
time Rubidium atomic
clock
10-10
vacuum 10-4 Pa
residual drag compensation
micro
seismisity super spring
test mass
in free
fall
Absolute-Gravimeter FG5atTU Hannover
position laser interferometry
time atomic clock
air resistance to be eliminated
silence no vibrations
test mass
in free
fall
test mass
in free
fall
terrestrial
absolute gravimetry
in the
mountains
10 0 spherical
Earth10-3 flattening
amp centrifugal
acceleration
10-4 mountains valleys ocean
ridges subduction10-5 density
variations
in crust
and mantle
10-6 salt
domes sediment
basins ores10-7 tides atmospheric
pressure
10-8 temporal variations oceans hydrology10-9 ocean
topography polar motion
10-10 general
relativity
gravity
(in laboratory
at TU Muumlnchen)9807 246 72 ms2
stat
iona
ryva
riabl
etest mass
in free
fall
test mass
in free
fall
map
with
global distribution
of in-situ
measurements
I Newton ldquoDe mundi
systemateldquo
1715
satellites
-
test masses
in free
fall
Newtonlsquos
brilliant
conclusionOrbit motion
of planets
(Kepler) obeys
the
same
law
as a
free
falling
bdquoappleldquo
(Galileo)
satellite orbitCase 1 homogeneous sphere space fixed (Kepler) ellipseCase 2 oblate sphere precessing
ellipse (spiral)Case 3 actual Earth modulation from gravitation
satellites
-
test masses
in free
fall
1957 Sputnik 1
earth
flattening
J2
=108410-6
earth
oblateness
deduced
from
orbit
plane precession
satellites
-
test masses
in free
fall
1957 Sputnik 1
today LAGEOS I and II
test mass
in free
fall
Cox amp Chao Science 297 2002
steady decrease of earth flattening change of trend in recent years
satellites
-
test masses
in free
fall
Dickey Marcus de Viron Fukumori 2002
Temporal changes
of the
Earthlsquos
flattening What
are
the
causes
candidates
ocean
masses
melting
ice
caps
atmospheric
masses
hydrology
satellites
-
test masses
in free
fall
observatories ldquoseerdquo
onlyshort arc segments
satellites
-
test masses
in free
fall
A new
era continuous
tracking
in 3D of low
earth
orbiters
(LEOs) by
navigation
satellites
(GPS GALILEO GLONASShellip)
satellites
-
test masses
in free
fall
Absolut-GravimeterFG5TU Hannover
bull location GPS
bull time synchronized atomic clocks
bull air resistance measured
bull silence no ground vibrations
satellites
-
test masses
in free
fall
atmospheric
pressure
at satellite
altitude
laboratory10-4Pa = 10-6mbar300 km altitude87710-8mbar
satellites
-
test masses
in free
fall
Emiliani
C1992 p272
CHAMP satelliteGeoForschungsZentrum
Potsdam
mission life time 2000 ndash
2010
star
sensorsGPS receiver
accelerometerat centre
of mass
satellites
-
test masses
in free
fall
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
positioning (orbit determination)of CHAMP by GPS
σ
= 3 cm
(Rothacher
amp Svehla 2003)
from
the
orbit
to gravitation
gravitation from
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
2 2x t 0 0x t
1 1x t
from
the
orbit
to gravitation
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
Absolute-Gravimeter FG5atTU Hannover
position laser interferometry
time atomic clock
air resistance to be eliminated
silence no vibrations
test mass
in free
fall
test mass
in free
fall
terrestrial
absolute gravimetry
in the
mountains
10 0 spherical
Earth10-3 flattening
amp centrifugal
acceleration
10-4 mountains valleys ocean
ridges subduction10-5 density
variations
in crust
and mantle
10-6 salt
domes sediment
basins ores10-7 tides atmospheric
pressure
10-8 temporal variations oceans hydrology10-9 ocean
topography polar motion
10-10 general
relativity
gravity
(in laboratory
at TU Muumlnchen)9807 246 72 ms2
stat
iona
ryva
riabl
etest mass
in free
fall
test mass
in free
fall
map
with
global distribution
of in-situ
measurements
I Newton ldquoDe mundi
systemateldquo
1715
satellites
-
test masses
in free
fall
Newtonlsquos
brilliant
conclusionOrbit motion
of planets
(Kepler) obeys
the
same
law
as a
free
falling
bdquoappleldquo
(Galileo)
satellite orbitCase 1 homogeneous sphere space fixed (Kepler) ellipseCase 2 oblate sphere precessing
ellipse (spiral)Case 3 actual Earth modulation from gravitation
satellites
-
test masses
in free
fall
1957 Sputnik 1
earth
flattening
J2
=108410-6
earth
oblateness
deduced
from
orbit
plane precession
satellites
-
test masses
in free
fall
1957 Sputnik 1
today LAGEOS I and II
test mass
in free
fall
Cox amp Chao Science 297 2002
steady decrease of earth flattening change of trend in recent years
satellites
-
test masses
in free
fall
Dickey Marcus de Viron Fukumori 2002
Temporal changes
of the
Earthlsquos
flattening What
are
the
causes
candidates
ocean
masses
melting
ice
caps
atmospheric
masses
hydrology
satellites
-
test masses
in free
fall
observatories ldquoseerdquo
onlyshort arc segments
satellites
-
test masses
in free
fall
A new
era continuous
tracking
in 3D of low
earth
orbiters
(LEOs) by
navigation
satellites
(GPS GALILEO GLONASShellip)
satellites
-
test masses
in free
fall
Absolut-GravimeterFG5TU Hannover
bull location GPS
bull time synchronized atomic clocks
bull air resistance measured
bull silence no ground vibrations
satellites
-
test masses
in free
fall
atmospheric
pressure
at satellite
altitude
laboratory10-4Pa = 10-6mbar300 km altitude87710-8mbar
satellites
-
test masses
in free
fall
Emiliani
C1992 p272
CHAMP satelliteGeoForschungsZentrum
Potsdam
mission life time 2000 ndash
2010
star
sensorsGPS receiver
accelerometerat centre
of mass
satellites
-
test masses
in free
fall
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
positioning (orbit determination)of CHAMP by GPS
σ
= 3 cm
(Rothacher
amp Svehla 2003)
from
the
orbit
to gravitation
gravitation from
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
2 2x t 0 0x t
1 1x t
from
the
orbit
to gravitation
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
test mass
in free
fall
terrestrial
absolute gravimetry
in the
mountains
10 0 spherical
Earth10-3 flattening
amp centrifugal
acceleration
10-4 mountains valleys ocean
ridges subduction10-5 density
variations
in crust
and mantle
10-6 salt
domes sediment
basins ores10-7 tides atmospheric
pressure
10-8 temporal variations oceans hydrology10-9 ocean
topography polar motion
10-10 general
relativity
gravity
(in laboratory
at TU Muumlnchen)9807 246 72 ms2
stat
iona
ryva
riabl
etest mass
in free
fall
test mass
in free
fall
map
with
global distribution
of in-situ
measurements
I Newton ldquoDe mundi
systemateldquo
1715
satellites
-
test masses
in free
fall
Newtonlsquos
brilliant
conclusionOrbit motion
of planets
(Kepler) obeys
the
same
law
as a
free
falling
bdquoappleldquo
(Galileo)
satellite orbitCase 1 homogeneous sphere space fixed (Kepler) ellipseCase 2 oblate sphere precessing
ellipse (spiral)Case 3 actual Earth modulation from gravitation
satellites
-
test masses
in free
fall
1957 Sputnik 1
earth
flattening
J2
=108410-6
earth
oblateness
deduced
from
orbit
plane precession
satellites
-
test masses
in free
fall
1957 Sputnik 1
today LAGEOS I and II
test mass
in free
fall
Cox amp Chao Science 297 2002
steady decrease of earth flattening change of trend in recent years
satellites
-
test masses
in free
fall
Dickey Marcus de Viron Fukumori 2002
Temporal changes
of the
Earthlsquos
flattening What
are
the
causes
candidates
ocean
masses
melting
ice
caps
atmospheric
masses
hydrology
satellites
-
test masses
in free
fall
observatories ldquoseerdquo
onlyshort arc segments
satellites
-
test masses
in free
fall
A new
era continuous
tracking
in 3D of low
earth
orbiters
(LEOs) by
navigation
satellites
(GPS GALILEO GLONASShellip)
satellites
-
test masses
in free
fall
Absolut-GravimeterFG5TU Hannover
bull location GPS
bull time synchronized atomic clocks
bull air resistance measured
bull silence no ground vibrations
satellites
-
test masses
in free
fall
atmospheric
pressure
at satellite
altitude
laboratory10-4Pa = 10-6mbar300 km altitude87710-8mbar
satellites
-
test masses
in free
fall
Emiliani
C1992 p272
CHAMP satelliteGeoForschungsZentrum
Potsdam
mission life time 2000 ndash
2010
star
sensorsGPS receiver
accelerometerat centre
of mass
satellites
-
test masses
in free
fall
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
positioning (orbit determination)of CHAMP by GPS
σ
= 3 cm
(Rothacher
amp Svehla 2003)
from
the
orbit
to gravitation
gravitation from
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
2 2x t 0 0x t
1 1x t
from
the
orbit
to gravitation
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
10 0 spherical
Earth10-3 flattening
amp centrifugal
acceleration
10-4 mountains valleys ocean
ridges subduction10-5 density
variations
in crust
and mantle
10-6 salt
domes sediment
basins ores10-7 tides atmospheric
pressure
10-8 temporal variations oceans hydrology10-9 ocean
topography polar motion
10-10 general
relativity
gravity
(in laboratory
at TU Muumlnchen)9807 246 72 ms2
stat
iona
ryva
riabl
etest mass
in free
fall
test mass
in free
fall
map
with
global distribution
of in-situ
measurements
I Newton ldquoDe mundi
systemateldquo
1715
satellites
-
test masses
in free
fall
Newtonlsquos
brilliant
conclusionOrbit motion
of planets
(Kepler) obeys
the
same
law
as a
free
falling
bdquoappleldquo
(Galileo)
satellite orbitCase 1 homogeneous sphere space fixed (Kepler) ellipseCase 2 oblate sphere precessing
ellipse (spiral)Case 3 actual Earth modulation from gravitation
satellites
-
test masses
in free
fall
1957 Sputnik 1
earth
flattening
J2
=108410-6
earth
oblateness
deduced
from
orbit
plane precession
satellites
-
test masses
in free
fall
1957 Sputnik 1
today LAGEOS I and II
test mass
in free
fall
Cox amp Chao Science 297 2002
steady decrease of earth flattening change of trend in recent years
satellites
-
test masses
in free
fall
Dickey Marcus de Viron Fukumori 2002
Temporal changes
of the
Earthlsquos
flattening What
are
the
causes
candidates
ocean
masses
melting
ice
caps
atmospheric
masses
hydrology
satellites
-
test masses
in free
fall
observatories ldquoseerdquo
onlyshort arc segments
satellites
-
test masses
in free
fall
A new
era continuous
tracking
in 3D of low
earth
orbiters
(LEOs) by
navigation
satellites
(GPS GALILEO GLONASShellip)
satellites
-
test masses
in free
fall
Absolut-GravimeterFG5TU Hannover
bull location GPS
bull time synchronized atomic clocks
bull air resistance measured
bull silence no ground vibrations
satellites
-
test masses
in free
fall
atmospheric
pressure
at satellite
altitude
laboratory10-4Pa = 10-6mbar300 km altitude87710-8mbar
satellites
-
test masses
in free
fall
Emiliani
C1992 p272
CHAMP satelliteGeoForschungsZentrum
Potsdam
mission life time 2000 ndash
2010
star
sensorsGPS receiver
accelerometerat centre
of mass
satellites
-
test masses
in free
fall
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
positioning (orbit determination)of CHAMP by GPS
σ
= 3 cm
(Rothacher
amp Svehla 2003)
from
the
orbit
to gravitation
gravitation from
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
2 2x t 0 0x t
1 1x t
from
the
orbit
to gravitation
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
test mass
in free
fall
map
with
global distribution
of in-situ
measurements
I Newton ldquoDe mundi
systemateldquo
1715
satellites
-
test masses
in free
fall
Newtonlsquos
brilliant
conclusionOrbit motion
of planets
(Kepler) obeys
the
same
law
as a
free
falling
bdquoappleldquo
(Galileo)
satellite orbitCase 1 homogeneous sphere space fixed (Kepler) ellipseCase 2 oblate sphere precessing
ellipse (spiral)Case 3 actual Earth modulation from gravitation
satellites
-
test masses
in free
fall
1957 Sputnik 1
earth
flattening
J2
=108410-6
earth
oblateness
deduced
from
orbit
plane precession
satellites
-
test masses
in free
fall
1957 Sputnik 1
today LAGEOS I and II
test mass
in free
fall
Cox amp Chao Science 297 2002
steady decrease of earth flattening change of trend in recent years
satellites
-
test masses
in free
fall
Dickey Marcus de Viron Fukumori 2002
Temporal changes
of the
Earthlsquos
flattening What
are
the
causes
candidates
ocean
masses
melting
ice
caps
atmospheric
masses
hydrology
satellites
-
test masses
in free
fall
observatories ldquoseerdquo
onlyshort arc segments
satellites
-
test masses
in free
fall
A new
era continuous
tracking
in 3D of low
earth
orbiters
(LEOs) by
navigation
satellites
(GPS GALILEO GLONASShellip)
satellites
-
test masses
in free
fall
Absolut-GravimeterFG5TU Hannover
bull location GPS
bull time synchronized atomic clocks
bull air resistance measured
bull silence no ground vibrations
satellites
-
test masses
in free
fall
atmospheric
pressure
at satellite
altitude
laboratory10-4Pa = 10-6mbar300 km altitude87710-8mbar
satellites
-
test masses
in free
fall
Emiliani
C1992 p272
CHAMP satelliteGeoForschungsZentrum
Potsdam
mission life time 2000 ndash
2010
star
sensorsGPS receiver
accelerometerat centre
of mass
satellites
-
test masses
in free
fall
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
positioning (orbit determination)of CHAMP by GPS
σ
= 3 cm
(Rothacher
amp Svehla 2003)
from
the
orbit
to gravitation
gravitation from
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
2 2x t 0 0x t
1 1x t
from
the
orbit
to gravitation
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
I Newton ldquoDe mundi
systemateldquo
1715
satellites
-
test masses
in free
fall
Newtonlsquos
brilliant
conclusionOrbit motion
of planets
(Kepler) obeys
the
same
law
as a
free
falling
bdquoappleldquo
(Galileo)
satellite orbitCase 1 homogeneous sphere space fixed (Kepler) ellipseCase 2 oblate sphere precessing
ellipse (spiral)Case 3 actual Earth modulation from gravitation
satellites
-
test masses
in free
fall
1957 Sputnik 1
earth
flattening
J2
=108410-6
earth
oblateness
deduced
from
orbit
plane precession
satellites
-
test masses
in free
fall
1957 Sputnik 1
today LAGEOS I and II
test mass
in free
fall
Cox amp Chao Science 297 2002
steady decrease of earth flattening change of trend in recent years
satellites
-
test masses
in free
fall
Dickey Marcus de Viron Fukumori 2002
Temporal changes
of the
Earthlsquos
flattening What
are
the
causes
candidates
ocean
masses
melting
ice
caps
atmospheric
masses
hydrology
satellites
-
test masses
in free
fall
observatories ldquoseerdquo
onlyshort arc segments
satellites
-
test masses
in free
fall
A new
era continuous
tracking
in 3D of low
earth
orbiters
(LEOs) by
navigation
satellites
(GPS GALILEO GLONASShellip)
satellites
-
test masses
in free
fall
Absolut-GravimeterFG5TU Hannover
bull location GPS
bull time synchronized atomic clocks
bull air resistance measured
bull silence no ground vibrations
satellites
-
test masses
in free
fall
atmospheric
pressure
at satellite
altitude
laboratory10-4Pa = 10-6mbar300 km altitude87710-8mbar
satellites
-
test masses
in free
fall
Emiliani
C1992 p272
CHAMP satelliteGeoForschungsZentrum
Potsdam
mission life time 2000 ndash
2010
star
sensorsGPS receiver
accelerometerat centre
of mass
satellites
-
test masses
in free
fall
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
positioning (orbit determination)of CHAMP by GPS
σ
= 3 cm
(Rothacher
amp Svehla 2003)
from
the
orbit
to gravitation
gravitation from
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
2 2x t 0 0x t
1 1x t
from
the
orbit
to gravitation
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
satellite orbitCase 1 homogeneous sphere space fixed (Kepler) ellipseCase 2 oblate sphere precessing
ellipse (spiral)Case 3 actual Earth modulation from gravitation
satellites
-
test masses
in free
fall
1957 Sputnik 1
earth
flattening
J2
=108410-6
earth
oblateness
deduced
from
orbit
plane precession
satellites
-
test masses
in free
fall
1957 Sputnik 1
today LAGEOS I and II
test mass
in free
fall
Cox amp Chao Science 297 2002
steady decrease of earth flattening change of trend in recent years
satellites
-
test masses
in free
fall
Dickey Marcus de Viron Fukumori 2002
Temporal changes
of the
Earthlsquos
flattening What
are
the
causes
candidates
ocean
masses
melting
ice
caps
atmospheric
masses
hydrology
satellites
-
test masses
in free
fall
observatories ldquoseerdquo
onlyshort arc segments
satellites
-
test masses
in free
fall
A new
era continuous
tracking
in 3D of low
earth
orbiters
(LEOs) by
navigation
satellites
(GPS GALILEO GLONASShellip)
satellites
-
test masses
in free
fall
Absolut-GravimeterFG5TU Hannover
bull location GPS
bull time synchronized atomic clocks
bull air resistance measured
bull silence no ground vibrations
satellites
-
test masses
in free
fall
atmospheric
pressure
at satellite
altitude
laboratory10-4Pa = 10-6mbar300 km altitude87710-8mbar
satellites
-
test masses
in free
fall
Emiliani
C1992 p272
CHAMP satelliteGeoForschungsZentrum
Potsdam
mission life time 2000 ndash
2010
star
sensorsGPS receiver
accelerometerat centre
of mass
satellites
-
test masses
in free
fall
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
positioning (orbit determination)of CHAMP by GPS
σ
= 3 cm
(Rothacher
amp Svehla 2003)
from
the
orbit
to gravitation
gravitation from
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
2 2x t 0 0x t
1 1x t
from
the
orbit
to gravitation
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
1957 Sputnik 1
earth
flattening
J2
=108410-6
earth
oblateness
deduced
from
orbit
plane precession
satellites
-
test masses
in free
fall
1957 Sputnik 1
today LAGEOS I and II
test mass
in free
fall
Cox amp Chao Science 297 2002
steady decrease of earth flattening change of trend in recent years
satellites
-
test masses
in free
fall
Dickey Marcus de Viron Fukumori 2002
Temporal changes
of the
Earthlsquos
flattening What
are
the
causes
candidates
ocean
masses
melting
ice
caps
atmospheric
masses
hydrology
satellites
-
test masses
in free
fall
observatories ldquoseerdquo
onlyshort arc segments
satellites
-
test masses
in free
fall
A new
era continuous
tracking
in 3D of low
earth
orbiters
(LEOs) by
navigation
satellites
(GPS GALILEO GLONASShellip)
satellites
-
test masses
in free
fall
Absolut-GravimeterFG5TU Hannover
bull location GPS
bull time synchronized atomic clocks
bull air resistance measured
bull silence no ground vibrations
satellites
-
test masses
in free
fall
atmospheric
pressure
at satellite
altitude
laboratory10-4Pa = 10-6mbar300 km altitude87710-8mbar
satellites
-
test masses
in free
fall
Emiliani
C1992 p272
CHAMP satelliteGeoForschungsZentrum
Potsdam
mission life time 2000 ndash
2010
star
sensorsGPS receiver
accelerometerat centre
of mass
satellites
-
test masses
in free
fall
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
positioning (orbit determination)of CHAMP by GPS
σ
= 3 cm
(Rothacher
amp Svehla 2003)
from
the
orbit
to gravitation
gravitation from
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
2 2x t 0 0x t
1 1x t
from
the
orbit
to gravitation
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
1957 Sputnik 1
today LAGEOS I and II
test mass
in free
fall
Cox amp Chao Science 297 2002
steady decrease of earth flattening change of trend in recent years
satellites
-
test masses
in free
fall
Dickey Marcus de Viron Fukumori 2002
Temporal changes
of the
Earthlsquos
flattening What
are
the
causes
candidates
ocean
masses
melting
ice
caps
atmospheric
masses
hydrology
satellites
-
test masses
in free
fall
observatories ldquoseerdquo
onlyshort arc segments
satellites
-
test masses
in free
fall
A new
era continuous
tracking
in 3D of low
earth
orbiters
(LEOs) by
navigation
satellites
(GPS GALILEO GLONASShellip)
satellites
-
test masses
in free
fall
Absolut-GravimeterFG5TU Hannover
bull location GPS
bull time synchronized atomic clocks
bull air resistance measured
bull silence no ground vibrations
satellites
-
test masses
in free
fall
atmospheric
pressure
at satellite
altitude
laboratory10-4Pa = 10-6mbar300 km altitude87710-8mbar
satellites
-
test masses
in free
fall
Emiliani
C1992 p272
CHAMP satelliteGeoForschungsZentrum
Potsdam
mission life time 2000 ndash
2010
star
sensorsGPS receiver
accelerometerat centre
of mass
satellites
-
test masses
in free
fall
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
positioning (orbit determination)of CHAMP by GPS
σ
= 3 cm
(Rothacher
amp Svehla 2003)
from
the
orbit
to gravitation
gravitation from
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
2 2x t 0 0x t
1 1x t
from
the
orbit
to gravitation
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
Cox amp Chao Science 297 2002
steady decrease of earth flattening change of trend in recent years
satellites
-
test masses
in free
fall
Dickey Marcus de Viron Fukumori 2002
Temporal changes
of the
Earthlsquos
flattening What
are
the
causes
candidates
ocean
masses
melting
ice
caps
atmospheric
masses
hydrology
satellites
-
test masses
in free
fall
observatories ldquoseerdquo
onlyshort arc segments
satellites
-
test masses
in free
fall
A new
era continuous
tracking
in 3D of low
earth
orbiters
(LEOs) by
navigation
satellites
(GPS GALILEO GLONASShellip)
satellites
-
test masses
in free
fall
Absolut-GravimeterFG5TU Hannover
bull location GPS
bull time synchronized atomic clocks
bull air resistance measured
bull silence no ground vibrations
satellites
-
test masses
in free
fall
atmospheric
pressure
at satellite
altitude
laboratory10-4Pa = 10-6mbar300 km altitude87710-8mbar
satellites
-
test masses
in free
fall
Emiliani
C1992 p272
CHAMP satelliteGeoForschungsZentrum
Potsdam
mission life time 2000 ndash
2010
star
sensorsGPS receiver
accelerometerat centre
of mass
satellites
-
test masses
in free
fall
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
positioning (orbit determination)of CHAMP by GPS
σ
= 3 cm
(Rothacher
amp Svehla 2003)
from
the
orbit
to gravitation
gravitation from
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
2 2x t 0 0x t
1 1x t
from
the
orbit
to gravitation
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
Dickey Marcus de Viron Fukumori 2002
Temporal changes
of the
Earthlsquos
flattening What
are
the
causes
candidates
ocean
masses
melting
ice
caps
atmospheric
masses
hydrology
satellites
-
test masses
in free
fall
observatories ldquoseerdquo
onlyshort arc segments
satellites
-
test masses
in free
fall
A new
era continuous
tracking
in 3D of low
earth
orbiters
(LEOs) by
navigation
satellites
(GPS GALILEO GLONASShellip)
satellites
-
test masses
in free
fall
Absolut-GravimeterFG5TU Hannover
bull location GPS
bull time synchronized atomic clocks
bull air resistance measured
bull silence no ground vibrations
satellites
-
test masses
in free
fall
atmospheric
pressure
at satellite
altitude
laboratory10-4Pa = 10-6mbar300 km altitude87710-8mbar
satellites
-
test masses
in free
fall
Emiliani
C1992 p272
CHAMP satelliteGeoForschungsZentrum
Potsdam
mission life time 2000 ndash
2010
star
sensorsGPS receiver
accelerometerat centre
of mass
satellites
-
test masses
in free
fall
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
positioning (orbit determination)of CHAMP by GPS
σ
= 3 cm
(Rothacher
amp Svehla 2003)
from
the
orbit
to gravitation
gravitation from
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
2 2x t 0 0x t
1 1x t
from
the
orbit
to gravitation
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
observatories ldquoseerdquo
onlyshort arc segments
satellites
-
test masses
in free
fall
A new
era continuous
tracking
in 3D of low
earth
orbiters
(LEOs) by
navigation
satellites
(GPS GALILEO GLONASShellip)
satellites
-
test masses
in free
fall
Absolut-GravimeterFG5TU Hannover
bull location GPS
bull time synchronized atomic clocks
bull air resistance measured
bull silence no ground vibrations
satellites
-
test masses
in free
fall
atmospheric
pressure
at satellite
altitude
laboratory10-4Pa = 10-6mbar300 km altitude87710-8mbar
satellites
-
test masses
in free
fall
Emiliani
C1992 p272
CHAMP satelliteGeoForschungsZentrum
Potsdam
mission life time 2000 ndash
2010
star
sensorsGPS receiver
accelerometerat centre
of mass
satellites
-
test masses
in free
fall
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
positioning (orbit determination)of CHAMP by GPS
σ
= 3 cm
(Rothacher
amp Svehla 2003)
from
the
orbit
to gravitation
gravitation from
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
2 2x t 0 0x t
1 1x t
from
the
orbit
to gravitation
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
A new
era continuous
tracking
in 3D of low
earth
orbiters
(LEOs) by
navigation
satellites
(GPS GALILEO GLONASShellip)
satellites
-
test masses
in free
fall
Absolut-GravimeterFG5TU Hannover
bull location GPS
bull time synchronized atomic clocks
bull air resistance measured
bull silence no ground vibrations
satellites
-
test masses
in free
fall
atmospheric
pressure
at satellite
altitude
laboratory10-4Pa = 10-6mbar300 km altitude87710-8mbar
satellites
-
test masses
in free
fall
Emiliani
C1992 p272
CHAMP satelliteGeoForschungsZentrum
Potsdam
mission life time 2000 ndash
2010
star
sensorsGPS receiver
accelerometerat centre
of mass
satellites
-
test masses
in free
fall
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
positioning (orbit determination)of CHAMP by GPS
σ
= 3 cm
(Rothacher
amp Svehla 2003)
from
the
orbit
to gravitation
gravitation from
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
2 2x t 0 0x t
1 1x t
from
the
orbit
to gravitation
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
Absolut-GravimeterFG5TU Hannover
bull location GPS
bull time synchronized atomic clocks
bull air resistance measured
bull silence no ground vibrations
satellites
-
test masses
in free
fall
atmospheric
pressure
at satellite
altitude
laboratory10-4Pa = 10-6mbar300 km altitude87710-8mbar
satellites
-
test masses
in free
fall
Emiliani
C1992 p272
CHAMP satelliteGeoForschungsZentrum
Potsdam
mission life time 2000 ndash
2010
star
sensorsGPS receiver
accelerometerat centre
of mass
satellites
-
test masses
in free
fall
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
positioning (orbit determination)of CHAMP by GPS
σ
= 3 cm
(Rothacher
amp Svehla 2003)
from
the
orbit
to gravitation
gravitation from
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
2 2x t 0 0x t
1 1x t
from
the
orbit
to gravitation
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
atmospheric
pressure
at satellite
altitude
laboratory10-4Pa = 10-6mbar300 km altitude87710-8mbar
satellites
-
test masses
in free
fall
Emiliani
C1992 p272
CHAMP satelliteGeoForschungsZentrum
Potsdam
mission life time 2000 ndash
2010
star
sensorsGPS receiver
accelerometerat centre
of mass
satellites
-
test masses
in free
fall
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
positioning (orbit determination)of CHAMP by GPS
σ
= 3 cm
(Rothacher
amp Svehla 2003)
from
the
orbit
to gravitation
gravitation from
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
2 2x t 0 0x t
1 1x t
from
the
orbit
to gravitation
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
CHAMP satelliteGeoForschungsZentrum
Potsdam
mission life time 2000 ndash
2010
star
sensorsGPS receiver
accelerometerat centre
of mass
satellites
-
test masses
in free
fall
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
positioning (orbit determination)of CHAMP by GPS
σ
= 3 cm
(Rothacher
amp Svehla 2003)
from
the
orbit
to gravitation
gravitation from
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
2 2x t 0 0x t
1 1x t
from
the
orbit
to gravitation
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
positioning (orbit determination)of CHAMP by GPS
σ
= 3 cm
(Rothacher
amp Svehla 2003)
from
the
orbit
to gravitation
gravitation from
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
2 2x t 0 0x t
1 1x t
from
the
orbit
to gravitation
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
gravitation from
0 5 10 15 20minus01
minus005
0
005
01
time at DoY 231 [h]
Δ x
[m]
position difference between kinematic and reducedminusdynamic POD
2 2x t 0 0x t
1 1x t
from
the
orbit
to gravitation
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
energy
conservationkinetic
energy
= potential energy
howevernon conservative
contributions
residual air
resistance
andgravitation
changes
due
to
direct solid earth
amp ocean
tidesatmosphere
oceanshellip
21mv2
from
the
orbit
to gravitation
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
gravitational
potential along
the
orbit
trajectory
σ
= 500 m2s2
from
the
orbit
to gravitation
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
gravitational
potential along
the
orbitmapped
onto
the
globe
from
the
orbit
to gravitation
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
0
0
60
60
120
120
180
180
240
240
300
300
360
360
-90 -90
-60 -60
-30 -30
0 0
30 30
60 60
90 90
-80 -60 -40 -20 0 20 40 60 80
potential along
the
orbitmapped
onto
the
globe
[ms2]
geoid
[m]
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
the
use
of several
free
falling
test masses
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
the
use
of several
free
falling
test masses
from
absolute to differential measurement
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
GRACENASA + DLR mission (in orbit since 2002)
Gravitation from very precise measurement (1μm) of changes of inter satellite distance
of two satellites following each other in the same orbit (200 km)
the
use
of several
free
falling
test masses
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
GRACE measures tiny changes of gravitational acceleration
Gerard Kruizinga JPL 2002
the
use
of several
free
falling
test masses
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
Tapley
et al Science 2004
the
use
of several
free
falling
test masses
GRACE measures
temporal gravitational
changesexample seasonal
changes
of continental
hydrology
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
the
use
of several
free
falling
test masses
gravitational
measurementin a micro-g
environment
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
the
use
of several
free
falling
test masses
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
earth surface
260 km
satellite
mass ration 1 6middot1021
tidal attraction of earth acting on a satellite
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
x x
y y
z z
g V x Vg g V y V V
g V z V
x x x xx xy xz
y y y yx yy yz
z z z zx zy zz
g x g y g z V V Vg x g y g z V V Vg x g y g z V V V
gravitational
gradiometry
ndash
principle
gravity
tensor
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
0 0
NS NSi
j ij OW OW
NS OW
k t fR V g t k f
gf f g z
gravitational
gradiometry
ndash
principle
gravity
tensor=
tidal
tensor=
curvature
tensor
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
single
accelerometer
one
axisgradiometer
three
axesgradiometer
consisting
of 6 accelerometers
GOCE and gravitational
gradiometry
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
measurement
of bdquomicro-gldquo
with
micro-precision
GOCE and gravitational
gradiometry
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
ion
thrusters
ion
thrustercontrol
unit
nitrogen
tankxenon
tank
gravity
gradiometer
star
sensor
GPS receiver
magneto-torquers
power supply
control
unit
source ESA
a perfect
laboratory
in space
GOCE and gravitational
gradiometry
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
instrument
and control
concept
translationalforces
angularforces
starsensors
drag control
angular control
GPSGLONASSSST -hl
GRAVITY GRADIOMETER
measures
gravity gradients
angular accelerationscommon mode acc
A B
GOCE and gravitational
gradiometry
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
1
The
first
gravitationalgravitational
gradiometergradiometer
in space
2
European geodetic
GPS-receiver
on board
3
Extremly
low
orbit
altitude
(260 km)
4
Free fall (air
drag is
compensated
along
track)
5
Very
bdquosoftldquo
angular
control
by
magnetic
torquing
6
Absolutely
quiet
and stiff
satellite
materials
and
environment
GOCE and gravitational
gradiometry
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
symmetric symmetric skew
symmetric
gravitationtensor
centrifugal
part(angular
velocities)
angularaccelerations
measurement
in a rotating
frame
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xx xy xz y z x y x z z y
yx yy yz y x z x y z z x
zx zy zz z x z y x y y x
V V VV V VV V V
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
A
A
A
A
A
A
X
X
X
X
X
X
Z
Z Z
Z
Z
Z
Y
Y Y
Y
Y
Y
O
O
O
O
O
O
1
2
1
1
1 1
2
2 2 44
4 4
4
33
3 3
3
5
5
5
5 5
66
66 6
2
O
X
ZY GRF
GRF
GRF
GRF
two
sensitive and one
less
sensitive
direction
GOCE and gravitational
gradiometry
2 2
2 2
2 2
00
0
xy x y z
yz y
xx xz y z x z y
yx yy y x z x z
zx zz z x x y
z x
zy yz y x
VV VV VV V
VV
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
x y
x
z
y
z
Vik
[E]
minus05 0 05
GOCE and gravitational
gradiometry
4 components
measured
with
high precision
and two
less
precise
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
GOCE and gravitational
gradiometry
trace
condition (Laplace
condition)the
sum
of the
measured
diagonal components
should
be
zero
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
GOCE gravity
field
meters
a global geoid
map
based
on two
months
of data
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
GOCE gravity
field
Map
compiled
by
MStudinger LDEO Using
data
from
Siegert
et al (2005) and NSIDC
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
400 200 130 100 80 65
half wavelength [km]
50 100 150 200 250 30010
minus14
10minus13
10minus12
10minus11
10minus10
10minus9
10minus8
spherical harmonic degree
Deg
ree
RM
S
SGG
SST minus ll
SST minus hl
GMsKaula
GOCEGOCE maximum resolution (s= 100 km)
GRACEGRACE maximum precision (geoid
lt μm)
GOCE versus
GRACE
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
Degree
Mea
nS
igna
lper
Deg
ree
Deg
ree
Err
orM
edia
n
50 100 150 200
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Mean Signal QL GOCE ModelMean Signal Kaula RuleError Median QL GOCE ModelError Median EIGEN-5SError Median EIGEN-5C
degree
variances
(median) of signal
and noise
GOCE versus
GRACE
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
GOCE versus
GRACE
GRACE measures
the
long
wavelength
structure
of gravity
and geoid
with
extremely
high precision
GRACE can
therefore
even
detect
temporal changes
in the
earth
system
due
to mass
redistribition
(ice sea
level continetal
hydrology)GOCE gives
much
higher
spatial
resolution
This
resolution
is
needed
when
using
the
geoid eg as refence
level
surface
for
studies
of ocean
circulation
or
for
geodynamics
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
The tale of two ants walkingon the surface of an appleldquoThey start at A and Arsquo
and walkon two adjacent paths along shortest distance (geodesics)on the curved apple to B and Brsquo We measure thechanging distance betweenthe two antsFrom these measured distanceswe deduce the localcurvature of the applerdquo(analogy to the satellite missionGRACE and GOCE)
gravitation
and the
story
pf
the
apple
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
S Dali Sans titre 1948
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-
summary
of lecture
three
bull uninterrupted
tracking
of a low
orbiting
satellite
(LEO) by
GPSin combination
with
measurement
of non-gravitational
forces
by
accelerometry
corresponds
to free
fall absolute gravimetry
in an laboratory
on earth
bull CHAMP (2000) was the
first
mission
of this
kindbull differential measurement
of the
relative motion
of two
satellites
increases
the
sensitivity (GRACE 2002)bull gravitational
gradiometry
is
differential accelerometry
between
several
test masses
inside
one
satellitebull GOCE is
the
first
satellite
with
a gravitational
gradiometer
bull GRACE can
be
regarded
as one-arm
gradiometer
with
anarm length
of 200 km
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Slide Number 10
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Slide Number 14
- Slide Number 15
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
- Slide Number 39
- Slide Number 40
- Slide Number 41
- Slide Number 42
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Slide Number 48
- Slide Number 49
- Slide Number 50
- Slide Number 51
- Slide Number 52
- Slide Number 53
- Slide Number 54
-