Lesson 2: Space Mission Geometry - Home | College of ... 5595_files/Lesson 2.pdf · Total Time in...
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Lesson 2: Space Mission
Geometry
Dr. Andrew KetsdeverMAE 5595
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Space Mission Geometry
• Must specify an appropriate coordinate system– Earth fixed– Spacecraft fixed– Other
• Coordinate system must have a specified– Origin– Fixed point
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Earth Geometry Viewed from Space
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Mission Viewing Geometry
angle. grazingor angleelevation satellitesatelliteby seen angleearth maximum
footprint) ofboundary (defines radiusearth angular n)combinatioany or Long, (Lat, angle centralearth
nadir from angle target torangeslant
satellite of altitudeearth of radius
0
========
ελρληDHRE
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λρλρη
cossin1sinsintan
−=
ρηε
sinsincos =
2πελη =++
ηλ sinsin DRE =
( ) 22max ⊕⊕ −+= RHRD
( ) ( ) λcos222 HRRHRRD +−++= ⊕⊕⊕⊕
HRR+
==⊕
⊕0cossin λρ
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Special Cases
Note,- If point of interest is SSP: 0 ,90 ,0 === λεη o
- If point of interest is true outer horizon: ρλερη −=== o90 ,0 ,
λ
λ0 ε D
H
ρ η
R⊕
Dmax
SSP
True outer horizon
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Satellite Motion for an Earth Observer
Circular, LEO
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Total Time in ViewFor a LEO satellite, assume brief pass (ignore Earth’s rotation). The time in view, T, for the satellite is given by:
( )180/coscoscos
180
maxmax
min
max1
λλλ
PeriodT
PeriodT o
=
= −
maxminmax 90 ηελ −−= o
minmax cossinsin ερη =
( ) ( ) ( ) ( ) ( )longlatlatlatlat GSpoleGSpole ∆+= coscoscossinsinsin minλ
pass of at time node ascendingorbit whereinertial)not c,(geographiEarth of longitude
90station ground and poleorbit between longitudein difference
station ground of latitude
90
=
−=
=∆=
−=
node
nodepole
GS
pole
L
Llonglong
lat
ilat
o
o
where:
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Satellite Slew Rate
• Maximum Slew Rate for a Satellite
( )minmin
max2PeriodD
HRDV Esat +
==• πθ
=
min
minmin sin
sinηλ
ERD
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Satellite Motion for an Earth Observer
Dominant factor:
(a) Inclination
(b) Eccentricity
center of ground track
(a) (b)
h
ω
GEO
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GEO Ground Track
equator
28.50 N
10 km rectenna array—beamwidth
0.8×10-2 deg
ground track—maximum latitude
SPS in 28.50 inclined orbit
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Sirius Radio Satellite Constellation
• Mission: – Continuous radio broadcasts over North
America– Radio reception to remote areas
• What mission geometry would you choose?
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• Geosynchronous• 60 deg inclination• Highly eccentric• Apogee over N.
Hemisphere
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Sirius Constellation
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How Did XM Do It?• Named "Rock" and "Roll,"
XM Radio’s two Boeing HS 702 satellites were placed in parallel geostationary orbit (GEO), 35,764 km above Earth.
• The first XM satellite, "Rock," was launched on March 18, 2001, with "Roll" following on May 8th.
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Sirius and XM Constellations
http://www.dogstarradios.com/sirasasecoma.html
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Swath Width
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Eclipse
• Knowing the mission geometry leads to a simple calculation for the eclipse time for a satellite (SMAD has a more complicated analysis)
+
= −
HRR
E
E1sinρ
xPeriodTEo360
2ρ=