Space platform and OrbitsSpace platform and Orbits

Introduction to Remote SensingInstructor: Dr. Cheng-Chien Liu

Department of Earth Sciences

National Cheng Kung University

Last updated: 11 October 2004

Chapter 2Chapter 2

Platform of remote sensing Platform of remote sensing

Various platformVarious platform• Towers, balloons, model aircraft, kites,

helicopter (Fig), light aircraft, jet aircraft, reconnaissance aircraft, low-earth orbit satellite, geostationary satellite, …

• Range and altitude (see Fig 10.1 in Rees 2001)

• Concept of multistage of remote sensing (Fig 1.21)

• Our focus

AircraftAircraft

CharacteristicsCharacteristics• Operation: convenient and flexible

Routes, time, speed, …Restriction of weather condition

• Range of payload• Altitude• Spatial resolution

DisadvantagesDisadvantages• Duration• Spatial coverage• Position

GPS (global position system)GCPs (ground control points)

• MotionFig

SatelliteSatellite

CharacteristicsCharacteristics• Temporally homogeneous observation• Spatial coverage• Stability

DisadvantagesDisadvantages• Expensive• Flexibility• Spatial resolution

Debate on the replacement of airborne Debate on the replacement of airborne remote sensing by satellite remote sensingremote sensing by satellite remote sensing

Launch of satelliteLaunch of satellite

Traditional approach – rocketTraditional approach – rocket New approach 1: space shuttleNew approach 1: space shuttle New approach 2:New approach 2: The X prizeThe X prize

Traditional approach – rocketTraditional approach – rocket

FuelFuel Classical mechanicsClassical mechanics

• Increasing speed v by burning a mass Mf of fuelwhere u is the speed of the exhaust gases relative to the rocket, Mi is the

initial mass

fi

i

MM

vv

MM

Muv

Muv

M

dMudv

MdvudM

ln

ln

0

2

1

2

1

Traditional approach – rocket (cont.)Traditional approach – rocket (cont.)

Placing a satellite in orbitPlacing a satellite in orbit• Way 1: (see Fig 10.3 in Rees 2001)

Launch vertically upwards

Increase an orbit velocity

• ExampleR = 7200 kmRE = 6400 km

GM = 3.986 x 1014 m3 s-2

v1 = 3.7 m s-1

v2 = 7.5 m s-1

v = 11.2 m s-1

RR

GMvE

1122

1

R

GMv 2

2

Traditional approach – rocket (cont.)Traditional approach – rocket (cont.)

Placing a satellite in orbit (cont.)Placing a satellite in orbit (cont.)• Way 2: (see Fig 10.4 in Rees 2001)

Launch tangentially

Increase an circular orbit velocity

• ExampleR = 7200 kmRE = 6400 kmGM = 3.986 x 1014 m3 s-2

v1 = 8.2 m s-1

v2 = 0.2 m s-1 v = 8.4 m s-1

Tangential speed of Earth’s surface = 0.5v = 7.9 m s-1

)(

21

EE RRR

GMRv

)(

22

EE RRR

GMR

R

GMv

Traditional approach – rocket (cont.)Traditional approach – rocket (cont.)

Placing a satellite in orbit (cont.)Placing a satellite in orbit (cont.)• Rationale of having a multi-stage rocket

v = 8 m s-1

u = 2.4 kmMf / Mi = 96%

Payload < 4% fi

i

MM

Muv

ln

The Elements of a Satellite OrbitThe Elements of a Satellite Orbit

Source: http://spaceinfo.jaxa.jp/note/eisei/e/eis04_e.html

The Elements of a Satellite Orbit (cont.)The Elements of a Satellite Orbit (cont.)

An ideal elliptical orbit An ideal elliptical orbit • Fig 10.5 in Rees 2001• Perigee P• Apogee A• Major axis, semi-major axis• Minor axis, semi-minor axis• Eccentricity e• b2 = a2 (1 – e2)• Period

• GM = (3.98600434 0.00000002) x 1014 m3 s-2

GM

aP

3

0 2

The Elements of a Satellite Orbit (cont.)The Elements of a Satellite Orbit (cont.)

An ideal elliptical orbit (cont.)An ideal elliptical orbit (cont.)• Position of the satellite

in the orbital plane• Relationship between and t

• Series expansion against e

• For most artificial satellite: e < 0.01• ∴ t

cos1

)1( 2

e

ear

cos1

sin1

21

)2tan()1(arctan

1 2

20 e

ee

e

e

P

t

0

2

00

2sin

4

52sin2

2

P

te

P

te

P

t

The Elements of a Satellite Orbit (cont.)The Elements of a Satellite Orbit (cont.)

An inclined elliptical orbitAn inclined elliptical orbit• Fig 10.6 in Rees 2001• Inclination

ProgradeRetrogradeExact polar orbitNear-polar orbit

Give the greatest coverage of the Earth’s surface Widely used for low-orbit satellite More expensive to launch

Ascending node Ascending Descending

The Elements of a Satellite Orbit (cont.)The Elements of a Satellite Orbit (cont.)

Sub-satellite pointSub-satellite point• Based on spherical trigonometry

Latitude b

Longitude l

• Fig 10.7 in Rees 2001Typical sub-satellite tracks for circular orbits of inclination 600, 890,

1500

Earth’s rotation westwards drift of sub-satellite track

ib sinsinsin

i

b

bll

tan

tan,

cos

cos2atan0

Effects of the Earth’s asphericityEffects of the Earth’s asphericity

Earth Earth oblate spheroidoblate spheroid• The gravitational potential

ae: the earth’s equatorial radius

J20.00108263: dynamical form factor

The most convenient way to describe mathematically the effect of this non-spherical Earth on the motion of a satellite is to write the gravitational potential as a sum of spherical harmonics

1sin3

21 2

22

2

br

Ja

r

GMV e

Effects of the Earth’s asphericityEffects of the Earth’s asphericity

Three effectsThree effects• Nodal period

• Precession (see Fig 10.8 in Rees 2001)

• Rotating the elliptical orbit in its own plane (Fig 10.9)

22

22

2

22

3

1

cos51cos31

4

312

e

ii

a

aJ

GM

aP en

22

272

2

12

cos3

e

iaaGMJ ep

22

2272

2

14

)cos51(3

e

iaaGMJ ep

Special orbitsSpecial orbits

Geostationary orbitsGeostationary orbits• Place the satellite into a circular orbit above the

equator• Nodal period Pn = Earth’s rotational period PE

Sidereal day = 24 /(1+1/365.24) = 23.9345 hr = 86164 s

• i = 00

• e = 0• a = 42170 km• h = 35000 km• GOES-2 visible band (Fig 6.36)

Not the full coverage but just over 810

In practice, 550 - 650

22

22

2

22

3

1

cos51cos31

4

312

e

ii

a

aJ

GM

aP en

Special orbits (cont.)Special orbits (cont.)

Geo-synchronous orbitsGeo-synchronous orbits• Place a satellite in a geostationary orbit above a point

that is not located on the equator

• Nodal period Pn = Earth’s rotational period PE

Sidereal day = 24 /(1+1/365.24) = 23.9345 hr = 86164 s

• i 00

• The sub-satellite path: figure-of-eight pattern• Not used in remote sensing

Special orbits (cont.)Special orbits (cont.)

Molniya orbitsMolniya orbits• Select orbital parameters highly eccentric with apogee

positioned above the desired point spend longer on station than in the wrong hemisphere

• i = 63.40 or 116.60

• Nodal period Pn = ½ Earth’s rotational period PEa = 26560 kmIf Pn = PE and small e unhelpful large distance of apogee

• Examplee = 0.74Perigee distance = 6900 km, apogee distance = 46200 kmSub-satellite track of Molniya orbit (see Fig 10.12 in Rees 2001)On station for 8 hours three satellite can provide continuous coverage

014

)cos51(322

2272

2

e

iaaGMJ ep

Special orbits (cont.)Special orbits (cont.)

Low Earth orbitsLow Earth orbits• Widely used

Increasing spatial resolution at the expense of reduced coverage

• Rangevan Allen belt

• Sun-synchronous orbitPrecess about the Earth’s polar axis at the same rate (one revolution

per year) that the Earth orbits the SunMean angular speed S = 2 per year = 1.991 10-7 s-1

Inclination and nodal period for circular sun-synchronous orbits(see Fig 10.14 in Rees 2001)

22

272

2

12

cos3

e

iaaGMJ eSp

Special orbits (cont.)Special orbits (cont.)

Low Earth orbits (cont.)Low Earth orbits (cont.)• Advantages of Sun-synchronous orbit

View a large fraction of the Earth’s surfaceCross the same latitude at the same local solar time

Special orbits (cont.)Special orbits (cont.)

Exactly repeating orbitsExactly repeating orbits

HomeworkHomework

C-prizeC-prize• Describe an innovative way of remote sensing that

could be deployed in the future• Explain the feasibility of your idea

Derive all equations that were used for Derive all equations that were used for placing a satellite in orbitplacing a satellite in orbit

The altitude of TERRA orbit is 705 km. The altitude of TERRA orbit is 705 km. Please calculate the required inclination to Please calculate the required inclination to achieve a circular sun-synchronous orbit.achieve a circular sun-synchronous orbit.