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.