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  1. Chapter 2 Space platform and Orbits Introduction to Remote Sensing Instructor: Dr. Cheng-Chien Liu Department of Earth Sciences National Cheng Kung University Last updated: 11 October 2004

  2. Platform of remote sensing • Various 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

  3. Aircraft • Characteristics • Operation: convenient and flexible • Routes, time, speed, … • Restriction of weather condition • Range of payload • Altitude • Spatial resolution • Disadvantages • Duration • Spatial coverage • Position • GPS (global position system) • GCPs (ground control points) • Motion • Fig

  4. Satellite • Characteristics • Temporally homogeneous observation • Spatial coverage • Stability • Disadvantages • Expensive • Flexibility • Spatial resolution • Debate on the replacement of airborne remote sensing by satellite remote sensing

  5. Launch of satellite • Traditional approach – rocket • New approach 1: space shuttle • New approach 2: • The X prize

  6. Traditional approach – rocket • Fuel • Classical mechanics • Increasing speed Dv by burning a mass Mf of fuel • where u is the speed of the exhaust gases relative to the rocket, Mi is the initial mass

  7. Traditional approach – rocket (cont.) • Placing a satellite in orbit • Way 1: (see Fig 10.3 in Rees 2001) • Launch vertically upwards • Increase an orbit velocity • Example • R = 7200 km • RE = 6400 km • GM = 3.986 x 1014 m3 s-2 • Dv1 = 3.7 m s-1 • Dv2 = 7.5 m s-1 • Dv = 11.2 m s-1

  8. Traditional approach – rocket (cont.) • Placing a satellite in orbit (cont.) • Way 2: (see Fig 10.4 in Rees 2001) • Launch tangentially • Increase an circular orbit velocity • Example • R = 7200 km • RE = 6400 km • GM = 3.986 x 1014 m3 s-2 • Dv1 = 8.2 m s-1 • Dv2 = 0.2 m s-1 • Dv = 8.4 m s-1 • Tangential speed of Earth’s surface = 0.5 • Dv = 7.9 m s-1

  9. Traditional approach – rocket (cont.) • Placing a satellite in orbit (cont.) • Rationale of having a multi-stage rocket • Dv = 8 m s-1 • u = 2.4 km • Mf / Mi= 96% • Payload < 4%

  10. The Elements of a Satellite Orbit Source: http://spaceinfo.jaxa.jp/note/eisei/e/eis04_e.html

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

  12. The Elements of a Satellite Orbit (cont.) • An ideal elliptical orbit (cont.) • Position of the satellite in the orbital plane • Relationship between q and t • Series expansion against e • For most artificial satellite: e < 0.01 • ∴ qt

  13. The Elements of a Satellite Orbit (cont.) • An inclined elliptical orbit • Fig 10.6 in Rees 2001 • Inclination • Prograde • Retrograde • Exact polar orbit • Near-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

  14. The Elements of a Satellite Orbit (cont.) • Sub-satellite point • Based on spherical trigonometry • Latitude b • Longitude l • Fig 10.7 in Rees 2001 • Typical sub-satellite tracks for circular orbits of inclination 600, 890, 1500 • Earth’s rotation  westwards drift of sub-satellite track

  15. Effects of the Earth’s asphericity • Earth  oblate spheroid • The gravitational potential • ae: the earth’s equatorial radius • J20.00108263: 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

  16. Effects of the Earth’s asphericity • Three effects • Nodal period • Precession (see Fig 10.8 in Rees 2001) • Rotating the elliptical orbit in its own plane (Fig 10.9)

  17. Special orbits • Geostationary 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

  18. Special orbits (cont.) • Geo-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

  19. Special orbits (cont.) • Molniya 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 PE • a = 26560 km • If Pn = PEand small e unhelpful large distance of apogee • Example • e = 0.74 • Perigee distance = 6900 km, apogee distance = 46200 km • Sub-satellite track of Molniya orbit (see Fig 10.12 in Rees 2001) • On station for 8 hours  three satellite can provide continuous coverage

  20. Special orbits (cont.) • Low Earth orbits • Widely used • Increasing spatial resolution at the expense of reduced coverage • Range • van Allen belt • Sun-synchronous orbit • Precess about the Earth’s polar axis at the same rate (one revolution per year) that the Earth orbits the Sun • Mean angular speed WS = 2p per year = 1.991  10-7 s-1 • Inclination and nodal period for circular sun-synchronous orbits(see Fig 10.14 in Rees 2001)

  21. Special orbits (cont.) • Low Earth orbits (cont.) • Advantages of Sun-synchronous orbit • View a large fraction of the Earth’s surface • Cross the same latitude at the same local solar time

  22. Special orbits (cont.) • Exactly repeating orbits

  23. Homework • C-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 placing a satellite in orbit • The altitude of TERRA orbit is 705 km. Please calculate the required inclination to achieve a circular sun-synchronous orbit.