Lecture 1d: Satellite Orbits

Transcription

1 Lecture 1d: Satellite Orbits

2

3 Outline 1. Newton s Laws of Motion 2. Newton s Law of Universal Gravitation 3. Kepler s Laws 4. Putting Newton and Kepler s Laws together and applying them to the Earth-satellite system 5. Orientation of orbit in space 6. Orbital parameters & orbit perturbation 7. Satellite positioning, tracking & navigation 8. Orbits of Meteorological Satellites (MetSat)

4 Orbits of Meteorological Satellites (MetSat) 1. Geostationary (GEO: ~ 36,000 km) 2. Low Earth Orbit (LEO: < 2,000 km) 3. Mid-Earth Orbit (MEO: in between GEO and LEO) 4. Sunsynchronous Orbit (a special LEO) 5. Molniya 6. Formation flight 7. Constellations

5 Some MetSat Orbits (highly elliptical) (LEO) (GEO) (MEO)

6 Geostationary Coverage Courtesy: NCAR

7 US US EU EU Japan Courtesy: Navy Research Lab

8 Geostationary Coverage NP Drawback: no polar coverage SP

9 Polar-orbiting LEO satellites see the poles, but being very close to the Earth, they only see narrow swath across the track. (LEO)

10 Sunsynchronous Satellites This is not a sunsynchronous orbit Sun Noon Morning Earth Midnight Evening

11 Sunsynchronous Satellites This is a sunsynchronous orbit Sun We don t need to carry extra fuel to make such adjustment of orbits. Noon Midnight Noon Earth Midnight

12 How to make a sunsynchronous orbit? The right ascension of ascending node changes: dω dt = n 3 2 J 2 r ee a 2 ( 1 ε 2 ) 2 cosi Make sure it follows the Sun. For the Sun, dw/dt>0, so cosi < 0 (i.e, i > 90 0 ) ε is close to zero for near-circular orbit N

13 How to make a sunsynchronous orbit? The right ascension of ascending node changes: dω dt = n 3 2 J 2 r ee a 2 ( 1 ε 2 ) 2 cosi The inclination angle can be chosen such that W changes at the same rate that the earth orbits the sun, 2p radians per tropical year or /day. Note that i > 90 (retrograde) for a sunsynchronous orbit. For most NOAA satellites, i» 99.

14 Sunsynchronous Groundtrack Polar regions are observed every orbit A particular equatorial region is observed twice per day per satellite

15 Mid-Earth Orbit (MEO) 1. Semimajor axis >LEO and <GEO 2. The Global Positioning System (GPS) is a good example a = km (4.2 earth radii) i = 55 1 e = 0

16 GPS Groundtrack Synchronized with the earth: Makes two complete orbits while the earth turns once with respect to the plane of the orbit (12 hr period) Groundtrack repeats

17 Molniya Orbit Molniya means lightning in Russian Used as communications satellites Highly elliptical orbit eccentricity = semi-major axis = 26,553 km apogee = 46,127 km (3,960 km higher than GEO) inclination = 63.4 period = min (»12 hr) Moves very slowly near apogee

18 Molniya Groundtrack Cusps (singular point) can be placed at any longitude.

19 Molniya Coverage Sees this for 8 hr... 4 hr gap......then sees this for 8 hr. Three satellites provide 24-hr coverage Kidder, S. Q., and T. H. Vonder Haar, 1990: On the use of satellites in Molniya orbits for meteorological observation of middle and high latitudes. J. Atmos. Ocean. Tech., 7,

20 Formation Flight: NASA A-Train CloudSat lags Aqua by a variable amount <120 s CALIPSO lags CloudSat by s CloudSat and CALIPSO fly about 220 km to the right of Aqua to avoid sun glint PARASOL lags Aqua by ~2 min Aura lags Aqua by ~15 min Stephens et al., 2002: The CloudSat mission: A new dimension of spacebased observations of clouds and precipitation. BAMS, 83,

21 A-Train Orbital Parameters Aqua ECT = 13:35:19 A-Train satellites make 233 orbits in 16 days and fly on the WRS-2 grid

22 The GPS Constellation Parameter GPS Purpose Navigation Number of planes 6 Plane spacing (degr ees) 60 Satellites per plane 4 Total satellites* 24 Orbital altitude (km) 20,181 Semi -major axis (km) 26,559 Inclination (degrees) 54.8 Nodal period (min) Satellites per launch 1 *Not including on-orbit spares Designed so that at any point or time, several satellites are above the horizon.