Satellites Motion around Earth : Orbital & Positional Parameters at Epoch
by R C Chakraborty, July 15, 2015, Pages 193 – 267.
(This is Sec. 6, pp 193 – 267, of Orbital Mechanics – Model & Simulation Software (OM-MSS), Sec. 1 to 10, pp 1 – 402.)
The Satellites Orbit around Earth Counterclockwise in the same way as Earth orbits around Sun.
In the previous section, the preliminaries about ‘Satellite Orbit’ followed by NASA / NORAD ‘Two-Line Elements’ (TLE) were presented. (Ref. https://myreaders.wordpress.com/2015/07/14/satellites-orbit-elements-ephemeris-keplerian-elements-state-vectors/).
Here presented Satellites Motion around Earth : Computing Orbital & Positional parameters, the OM-MSS software utility. This utility is applied one-by-one to six satellites, LANDSAT 8, SPOT 6, CARTOSAT-2B, ISS (ZARYA), GSAT-14, & Moon. The Input is NASA / NORAD ‘Two-Line Elements’ (TLE) Bulletin of the respective satellite. The Output is corresponding satellite’s motion around earth, the orbital & positional parameters.
Satellite motion around Earth is represented by computing about 120 orbital parameters, put into 28 groups. The number is large, because some parameters are computed using more than one model equation, that require different inputs. This confirms accuracy & validation of results and understanding the different input considerations.
Satellite Orbital & Positional parameters for computation purpose are put into following groups :
1. UT Year and Days decimal of year : Convert into UT YY MM DD hh min sec & Julian day.
2. Satellite Orbit Semi-major axis in km, Ignoring and also Considering earth oblatenes.
3. Satellite Mean motion in rev per day, Ignoring and also Considering earth oblatenes.
4. Satellite Orbit Time Period in minute at time_t Considering earth oblatenes.
5. Satellite Rate of change of Right Ascension and Argument of Perigee in deg per day at time_t.
6. Satellite Mean anomaly, Eccentric anomaly, True anomaly in deg at time_t considering earth oblateness.
7. Satellite Position vector [rp, rq] from Earth Center (EC) to Satellite in PQW frame, perifocal coordinate system.
8. Satellite Position Range Vector from Earth Center (EC) to Satellite (SAT) – finding Range Vector [rI, rJ, rK, r] Components in km in frame IJK.
9. GST Greenwich sidereal time and GHA Greenwich hour angle in 0 to 360 deg, at input at time_t.
10. Satellite (SAT) Orbit point direction : Finding Right Ascension (Alpha) deg and Declination (Delta) deg using angles.
11. Satellite Longitude & Latitude in deg at time_t ; (ie Sub-Sat point log & lat on earth surface).
12. Satellite height in km from EC to Sat and from Earth surface to Sat at time_t.
13. Distance of Sub-Sat point To Earth Stn (ES) in km over Earth surface at time_t.
14. Local sidereal time (LST) and Local mean time (LMT) over Sub-Sat point Longitude on earth.
15. Local sidereal time (LST) and Local mean time (LMT) over Earth stn (ES) or Earth point (EP) Longitude.
16. Earth Stn Position Vector from Earth Center (EC) to Earth Stn (ES) : Finding Range Vector [RI, RJ, RK, R] Components in IJK frame.
17. Satellite Position Range Vector from Earth Stn (ES) to SAT : finding Range Vector [rvI, rvJ, rvK, rv] components in km in IJK frame.
18. Satellite Position Range Vector from Earth Stn (ES) to SAT : finding Range Vector [rvS, rvE, rvZ, rv] components in km in SEZ frame.
19. Elevation (EL) and Azimuth (AZ) angle of Satellite at Earth Observation point ES or EP.
20. Satellite Velocity meter per sec in orbit.
21. Satellite Velocity Vector [vX, vY, vZ] in meter per sec in orbit in frame XYZ.
22. Satellite Pitch and Roll angles.
23. Satellite State Vectors – Position [ X, Y, Z ] in km and Velocity [ Vx, Vy, Vz ] in meter per sec at time_t.
24. Satellite Direction ie Right Ascension Alpha deg and declination Delta deg using sat position vector.
25. Satellite Angular momentum km sqr per sec : finding [Hx, Hy, Hz, H] using state vector position and velocity.
26. Satellite Orbit normal Vector : finding [Wx, Wy, Wz, W] , Delta, Alpha, using r_sat_pos frame IJK, i, RA.
27. Satellite Position Keplerian elements computed using State Vector, at time input UT.
28. Satellite Position State Vectors, computed using Keplerian elements at time input UT.
All these Orbital & Positional parameters are computed respectively for six satellites LANDSAT 8, SPOT 6, CARTOSAT 2B, ISS (ZARYA), GSAT-14, & Moon.
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Comment by Artificial — February 1, 2017 @ 4:16 am