Satellite Orbit and Ephemeris Determination using Inter Satellite Links

Inter Satellite LinksSoftware Description5.4.2 NutationThe nutation matrix is given byR N⎡ 1 − ∆ψ cosε− ∆ψ sin ε⎤=⎢⎥⎢∆ψ cosε1 − ∆ε⎥⎢⎣∆ψ sin ε ∆ε 1 ⎥⎦with the mean obliquity of the rotation axis given byEq. 5.4-5whereT23ε = 23°26'21".448 − 46".8150 ⋅ T − 0".00059 ⋅ T + 0".001813⋅TEq. 5.4-6Time interval between the observation epoch and the J2000.0 standard epoch∆ψ Nutation parameter in longitude∆ε Nutation parameter in obliquityThe nutation parameters ∆ψ and ∆ε can be obtained from a series expansion, which can befound in [ITN-96]. A drawback the series expansion method is that a lot of trigonometricfunctions have to be evaluated, causing a high computation load. Fortunately, the nutationparameters are available as pre-computed values in the JPL DE200 ephemeris files.5.4.3 Polar MotionThe transformation matrix accounting for polar motion can be expressed byRN⎡ 1=⎢⎢0⎢⎣− xPy01PxP− y1P⎤⎥⎥⎥⎦Eq. 5.4-7The values for co-ordinates of the earth pole are available from the IERS (International EarthRotation Service), either as predicted values in the Bulletin A, or as post processed values inthe Bulletin B. In precise orbit determination, these parameters are estimated, using IERSBulletin A as predicted values.5.4.4 Earth Rotation (Hour Angle)While the time derived from earth's revolution is defined from one midday to the next andindicated as Universal Time (UT), earth's rotation with respect to an inertial frame is obtainedfrom the sidereal time. The so called hour angle is related to UT1, that is UT corrected forpolar motion, byΘ0 = 1.0027379093⋅UT1 + ϑ0+ ∆ψ cosεEq. 5.4-8R. Wolf Page 85