Coordinates and Satellite Orbits

2013/3/6GPS Orbit PerturbationJyh-Ching Juang, EE, NCKUPerturbationMaximumperturbation (g)Dominantperturbationperiod (hour)Earth attraction 5 x 10 -2 12 _2nd zonal harmonic 5 x 10 -6 Secular + 6 1000Lunar gravity 5 x 10 -7 Secular + 12 130Solar gravity 3 x 10 -7 Secular + 12 654th zonal harmonic 1 x 10 -8 3 2Solar radiation 1 x 10 -8 Secular + 3 2pressureGravity anomalies 1 x 10 -9 various 0.2others 1 x 10 -9 various 0.2Maximalexcursion growth(ft) in one hourThe 2nd zonal harmonic coefficient induces secular motions of the right ascensionof the ascending node and the argument of perigee of an orbit. As a result,the orbit regresses each revolution and is no longer a closed ellipse.37GPS Orbit ParametersJyh-Ching Juang, EE, NCKUGPS orbit parameters (16 parameters in total)Keplerian parametersEphemeris reference time t oeSquare root of the semi-major axis a 1/2Eccentricity eInclination at the reference time i 0Longitude of the ascending node at the beginning of the GPS week 0Argument of perigee Mean anomaly at the reference time M 0CorrectionsCorrection to the computed mean motion nRate of change of inclination with time di/dtRate of change of right ascension of the ascending node with timed/dtAmplitudes of harmonic correction terms for the computed argument oflatitude C uc and C usAmplitudes of harmonic correction terms for the computed orbit radiusC rc and C rsAmplitudes of harmonic correction terms for the computed inclinationC ic and C is3819