Satellite Orbit and Ephemeris Determination using Inter Satellite Links

Orbit ComputationInter Satellite LinksA draw back of all multistep procedures is the necessity of n-1 preceding state vector. Thismeans, multistep procedures require a "starter", usually a Runge-Kutta procedure. Anotherdraw back is the inflexibility in adapting integration step width h to the required accuracydemands. Fortunately, nearly circular orbit can be computed using a fixed step width. Thisallows, after a starting phase with a low order Runge-Kutta type, the usage of higher orderAdams-Bashford-Moulton type of numerical integrator.Necessary for all numerical integration algorithms are starting values x0, x D0as well as theexplicit calculation of the sum of all acting forces or accelerations at each instant of time.∑k Eq. 4.2-9a = a + a + a + a + a + a + a + a + a + a + ...GLSSPDTwith the indicesG GravityL Lunar attractionS Solar attractionSP Solar PressureD Aerodynamic drag forcesT Thrust (vehicles propulsion system)SET Solid earth tidesOT Ocean tidesA Earth AlbedoThe following chapters deal with the computation of these contributors to the sum ofaccelerations.SETOTAMinor4.2.1 Earth’s GravityThe major part of the earth's gravity field is the spherical term, expressed byGMg = −2rEq. 4.2-10is already taken into account in Kepler's formulation of the orbital movement. The largestorbit error, if compared to an unperturbed Keplerian orbit is the non-spherical part of theearth's gravity field. The gravity potential of the Earth can be described analytically in termsof spherical harmonics using the following expression:withU =GMr+ GMNn∑∑n= 2 m=0na e P ϕ λ + λn+1 nm(sin)(Cnmcos m Snmsin m )rEq. 4.2-11Page 26R. Wolf