Satellite Orbit and Ephemeris Determination using Inter Satellite Links

Orbit ComputationInter Satellite LinksRadial [m] Along Track [m] Cross Track [m]500 km LEO 0 0 0800 km LEO 0 0 01250 km LEO 0.001 0 0MEO 0 0.005 0.005GEO 0.002 0.005 0.012IGSO 0.003 0.047 0.022Table 4-17 Attraction from Major planets Perturbation after 1 Week4.3.6 Numerical ErrorsNumerical integration algorithms have the possibility to estimate the so called local error byhalving or doubling the step width and comparing the results. Unfortunately, the global errordue to round off introduced by numerical integration can not be estimated that way. To assessthe global error following calculation have been conducted:Neglecting all accelerations except the central force, exact one revolution of a satellite orbithas been propagated. The resulting end state vector has been compared to the initial statevector, which would have to be identical presuming a perfect integration procedure. Threedifferent integration algorithms have been evaluated:• 4 th order Runge-Kutta• 4 th order Adams-Bashford-Moulton• 8 th order Adams-Bashford-MoultonThe step width has been varied to keep the local error below 1 cm.Figure 4-13 shows the necessary step width for each integration method. It can be generallysaid, if the orbit altitude is low the step width has to be small due to the strong acceleration.Page 58R. Wolf