Knowledge Bank

Following a proposal by Moritz and Schwarz the collocation method is applied to determine zonal coefficients from satellite observations. The perturbation equations are specialized from Kaula's more general formulas and are supplemented by a recurrence relation for the inclination function. The computational formulas for the collocation procedure are summarized and a method is given to determine the optimal number of coefficients by an eigenvalue analysis of the error covariance matrix. Two programs have been developed. The first one computes the coefficients of the perturbation equation, the second one determines the collocation solution and performs the accuracy analysis.