Aas 15-359 an Rbf-collocation Algorithm for Orbit Propagation

Several analytical and numerical methods exist to solve the orbit propagation of the two-body problem. Analytic solutions are mainly implemented for the unperturbed/classical two-body problem. Numerical methods can handle both the unperturbed and the perturbed two-body problem. The literature is rich with numerical methods addressing orbit propagation problems such as, Gauss-Jackson, Higher order adaptive Runge-Kutta and Talyor series based methods. More recently, iterative methods have been introduced for orbit propagation based on the Chebyshev-Picard methods. In this work, Radial Basis Functions, RBFs, are used with time collocation to introduce a fast, accurate integrator that can readily handle orbit propagation problems. Optimizing the shape parameter of the RBFs is also introduced for more accurate results. The algorithm is also applied to Lmabert’s problem. Two types of orbits for the unperturbed two-body problem are presented; (1) a Low Earth Orbit (LEO) and (2) a High Eccentricity Orbit (HEO). The initial conditions for each orbit are numerically integrated for 5, 10 and 20 full orbits and the results are compared against the Lagrange/Gibbs F&G analytic solution, Matlab ode45 and the higher order rkn12(10). An Lambert’s orbit transfer numerical example is also introduced and the results are compared against the F&G solution. The algorithm is shown to be capable of taking large time steps while maintaining high accuracy which is very significant in long-term orbit propagation problems.