The numerical computation of orbits in celestial mechanics can be performed by applying Urabe's method for the Galerkin procedure. High order Galerkin approximations are computed for two examples: Hill's variation orbit of the moon and the orbit of an artificial earth satellite. Excellent agreement with known results is obtained.
Cite this article
René Van Dooren, Orbit Computation in Celestial Mechanics by Urabe's Method. Publ. Res. Inst. Math. Sci. 9 (1973), no. 3, pp. 535–542DOI 10.2977/PRIMS/1195192441