The joint effect of relativistic and direct solar radiation pressure on an axially symmetric spacecraft.: II. The solution and the elements of transformation.

Abstract

In this work we are concerned with the solution of a dynamical system that represents the coupling effects between the perturbing forces arising from the direct solar radiation pressure (S.R.P.) and Earth’s oblateness, limited to the principal term and the second zonal harmonic ( J 2), in the post Newtonian potential (P.N.). The Hamiltonian of the system, in terms of the Delaunay elements, is outlined. The phase space was augmented so as to remove the explicit time dependence, due to the mean longitude of the Sun. The second zonal harmonic of the geopotential, J 2 (considered to be the 1st order) was considered to be the small parameter of the problem. The solution is affected through two canonical transformations retaining, in successive, secular and periodic terms up to orders 4 and 3, respectively. The elements of the transformation and its inverse as well as a procedure for the computation of position and velocity are outlined.