Abstract
We present an accurate simple-to-implement numerical method for the computation of the relative motion of two-satellites. This is presented for both the linearized approximation and in an exact formulation. We also derive a basic set of analytical solutions for the variational equations of the two-body motion. This is shown to be a useful approximation for the relative motion of two-satellites even in the so called J2 problem, provided one uses the secular J2-theory to obtain the orbit precession. The numerical method results are compared with approximations produced by the two-body variational but precessed approximation. We find a good agreement for quasi-circular orbits with same inclination.
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