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 J(2) problem, provided one uses the secular J(2)-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. (C) 2014 Elsevier B.V. All rights reserved.