Improvement on the second-order solution of artificial satellite orbits

Three methods are proposed in this paper to lessen the complexity in the derivation and the resulting expressions of second-order analytical solutions of artificial satellite orbits while retaining the advantages of analytical solutions. Of the three, the one combining the theories of elliptical perturbation and of intermediate orbits is noteworthy for its simplicity. It can also be used with advantage in first-order and third- or higher order solutions.