Long term prediction for high altitude orbits

A first-order theory is developed for the rapid and accurate calculation of secular and long-period changes in the elements of a high-altitude earth orbit due to the action of the sun and moon. The third body disturbing potential is first derived in nonsingular orbital elements with the satellite orbit plane used as the frame of reference and third body resonance taken into account. The generalized method of averaging is then applied to the conservative variation of parameters formulation of the satellite dynamical equations to create a first order averaging theory. The computer implementation of the first-order theory as it applies to the third body problem is discussed, and the speed and accuracy of high-precision integration and the averaging theory are compared for five test orbits, demonstrating the capabilities of the theory over a wide range of orbital geometries.