An Analytical Integration of the Averaged Equations of Variation due to Sun-Moon Perturbations and its Application

摘要

The perturbed variations of the motion of earth satellites due to the sun and the moon are derived from a singly averaged disturbing function. A first-order solution is obtained by analytically integrating the equations of variation including J2, J2-squared, J3, and J4. The literal expansions are carried out by computer in terms of classical elements. The secular part of the first-order solution is included in the reference orbit. The orbits of the sun and the moon are assumed circular, and the motion of the moon is converted to the earth equatorial system with certain approximations. Results based on the GPS (Global Positioning System) satellites compare favorably with numerical integration for time spans of up to three years. An algorithm applying the first-order solution has been developed to achieve the desired strategy of orbit maintenance for the GPS Phase III system. The analytical solutions provide insight into the long-term (10-yr) variations of the orbit elements of GPS satellites. (Author)