An analytical integration of the averaged equations of variation due to sun-moon perturbations and its application

Details An analytical integration of the averaged equations of variation due to sun-moon perturbations and its application An analytical integration of the averaged equations of variation due to sun-moon perturbations and its application

Jun 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979aiaa.conft....c&link_type=abstract

American Astronautical Society and American Institute of Aeronautics and Astronautics, Astrodynamics Specialist Conference, Prov

Astronomy and Astrophysics

Astronomy

Global Positioning System, Lunar Gravitational Effects, Numerical Integration, Satellite Perturbation, Solar Gravitation, Variational Principles, Algorithms, Computer Techniques, Forecasting, Mathematical Models, Orbit Calculation, Orbital Mechanics, Tables (Data)

Scientific paper

The paper expands the singly averaged disturbing function of third-body perturbation and applies the concept of the intermediate reference orbit for obtaining a first-order solution by analytical integration. The perturbed variations of the motion of earth satellite 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 a computer in terms of classical elements, and 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. 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 was developed to achieve orbit maintenance for the GPS Phase III system.

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