The fifth-order analytical solution of the equations of motion of a satellite in orbit around a non-spherical planet

Details The fifth-order analytical solution of the equations of motion of a satellite in orbit around a non-spherical planet The fifth-order analytical solution of the equations of motion of a satellite in orbit around a non-spherical planet

Mar 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995cemda..61..207k&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 61, no. 3, p. 207-215

Astronomy and Astrophysics

Astronomy

5

Asphericity, Celestial Mechanics, Equations Of Motion, Mathematical Models, Orbital Mechanics, Perturbation Theory, Planets, Satellite Orbits, Algorithms, Geodynamics, Harmonic Analysis, Kepler Laws, Periodic Variations

Scientific paper

A high-precise analytical theory of a satellite in orbit around a non-spherical planet has been developed. The Poisson's small parameter method has been used. All secular and short-periodic perturbations proportional up to and including a product of five arbitrary harmonic coefficients of the planetary expansion are calculated. Long-periodic perturbations are derived with the accuracy of up to the fourth-order, inclusive. The influence of the high-order perturbations on the motion of ERALON-1 satellite has been investigated. The results of comparison of the numerical and analytical integration of the equations of its motion over a five year interval are as follows: the r.m.s difference between the positions is 1.1 cm; and the r.m.s. difference between the ranges is 0.5 cm. The theory is intended to be used for processing precise laser range measurements of the Earth geodynamical satellites over long-term intervals.

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