Third-Body Perturbation using Single Averaged Nonsingular Variables

Abstract

The Lagrange’s planetary equations have the disadvantage of singularities in eccentricity and inclination, when those variables go to zero. These singularities are more mathematical then physical. We studied the third-body perturbation using a single averaged model in nonsingular variables. If no resonances occur with the Moon or the Sun, short terms are eliminated. The present paper has the goal of developing a semi-analytical study of the perturbation caused in a spacecraft by a third body with a single averaged model 1,2,5 to eliminate the terms due to the short time periodic motion of the spacecraft. Others researches developed the double averaged model 1,2,5 . The single average eliminates the mean longitude. The equations of motion of an artificial satellite are given in nonsingular variables. One of the most important applications is to calculate the effect of Lunar and Solar perturbations on high-altitude Earth satellites. We defined the nonsingular elements for I ∫ 180 0 and e < 1, for this set of elements, we find the Lagrange’s planetary equations. After that, we develop the Luni-Solar potential in nonsingular variables by using the functions Flmp and Jlmp, and the eccentricity functions Glpq and Klpq. The expansion are truncated after the term with second order in eccentricity 6 .