Analytical Theories of the Motion of Artificial Satellites

Abstract

The present paper gives a general review of various analytical theories of the motion of artificial satellites presented for these fifteen years or so. Most theories treat the main problem (i.e. problem of the oblateness perturbations), and they are classified according to a) intermediaries adopted, b) perturbation techniques used, and c) orders of approximations carried out. We next review the theories that treat of other sources of perturbations such as tesseral harmonics of the earth’s potential, luni-solar attraction, drag of the earth’s atmosphere, solar radiation, and so on. All of them are of the second order in magnitude, but are still very important especially in view of secular and long-period perturbations. The resonance cases (i.e. problem of the critical inclination and motion of 24-hours satellites) are also treated by many authors. The orders of perturbations needed for analytical theories to attain an accuracy of 10−6 and 10−8 are shown in concluding the review.