Artificial satellites and the three-body problem: A general case

Abstract

The three-body problem is the most celebrated problem of classical celestial mechanics that is not soluble in finite terms by means of any of the functions at present known to mathematical analysis. In the modern celestial mechanics is known as the main problem of the theory of the satellites and it too is not soluble in finite terms. The low-altitude satellites, which move along close orbits, are encountered. They may be done case in which the centers of masses of the bodies form an isosceles or nearly equilaterial triangle with the center of the oblate planet, and another one in which they are always located in the straight line. We study the planar problem, in which the satellites move along close orbits in a plane which forms an angle θ with the equatorial plane of the planet; the oblateness of which exercises a great effect. The practical importance of this problem arises from its applications. Differential equations of motion are given and particular solutions are shown to exist when the centers of masses are at the vertices of a nearly equilateral triangle or are collinear. Of course, if we take the first two terms of the Legendre series with θ=0, we shall obtain the same results as Aksenov (1988).