Commensurable eccentric orbits near critical inclination

Abstract

Artificial satellites whose mean motion is commensurable with the rotation of the Earth are subject to resonance effects arising from the slight longitude-dependence of the geopotential. Previous papers have discussed this problem where one or other of the eccentricity or inclination is sufficiently small that it can be considered to be zero. The situation for orbits which are both inclined and eccentric is in general more complicated, but again becomes relatively simple near the critical inclination since the argument of perigee is approximately constant. The particular example of 12-hr orbits is discussed in some detail; it is of special interest since the U.S.S.R. has now launched twelve Molniya 1 satellites in highly eccentric 12-hr orbits at about 65o inclination, and eight of these have had at least partially stabilished ground tracks. It is shown that the gravity coefficientJ 2, 2 becomes dominant whene exceeds ∼ 0.05, taking over fromJ 3, 2 which is in control fore=0. The appropriate resonant variable is of the novel form∏ 1,2=M + 2 (Ω−not) which does not seem capable of physical or geometrical interpretation. This description is valid over a wide range of eccentricity (e>0.15) and a fairly wide range of inclination (50o<I<90o) and is illustrated by the behaviour of Molniyas 1J and 1K.