Long term evolution of Molniya orbit under the effect of Earth's non-spherical gravitational perturbation

A double resonance model is applied to study the long term evolution of a Molniya orbit, which is highly elliptical (e >= 0.7), critically inclined (i approximate to 63.4 degrees), and in the state of the 2:1 mean motion resonance with the Earth rotation. The dynamics of a Molniya orbit can be divided into three kinds: short (12 h), intermediate (several years) and long (several centuries) period motions, with the latter two studied in this paper. The J(2) and J(12) (l = 2, 3,..., 8) harmonics are modelled, based on a careful selection. The analytic solution for the intermediate period motion is obtained, a first integral, (I) over bar (3), for the long period motion is derived analytically, and the phase structures are obtained by the level curves of (I) over bar (3). Three types of the phase structures, depending on the equilibria and stabilities, are observed when the Hamiltonian constant varies. Compared with the near circular 12-h satellite orbits and with the critically inclined orbits without mean motion resonance with the Earth rotation, the features of the Molniya orbits are discussed in detail. It is pointed out that (1) unlike the case of near circular orbits, the J(32) term does not dominate the 2:1 mean motion resonance problem (intermediate period motion), and that (2) instead of the J(2)(2) terms, the resonant tesseral harmonics dominate the critical inclination problem (long period motion). (C) 2014 COSPAR. Published by Elsevier Ltd. All rights reserved.