A Short Study on the Motion of Artificial Satellites of Mercury and Venus

Abstract

The author studies the motion of possible artificial satellites of the planets Mercury and Venus under the perturbing action of the Sun. All bodies are considered dimensionless, the orbital eccentricities of both planets are neglected. Approximative secular perturbations of node and pericentre are deduced, periodic perturbations are not investigated. The semi-major axis of critical orbits are determinated on the base of closed Hill’s limiting curve. Variation, evection and eccentricity are taken into account here.

The critical semi-major axis of the Mercury satellite orbits are, respectively, 126000 km for the direct motion and 142000 km for the retrograde motion. The corresponding orbital periods are about 22 days and 26 days, respectively. The critical semi-major axis of the direct and retrograde Venus satellite orbits are 581000km or 655000 km, respectively. The corresponding orbital periods are about 57 days and 68 days. These values diminish with increasing eccentricity. It is convenient to note the greater stability of retrograde satellites.

The effect of solar radiation pressure is obviously more intensive than in the case of satellites of the Earth. The resonance condition for the secular perturbation in eccentricity occurs in the instability area.