Spacecraft Motion in an Ultra-Low Lunar Orbit under Lunar Gravitational Anomalies

Abstract

The study centers around the interdisciplinary problem: gravimetry and celestial mechanics. A spacecraft is aimed at a flight from one point of the Moon to another at an altitude of 1 km in a flat circular orbit. Under gravitational anomalies, the orbit deviates from a circular one, acquiring a spatial character. To account for gravitational anomalies, we introduce the mass concentration method, according to which the resulting gravitational field is a superposition of elementary fields of individual mass concentrations (mascons). The elementary field of an individual mascon has four parameters: latitude, longitude, depth, and positive or negative mass. Each parameter of the mascon is associated with a pseudo-random variable with a uniform distribution law in a given interval. The pseudo-random values ??are generated by the Wichmann-Hill PRNG. The problem under consideration is reduced to the Cauchy problem with initial conditions. Under gravitational anomalies, a few orbits after the launch, the spacecraft falls onto the lunar surface. The study shows that one orbit is enough for a safe flight. The spacecraft moves in the specified ultra-low orbit under gravity-anomaly noise. Anomalous gravitational overload is 0.1 m/sec2.