Numerical study of low-cost alternative orbits around the Moon

In this paper, we have investigated a region of direct stable orbits around the Moon, whose stability is related to the H2 Family of periodic orbits and to the quasi-periodic orbits that oscillate around them. The stability criteria adopted was that the path did not escape from the Moon during an integration period of 1000 days (remaining with negative two-body Moon-probe orbital energy during this period). Considering the three-dimensional four-body Sun-Earth-Moon-probe problem, we investigated the evolution of the size of the stability region, taking into account the eccentricity of the Earth's orbit, the eccentricity and inclination of the Moon's orbit, and the solar radiation pressure on the probe. We also investigated the evolution of the region's size and its location by varying the inclination of the probe's initial osculating orbit relative to the Moon's orbital plane between 0° and 180°. The size of the stability region diminishes; nevertheless, it remains significant for 0 ⩽ i ⩽ 25° and 35° ⩽ i ⩽ 45°. The orbits of this region could be useful for missions by space vehicles that must remain in orbit around the Moon for periods of up to 1000 days, requiring low maintenance costs.