Calculating the Effect of Third-Body Gravity on Orbits around the Moon

Abstract

This work includes calculating the orbital elements around the Moon with different heights, ranging from 100 to 1000 km, at an eccentricity of (e = 0.05 and 0.1) with an inclination=28.48 deg. Cowell’s equation was used to calculate the effect of the Earth's attraction on a satellite orbiting around the Moon using the MATLAB program. In this paper, research was conducted to find the best orbit of a satellite orbiting the Moon, which has the least possible perturbation and the least possible change of orbital elements, in order to get the longer life of the sent satellites. The lowest height was found to be the best way to obtain more efficient images with the lower-cost camera. Newton-Raphson method was used to solve Kepler’s equation for the ellipse orbit. Cowell’s method was used to solve the perturbation with the equation of motion which was solved by the 4^TH order Runge–Kutta integration. Results showed that each orbital element changed across time due to the Earth's gravity only. The altitude change of an orbit had a relatively slight effect, while the eccentricity of the orbit had a greater effect on the orbital elements. When altitudes were changed between 100 to 1000 km, the results showed that the behavior of the orbital elements remained almost the same. Whereas when the value of eccentricity was changed from 0.1 to 0.05, it had a greater impact on the orbital elements. It was also found that inclination had an important effect on the orbital elements. It was found that the best orbit around the Moon had a height of 100km and an eccentricity of 0.05. It was also found that inclination had an important effect on the orbital elements.