Influence of lunar perturbation as a third-body perturbation on satellite visibility intervals

This study presents an analytical formulation to calculate the perturbed visibility function between two satellites. We begin with the representation of the visibility function in terms of the orbital elements of the two satellites up to the fourth order in eccentricity. Subsequently, the third-body perturbation on the satellite orbital elements is derived, leading to the construction of the perturbed visibility function in its final form. This technique is applicable to all eccentricities, altitudes, and perturbed satellite motions. Numerical simulations were conducted for select satellites at different altitudes with the visibility function perturbed by a third body, particularly the Earth's moon.