A semi-analytic theory for the motion of a lunar satellite

Abstract

A semi-analytical solution to the problem of the motion of a satellite of the moon is presented. The theory is developed to third order, where first order is 10-2. Perturbative effects which are considered include those due to the attraction of the moon, earth, and sun, the non-sphericity of the moon's gravitational field, the oblateness of the earth, coupling of lower-order terms, solar radiation pressure, and physical libration. Short-period terms and those with the period of the moon's longitude are produced by means of von Zeipel's method; it is proposed to obtain the secular perturbations, and those depending only on the argument of perilune, by numerical integration of the equations of motion.

Some orbital characteristics of lunar artificial satellites

“…However, λ 22 contains the time explicitly (Giacaglia et al 1970). Using spherical trigonometry we have sin(φ) = sin(i) sin( f + g).…”

“…, we call this term n M H as used by Giacaglia et al (1970). The Hamiltonian is still time-dependent through λ ⊗ .…”

“…In terms of the orbital elements, the Legendre associated functions for zonal up to J 5 and sectorial terms C 22 and C 31 , can be written in the form (Giacaglia et al 1970;Radwan 2003):…”

Effects of the physical libration of the moon on lunar orbiters

“…Because the phenomenon of order reduction often arises in long-period perturbation terms of lunar satellite, so early solutions wcrc always given in semi-analytical form [1][2][3]. However some modifications were made in Ref.…”

The Effects of Moon's Uneven Mass Distribution on the Critical Inclinations of a Lunar Orbiter

“…In the main problem, the following approximations are made by Giacaglia et al (1970): i) the Moon's orbit around the Earth lies on the lunar equatorial plane; ii) the orbit of the Moon around the Earth is circular; iii) the longitude of lunar longest meridian λ 22 is equal to the longitude of the Earth λ ⊕ . The classical Keplerian orbital elements are used to define the orbit of a lunar orbiter; i.e.…”