Non-autonomous Equations of Restricted Three-Body Problem with Variable Masses and Zonal Harmonics up to J4
Joel John Taura
Oni Leke
Jagadish Singh
Abstract
This paper investigates the derivations of the time-dependent equations of motion of a test particle in the frame of the R3BP with variable masses and zonal harmonics. The motion and mass variations of the primaries are described by the Gylden-Mestschersky problem (GMP) and the unified Mestschersky law (UML), respectively, with further assumptions that the oblateness of the bigger primary varies with zonal harmonics coefficients up to J4 terms. The non-autonomous equations of the test mass in a reference frame rotating are derived using the Hamiltonian method. These equations are DE with variable coefficients and are defined by the oblateness of the bigger body with zonal harmonics coefficients up to J4, the angular velocity of revolution and the masses of the primaries. This study will in no doubt expand the knowledge base of celestial mechanics and will allow for more extensions with applications to space missions.
References