EQUATIONS OF MOTION OF THE RESTRICTED THREE-BODY PROBLEM WITH NON-ISOTROPICALLY VARIABLE MASSES WITH REACTIVE FORCES

Аннотация

During the formation of planetary systems, especially at the non-stationary stage, the gravitational
field of the central protostar (e.g., protosun) and the most massive protoplanets (e.g., protojupiter) often dominate. In
this regard, we consider the restricted three-body problem with variable masses changing non-isotropically at
different rates, as a celestial-mechanical model of small-body motion in a non-stationary protoplanet system. Based
on the generalized Meshchersky equation, the differential equations of the restricted three-body problem are derived
in the absolute coordinate system and in the presence of a reactive forces. At the same time it is assumed that the
masses of the bodies are increasing due to accreting particles from the outer space, and decreasing due to the
particle loss. Based on the equation of motion obtained in the absolute coordinate system, the equations of motion in
a relative coordinate system whose origin is at the center of the protostar are derived in the presence of a reactive
forces. Special cases of the obtained differential equations of motion of a non-stationary dynamic system in a
relative coordinate system are discussed.