ON THE RESTRICTED THREE-BODY PROBLEM

Аннотация

The paper analytically investigates the classical restricted three-body problem in a special non-inertial
central coordinate system, with the origin at center of forces. In this coordinate system, an analytical expression of
the invariant of the centre of forces is given. The existence of the invariant of the centre of forces admits the correct
division of the problem into two problems. The first is a triangular restricted three-body problem. The second is a
collinear restricted three-body problem. In this paper the collinear restricted three-body problem is investigated.
Using the properties of the invariant of centre of forces of the restricted three-body problem in the special noninertial
central coordinate system, the basic differential equations of motion for the collinear restricted three-body
problem are obtained when three bodies lie on the same line during all motion. Differential equations of the collinear
restricted three-body problem in the rotating non-inertial central coordinate system in pulsating variables are derived.
New differential equations of motion for the collinear restricted three-body problem in three regions of possible
location of the massless body with stationary solutions corresponding to the three Euler libration points have been
derived. The circular collinear restricted three-body problem is investigated in detail. The corresponding Jacobi
integrals are obtained. New exact non-stationary partial analytical solutions of the obtained new differential
equations of motion of the collinear restricted three-body problem have been found for the considered case.