Investigation of the restricted three-body problem in a special non-inertial central coordinate system

Abstract

In this work we analytically investigated the spatial classical restricted three - body problem. A new special non - inertial central coordinate system has been introduced. The origin of the introduced coordinate system coincides with center of forces of the investigated problem. In the special non - inertial central coordinate system are obtained new basic differential equations of motions of the restricted three - body problem. In the new coordinate system is found the analytic expression for the invariant of the center of forces. In the introduced coordinate system the restricted three - body problem is divided into two separate problems, and various basic differential equations of these two problems are obtained . The correctness of such division of the investigated problem into two is provided by the invariant of the center of force finding in the same coordinate system. The first is a triangular restricted three - body problem when three bodies form a triangle at all time of motion. The second is a collinear restricted three - body problem when three bodies lie on the same line at all time of motion. The differential equations of motion of the triangular restricted three - body problem in the rotational special non - inertial central coordinate system in pulsating variables are derived separately. Also the differential equations of the collinear restricted three - body problem in the non - inertial central coordinate system are obtained separately. The new obtained forms of differential equations of the restricted three - body problem in the special non - inertial coordinate system open the new perspectives in the investigation of this problem.