New exact particular analytical solutions of the triangular restricted three-body problem

Abstract

The triangular restricted three-body problem is studied in special non-inertial central reference frame with origin at forces centre of this problem. Masses are arbitrary values. We studied the solutions of dimensionless differential equations of motion of the triangular restricted three-body problem in rotating reference frame in the pulsating variables. For the non-circular planar restricted three-body problem we have found out new exact analytical solutions. In these solutions, all the three bodies form an isosceles triangle with variable height. Also, we have found new class of analytical solutions of the planar circular restricted three-body problem in the form of non-isosceles triangle. The basis of this non-isosceles triangle is distance between the primary bodies, the ratio of sides of non-isosceles triangle is constant and infinitesimal small body is at vertex of this non-isosceles triangle. Obtained exact particular analytical solutions can be used for topological analysis of the general three-body problem.