Physics

Oblate spheroid

Mathematics

Infinitesimal

Motion (physics)

Computer graphics (images)

Mathematical analysis

Planar

Equilateral triangle

Plane (geometry)

Variable (mathematics)

Geometry

Computer science

Three-body problem

Center of mass (relativistic)

Energy–momentum relation

Classical mechanics

The Astronomical Journal

The aim of the present paper is to study the effects of heterogeneous oblate spheroid and variable mass on the motion of the fifth infinitesimal body in the frame of the circular restricted five-body problem, with the imposition that the three primaries are placed at the vertices of an equilateral triangle and the fourth primary is placed at the center of the equilateral triangle. By using Jeans law and Meshcherskii space transformation, we evaluate the equations of motion and find a quasiJacobian integral. We determine the locations of equilibrium points, the regions of motion, and the attracting domain of in-plane motion. Furthermore, the effects of heterogeneous oblate spheroid and variable mass have been examined with the help of Poincaré surfaces of section. We studied the linear stability of equilibrium points and found that all of them are unstable.

A Planar Five-body Problem in a Framework of Heterogeneous and Mass Variation Effects