Geodesy

Motion (physics)

Mathematical physics

Continuation

Applied mathematics

Astrophysics

Stability (learning theory)

Jacobian matrix and determinant

Computer science

Three-body problem

Classical mechanics

Earth (classical element)

Geology

Infinitesimal

Physics

Mathematics

Astronomy

Mathematical analysis

Astrobiology

Programming language

Machine learning

Constant (computer programming)

Celestial mechanics

New Astronomy

In this paper, we investigate the cases which admit Jacobian and energy conversation are constants, in the Sun perturbed Earth–Moon system. We prove that the Jacobian integral is a constant in two special cases, which can be used to determine the regions of motion from the zero velocity surfaces. On continuation of our study, we numerically illustrate the equilibrium points and their stability and Poincaré surfaces of section. In addition we reveal the basins of attraction, associated with the points of equilibrium using color–coded diagrams.

The motion properties of the infinitesimal body in the framework of bicircular Sun perturbed Earth–Moon system