What is it about?

One of the most important dynamical systems in both celestial mechanics and astrodynamics is bicircular restricted three–body problem (BCP). This problem (BCP) is considered a four–body problem with a simple form, either a perturbed restricted three–body problem or its extension. It is an interesting problem in the present time that is why it is attracting to the researchers. This model consists of two restricted three–body problems. Firstly, two bodies are moving in circular orbits around their common center of mass (i.e. barycenter) which is taken as origin. Secondly, the center of mass of above stated system and the third body are moving in circular orbits around the barycenter of all system at the same time. In this model the fourth body (the infinitesimal body) is moving under the influence of all these three celestial bodies but not influencing them motions.

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Why is it important?

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.


In this work, I think that we have presented more realistic model for the restricted three-body problem

Elbaz I. Abouelmagd
National Research Institute of Astronomy and Geophysics (NRIAG)

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This page is a summary of: The motion properties of the infinitesimal body in the framework of bicircular Sun perturbed Earth–Moon system, New Astronomy, November 2019, Elsevier, DOI: 10.1016/j.newast.2019.101282.
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