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| Paper: |
The Solar System's Lagrangian Points in the Framework of the Relativistic Restricted Three--Body Problem |
| Volume: |
107, Completing the Inventory of the Solar System |
| Page: |
147 |
| Authors: |
Maindl, T. I. |
| Abstract: |
The Lagrangian points of configurations consisting of the Sun and one planet as the primary bodies in the relativistic restricted three-body problem are investigated. We take care of relativistic effects using the post-Newtonian approximation of general relativity and its application to the restricted three-body problem. Starting with the respective equations of motion expressions for the relativistic displacements of the Lagrangian equilibrium points valid for any mass ratio are derived. Then the resulting formulae are applied to the Solar System which leads to relativistic corrections of $\le 1$~km. This is orders of magnitude smaller than the typical size of the stability regions around the triangular points for the considered mass ratios. |
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