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Exploring the Planar Circular RestrictedThree-body Problem with Prolate Primaries |
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KeyWord:Restricted three-body problem Oblateness parameter Basins of convergence |
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Abstract: |
We numerically investigate the convergence properties of the circu-
lar restricted three-body problem with prolate primaries, by using the Newton-
Raphson iterative scheme. In particular, we examine how the oblateness co-
efficient A influences several aspects of the method, such as its speed and
efficiency. Color-coded diagrams are used for revealing the basins of conver-
gence on the configuration space. Additionally, we compute the degree of
fractality of the convergence basins on the physical plane, as a function of
the oblateness coefficient, by using different computational tools, such as the
uncertainty dimension and the (boundary) basin entropy. |
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