Newtonian and Pseudo-Newtonian Hill Problem

Abstract

A pseudo-Newtonian Hill problem based on the Paczynski-Wiita pseudo-Newtonian potential that reproduces general relativistic effects is presented and compared with the usual Newtonian Hill problem. Poincare maps, Lyapunov exponents and fractal escape techniques are employed to study bounded and unbounded orbits. In particular we consider the systems composed by Sun, Earth and Moon and composed by the Milky Way, the M2 cluster and a star. We find that some pseudo-Newtonian systems - including the M2 system - are more stable than their Newtonian equivalent.

12 pages, 4 figures, 1 table

References in corpus (3)

• The tidal disruption rate in dense galactic cusps containing a supermassive binary black hole
• Chaos in Pseudo-Newtonian Black Holes with Halos
• Pseudo-Newtonian models of a rotating black hole field

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• Free motion around black holes with discs or rings: between integrability and chaos - I
• Free motion around black holes with discs or rings: between integrability and chaos -- IV
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• Beyond-Newtonian dynamics of a planar circular restricted three-body problem with Kerr-like primaries
• Stability of Orbits around a Spinning Body in a Pseudo-Newtonian Hill Problem
• Orbit classification in an equal-mass non-spinning binary black hole pseudo-Newtonian system
• Revealing the Newton-Raphson basins of convergence in the circular pseudo-Newtonian Sitnikov problem
• Orbit classification in a pseudo-Newtonian Copenhagen problem with Schwarzschild-like primaries
• Orbit classification in a disk galaxy model with a pseudo-Newtonian central black hole
• Partial suppression of chaos in relativistic three-body problems
• Integrability of non-homogeneous Hamiltonian systems with gyroscopic coupling