Modified Kepler's law, escape speed, and two-body problem in modified Newtonian dynamics-like theories

Journal Article · Mon Nov 15 00:00:00 EST 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.82.103001· OSTI ID:21503579

Hongsheng, Zhao ^[1]; Baojiu, Li ^[2]; Bienayme, Olivier ^[3]

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1. Scottish University Physics Alliance, University of St. Andrews, KY16 9SS (United Kingdom)
2. DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
3. Observatoire Astronomique, Universit de Strasbourg, 11, rue de l'Universit, F-67000 Strasbourg (France)

We derive a simple analytical expression for the two-body force in a subclass of modified Newtonian dynamics (MOND) theories and make testable predictions in the modification to the two-body orbital period, shape, precession rate, escape speed, etc. We demonstrate the applications of the modified Kepler's law in the timing of satellite orbits around the Milky Way, and checking the feasibility of MOND in the orbit of the large Magellanic cloud, the M31 galaxy, and the merging bullet clusters. MOND appears to be consistent with satellite orbits although with a tight margin. Our results on two-bodies are also generalized to restricted three-body, many-body problems, rings, and shells.

• OSTI ID: 21503579
• Journal Information: Physical Review. D, Particles Fields, Vol. 82, Issue 10; Other Information: DOI: 10.1103/PhysRevD.82.103001; (c) 2010 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
FORECASTING
MAGELLANIC CLOUDS
MILKY WAY
MODIFICATIONS
ORBITS
PRECESSION
THREE-BODY PROBLEM
TWO-BODY PROBLEM
VELOCITY
GALAXIES
MANY-BODY PROBLEM