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The effect of a fifth large-scale space-time dimension on orbital dynamics

M. B. Gerrard·T. J. Sumner
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Abstract

A model based on simple assumptions about 4-dimensional space-time being closed and isotropic, and embedded in a 5th large-scale dimension, r, representing the radius of curvature of space-time, has been used in an application of Newton's Second Law to describe a system with angular momentum. It has been found that the equations of MOND used to explain the rotation curves of galaxies appear as a limit within this derivation and that there is a universal acceleration constant, ao, with a value, again consistent with that used by MOND. This approach does not require modification of Newtonian dynamics, only its extension into a fifth large-scale dimension. The transition from the classical Newtonian dynamics to the MOND regime emerges naturally and without the introduction of arbitrary fitting functions, if this 5-dimensional model is adopted. The paper also includes the derivation of an effect in 5-dimensional orbital dynamics which is in reasonable agreement with the observed Pioneer Anomaly.

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M. B. Gerrard, T. J. Sumner. 2007-10-10. The effect of a fifth large-scale space-time dimension on orbital dynamics. https://arxiv.org/abs/gr-qc/0605080

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