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arXiv · 2405.15639

Well Posed Origin Anywhere Consistent Systems in Celestial Mechanics

Harry Gingold·Jocelyn Quaintance
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Abstract

Certain measurements in celestial mechanics necessitate having the origin O of a Cartesian coordinate system (CCS) coincide with a point mass. For the two and three body problems we show mathematical inadequacies in Newton's celestial mechanics equations (NCME) when the origin of a coordinate system coincides with a point mass. A certain system of equations of relative differences implied by NCME is free of these inadequacies and is invariant with respect to any CCS translation. A new constant of motion is derived for the relative system. It shows that the universe of relative differences of the $N$-body problem is ``restless''.

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Harry Gingold, Jocelyn Quaintance. 2024-05-24. Well Posed Origin Anywhere Consistent Systems in Celestial Mechanics. https://arxiv.org/abs/2405.15639

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