Well Posed Origin Anywhere Consistent Systems in Celestial Mechanics
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929357527711744 |
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| author | Gingold, Harry Quaintance, Jocelyn |
| author_facet | Gingold, Harry Quaintance, Jocelyn |
| contents | 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''. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_15639 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well Posed Origin Anywhere Consistent Systems in Celestial Mechanics Gingold, Harry Quaintance, Jocelyn Mathematical Physics Earth and Planetary Astrophysics Dynamical Systems Space Physics 70F15, 85A04, 70K99 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''. |
| title | Well Posed Origin Anywhere Consistent Systems in Celestial Mechanics |
| topic | Mathematical Physics Earth and Planetary Astrophysics Dynamical Systems Space Physics 70F15, 85A04, 70K99 |
| url | https://arxiv.org/abs/2405.15639 |