Submitted:
17 October 2022
Posted:
19 October 2022
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Abstract
We point out an inconsistency in Newton's equations of celestial mechanics. A set of differential equations implied by Newton's equations are shown to be free of this inconsistency. We then investigate the integrals of motion associated with this relative difference system.
Keywords:
Newton's celestial mechanics equations
; $N$-body problem
; Kepler problem
; relative difference
; origin invariance
; integrals of motion
; conservation of energy
; conservation of angular momentum
; inertia
; Lagrange-Jacobi formula
; total collapse.
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