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- W4313703363 abstract "In Book 1, Proposition 7, Problem 2 of his 1687 Philosophiae Naturalis Principia Mathematica, Isaac Newton poses and answers the following question: Let the orbit of a particle moving in a central force field be an off-center circle. How does the magnitude of the force depend on the position of the particle onthat circle? In this article, we identify a potential that can produce such a force, only at zero energy. We further map the zero-energy orbits in this potential to finite-energy free motion orbits on a sphere; such a duality is a particular instance of a general result by Goursat, from 1887. The map itself is an inverse stereographic projection, and this fact explains the circularity of the zero-energy orbits in the system of interest. Finally, we identify an additional integral of motion - an analogue of the Runge-Lenz vector in the Coulomb problem - that is responsible for the closeness of the zero-energy orbits in our problem." @default.
- W4313703363 created "2023-01-08" @default.
- W4313703363 creator A5025413463 @default.
- W4313703363 date "2023-01-07" @default.
- W4313703363 modified "2023-10-14" @default.
- W4313703363 title "A Novel Potential Featuring Off-Center Circular Orbits" @default.
- W4313703363 doi "https://doi.org/10.3842/sigma.2023.001" @default.
- W4313703363 hasPublicationYear "2023" @default.
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