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Circular Orbits under Central Forces in Special Relativity

J M Aguirregabiria·A Hernández·M Rivas
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Abstract

We discuss the existence and stability of circular orbits of a relativistic point particle moving in a central force field. The stability condition is somewhat more restrictive in Special Relativity. In the particular case of attractive central force fields proportional to $1/r^n$, we find the values the angular momentum may have in circular orbits and show that, unlike in the non-relativistic limit, the latter are not always stable in Special Relativity for $2<n<3$.

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J M Aguirregabiria, A Hernández, M Rivas. 2004-07-12. Circular Orbits under Central Forces in Special Relativity. https://arxiv.org/abs/physics/0407049

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