An inverse cube central force allows rescaling of angular velocity by a constant factor without affecting radial motion, as identified by Newton.
Available at https://en.wikipedia.org/wiki/Newton's_theorem_of_revolving_orbits https://en.wikipedia.org/wiki/Newton's \;\; theorem \;\; of \;\; revolving \;\; orbits
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The Inverse Cube Force Law
An inverse cube central force allows rescaling of angular velocity by a constant factor without affecting radial motion, as identified by Newton.