Adding an inverse-cube force can preserve radial motion while rescaling angular motion. For potential and angular momentum , the radial effective potential equals that of with effective angular momentum when this is real.
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Newton's theorem of revolving orbits, often referred to simply as Newton's theorem, relates to the motion of celestial bodies under the influence of gravitational forces, particularly in circular or elliptical orbits. The theorem describes a specific property of orbits and the forces that govern them. In essence, Newton's theorem states that if an object is in a circular orbit around a central mass, the gravitational force acting on the orbiting object can be expressed as the centripetal force necessary to maintain that orbit.