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In classical mechanics, Bertrand's theorem states that among central-force potentials with bound orbits, there are only two types of central-force scalar potentials with the property that all bound orbits are also closed orbits.
The first such potential is an inverse-square central force such as the gravitational or electrostatic potential:
The second is the radial harmonic oscillator potential:
The theorem is named after its discoverer, Joseph Bertrand.
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