Examples
Gravitational force and Coulomb force are two familiar examples with F(r) being proportional to 1/r2. An object in such a force field with negative F (corresponding to an attractive force) obeys Kepler's laws of planetary motion.
The force field of a spatial harmonic oscillator is central with F(r) proportional to r and negative.
By Bertrand's theorem, these two, F(r) = −k/r2 and F(r) = −kr, are the only possible central force field with stable closed orbits.
Read more about this topic: Central Force
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