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In classical mechanics, a **central force** on an object is a force that is directed towards or away from a point called **center of force**.^{[a]}^{[1]}^{: 93 }

where is the force,

Not all central force fields are conservative or spherically symmetric. However, a central force is conservative if and only if it is spherically symmetric or rotationally invariant.^{[1]}^{: 133–38 }

Central forces that are conservative can always be expressed as the negative gradient of a potential energy:

In a conservative field, the total mechanical energy (kinetic and potential) is conserved:

It can also be shown that an object that moves under the influence of *any* central force obeys Kepler's second law. However, the first and third laws depend on the inverse-square nature of Newton's law of universal gravitation and do not hold in general for other central forces.

As a consequence of being conservative, these specific central force fields are irrotational, that is, its curl is zero, *except at the origin*:

Gravitational force and Coulomb force are two familiar examples with being proportional to 1/*r*^{2} only. An object in such a force field with negative (corresponding to an attractive force) obeys Kepler's laws of planetary motion.

The force field of a spatial harmonic oscillator is central with proportional to *r* only and negative.

By Bertrand's theorem, these two, and , are the only possible central force fields where all bounded orbits are stable closed orbits. However, there exist other force fields, which have some closed orbits.

**^**This article uses the definition of central force given in Taylor.^{[1]}^{: 93 }Another common definition (used in*ScienceWorld*^{[2]}) adds the constraint that the force be spherically symmetric, i.e. .