Central force

In classical mechanics, a central force on an object is a force whose magnitude only depends on the distance r of the object from the origin and is directed along the line joining them:

where ${\displaystyle \scriptstyle {\vec {\text{ F }}}}$ is the force, F is a vector valued force function, F is a scalar valued force function, r is the position vector, ||r|| is its length, and ${\displaystyle \scriptstyle {\hat {\mathbf {r} }}}$ = r/||r|| is the corresponding unit vector.

Not all central force fields are conservative nor spherically symmetric. However, it can be shown that a central force is conservative if and only if it is spherically symmetric.

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