Two-body Problem - Central Forces

Central Forces

For many physical problems, the force F(r) is a central force, i.e., it is of the form

where r = |r| and r̂ = r/r is the corresponding unit vector. We now have:

\mu \ddot{\mathbf{r}} = {F}(r) \hat{\mathbf{r}} \ ,

where F(r) is negative in the case of an attractive force.

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