Kepler Problem - Mathematical Definition

Mathematical Definition

The central force F that varies in strength as the inverse square of the distance r between them:

\mathbf{F} = \frac{k}{r^{2}} \mathbf{\hat{r}}

where k is a constant and represents the unit vector along the line between them. The force may be either attractive (k<0) or repulsive (k>0). The corresponding scalar potential (the potential energy of the non-central body) is:

V(r) = \frac{k}{r}

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