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Section 21.4 Central Forces
In the introduction
Section 21.1 , we defined a central force as satisfying two characteristics. We can now write turn these descriptions of the characteristics into equations:
A central force depends only on the separation between the two bodies
\begin{equation}
\ff_{21} = -\ff_{12} = \ff(\rr_2-\rr_1)\tag{21.4.1}
\end{equation}
A central force points along the line connecting the two bodies
\begin{equation}
\ff_{21} = -\ff_{12} = \ff(\rr_2-\rr_1) = f(\rr) \,\rhat\tag{21.4.2}
\end{equation}
