Solution
= Solution
The <torque> about the origin is
$$
\tau=r\times F=-\frac{km}{r^3}r\times r=0.
$$
Since $\dot L=\tau$, the <angular momentum> $L=mr\times\dot r$ is conserved. The force is the negative gradient of the <inverse-square potential>
$$
V(r)=-\frac{km}{r},
$$
so the conserved <energy> is
$$
E=\frac12m|\dot r|^2-\frac{km}{r}.
$$
Directly, $\dot E=\dot r\mathbin{\cdot}(m\ddot r+km r/r^3)=0$.