  For zero energy, $E=0$, we derive exact, classical solutions for {\em all}
power-law potentials, $V(r)=-\gamma/r^\nu$, with $\gamma>0$ and $-\infty
<\nu<\infty$. When the angular momentum is non-zero, these solutions lead to
the orbits $\r(t)= [\cos \mu (\th(t)-\th_0(t))]^{1/\mu}$, for all $\mu \equiv
\nu/2-1 \ne 0$. When $\nu>2$, the orbits are bound and go through the origin.
This leads to discrete discontinuities in the functional dependence of $\th(t)$
and $\th_0(t)$, as functions of $t$, as the orbits pass through the origin. We
describe a procedure to connect different analytic solutions for successive
orbits at the origin. We calculate the periods and precessions of these bound
orbits, and graph a number of specific examples. Also, we explain why they all
must violate the virial theorem. The unbound orbits are also discussed in
detail. This includes the unusual orbits which have finite travel times to
infinity and also the special $\nu = 2$ case.
