Exact, E=0, classical solutions for general power-law potentials

For zero energy, E=0, we derive exact, classical solutions for all power-law potentials, V(r)=-γ/rν, with γ>0 and <ν<az. When the angular momentum is nonzero, these solutions lead to the orbits ρ(t)=(cos{μ[cphi(t)-cphi0(t)]})1/μ, for all μν/2-10. When ν>2, the orbits are bound and go through the origin. This leads to discrete discontinuities in the functional dependence of cphi(t) and cphi0(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. In addition to the special ν=2 case, the unbound trajectories are also discussd in detail. This includes the unusual trajectories which have finite travel times to infinity.