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

For zero energy, {ital E}=0, we derive exact, classical solutions for {ital all} power-law potentials, {ital V}({ital r})={minus}{gamma}/{ital r}{sup {nu}}, with {gamma}{gt}0 and {minus}{infinity}{lt}{nu}{lt}{infinity}. When the angular momentum is nonzero, these solutions lead to the orbits {rho}({ital t})=(cos{l_brace}{mu}[{ital cphi}({ital t}){minus}{ital cphi}{sub 0}({ital t})]{r_brace}){sup 1/{mu}}, for all {mu}{equivalent_to}{nu}/2{minus}1{ne}0. When {nu}{gt}2, the orbits are bound and go through the origin. This leads to discrete discontinuities in the functional dependence of {ital cphi}({ital t}) and {ital cphi}{sub 0}({ital t}), as functions of {ital 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 {nu}=2 case, the unbound trajectories are also discussd in detail. This includes the unusual trajectories which have finite travel times to infinity.