On a class of exact geodesics of the erez-rosen metric

In a previous paper, a class of exact geodesics for the motion of a particle in a gravitational-monopole-prolate-quadrupole field was investigated, both in Newtonian mechanics and in general relativity. This paper consists of both an amplification of the analysis contained in the previous paper and an extension of the analysis to the case for negative quadrupole moment, which was not treated previously. The relativistic results are based on the monopole-quadrupole metric of Erez and Rosen, the Newtonian results on the monopole-quadrupole potential of Laplace. In the limit of vanishing quadrupole parameter (q 0), the relativistic results reduce to those of the familiar Schwarzschild case; in the weak-field limit (r/m ), the relativistic results reduce to those of the Newtonian case. The existence and stability thresholds in the relativistic case yield values that uniquely characterize the Erez-Rosen metric.