Timelike Geodesics in Naked Singularity and Black Hole Spacetimes II
  We derive here the orbit equations of particles in naked singularity
spacetimes, namely the Bertrand (BST) and Janis-Newman-Winicour (JNW)
geometries, and for the Schwarzschild black hole. We plot the orbit equations
and find the Perihelion precession of the orbits of particles in the BST and
JNW spacetimes and compare these with the Schwarzschild black hole spacetime.
We find and discuss different distinguishing properties in the effective
potentials and orbits of particle in BST, JNW and Schwarzschild spacetimes, and
the particle trajectories are shown for the matching of BST with an external
Schwarzschild spacetime. We show that the nature of perihelion precession of
orbits in BST and Schwarzschild spacetimes are similar, while in the JNW case
the nature of perihelion precession of orbits is opposite to that of the
Schwarzschild and BST spacetimes. Other interesting and important features of
these orbits are pointed out.
