IMPACT OF SOLAR SPIN ON PLANETARY ORBITS - Iqbal, M. J.; Quamar, J. (Journal of Research (Science), 2007)
This paper examines the possible effect of solar spin in the planetary orbit. We show in our earlier paper that if we incorporate the contribution of spin of the central gravitating body in orbital calculations, a residual slight perturbation on the standard constant areal velocity should exist. In particular, the second law of planetary motion requires a revision. However, it turns out that the classical result of Kepler is recoverable from our result as a special case. To be able to appreciate the need for the revision suggested by the new perturbation considered here, this paper looks into the genesis of orbital theory. We herein propose to reduce spin theory to non-relativistic regime. In fact, we consider restricted three-body problem. Confining, for the moment, again to the specific context of solar system, our initial calculations show that the transverse component the transverse component of the force field is nonzero, in contrast to the GN-physics (Galilei-newtonian physics) wherein such a component vanishes. In particular, the transverse component of the central force field does vanish if we neglect the spin of the gravitating star. This situation is radically different from that of GN-theory (where linearisation often does result). However, if we set the spin equal to zero, we retrieve the orbit equation of GN-physics. As regards solution, we here apply numerical schemes to determine solution of nonlinear orbit equation for Earth. Our results exhibit that the new light on issue in relativistic celestial mechanics and models of planetary motion.