Azimuthally symmetric theory of gravitation - I. On the perihelion precession of planetary orbits

Abstract

From a purely non-general relativistic standpoint, we solve the empty space Poisson equation (∇2Φ = 0) for an azimuthally symmetric setting (i.e. for a spinning gravitational system like the Sun). We seek the general solution of the form Φ =Φ(r, θ). This general solution is constrained such that in the zeroth-order approximation it reduces to Newton's well-known inverse square law of gravitation. For this general solution, it is seen that it has implications on the orbits of test bodies in the gravitational field of this spinning body. We show that to second-order approximation, this azimuthally symmetric gravitational field is capable of explaining at least two things: (i) the observed perihelion shift of solar planets; (ii) the fact that the mean Earth-Sun distance must be increasing (this resonates with the observations of two independent groups of astronomers, who have measured that the mean Earth-Sun distance must be increasing at a rate between about 7.0 ± 0.2 m century-1 and 15.0 ± 0.3 m cy-1). In principle, we are able to explain this result as a consequence of the loss of orbital angular momentum; this loss of orbital angular momentum is a direct prediction of the theory. Further, we show that the theory is able to explain at a satisfactory level the observed secular increase in the Earth year (1.70 ± 0.05 ms yr-1). Furthermore, we show that the theory makes a significant and testable prediction to the effect that the period of the solar spin must be decreasing at a rate of at least 8.00 ± 2.00 s cy-1. © 2010 The Author. Journal compilation © 2010 RAS.