Azimuthally Symmetric Theory of Gravitation (I)

Abstract

From a purely none-general relativistic standpoint, we solve the empty space Poisson equation (${\nabla }^2\Phi =0$) for an azimuthally symmetric setting, i.e., for a spinning gravitational system like the Sun. We seek the general solution of the form $\Phi =\Phi (r,\theta )$. 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 (1) the observed perihelion shift of solar planets (2) that the mean Earth-Sun distance must be increasing -- this resonates with the observations of two independent groups of astronomers (Krasinsky & Brumberg 2004; Standish 2005) who have measured that the mean Earth-Sun distance must be increasing at a rate of about $7.0\pm 0.2m/cy$ (Standish 2005) to $15.0\pm 0.3m/cy$ (Krasinsky & Brumberg 2004). In-principle, we are able to explain this result as a consequence of 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 Earth Year ($1.70\pm 0.05ms/yr$; Miura et al. 2009}). 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 $8.00\pm 2.00s/cy$.

2 figures, 2 tables, 13 pages. Accepted to MNRAS 2009 December 9. Received 2009 December 9; in original form 2009 September 5: ref. MN-09-1767-MJ.R3)

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Cited by in corpus (12)

• Analysis of the Yukawa gravitational potential in $f(R)$ gravity I: semiclassical periastron advance
• Estimations of changes of the Sun's mass and the gravitation constant from the modern observations of planets and spacecraft
• Azimuthally Symmetric Theory of Gravitation (I)
• An Empirical Explanation of the Anomalous Increases in the Astronomical Unit and the Lunar Eccentricity
• Unified $f(R)$ gravity at local scales
• Weyl conformastatic perihelion advance of small body objects
• The solar system test for the general modified gravity theories
• Application of Time Transfer Function to McVittie Spacetime: Gravitational Time Delay and Secular Increase in Astronomical Unit
• Anomalous precession of planets on a Weyl conformastatic solution
• Bipolar outflows as a repulsive gravitational phenomenon -- Azimuthally Symmetric Theory of Gravitation (II)
• $f(R)$ gravity in the solar system and cosmological scalarons
• Effective perihelion advance and potentials in a conformastatic background with magnetic field