## Azimuthally Symmetric Theory of Gravitation I

**Authors:** Golden Gadzirayi Nyambuya

From a purely none-general relativistic standpoint, we solve the empty space Poisson equation,
i.e. ∇^{2}Φ = 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 (1) the observed perihelion shift of solar planets (2) that the Astronomical Unit must
be increasing - this resonates with the observations of two independent groups of astronomers
(Krasinsky & Brumberg 2004; Standish 2005) who have measured that the Astronomical Unit
must be increasing at a rate of about 7.0±0.2m/cy (Standish 2005) to 15.0±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±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 ± 2.00 s/cy.

**Comments:** 12 pages, 2 figures, 3 tables, Published: MNRAS, Vol. 403, Issue 3, pp.1381-1392 doi:10.1111/j.1365-2966.2009.16196.x

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### Submission history

[v1] 4 Nov 2009

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