Journal of Modern Physics, 2015, 6, 1195-1206 Published Online August 2015 in SciRes. http://www.scirp.org/journal/jmp http://dx.doi.org/10.4236/jmp.2015.69124 How to cite this paper: Nyambuya, G.G. (2015) Four Poission-Laplace Theory of Gravitation (I). Journal of Modern Physics, 6, 1195-1206. http://dx.doi.org/10.4236/jmp.2015.69124 Four Poission-Laplace Theory of Gravitation (I) Golden Gadzirayi Nyambuya Department of Applied Physics, National University of Science and Technology, Bulawayo, Republic of Zimbabwe Email: physicist.ggn@gmail.com , golden.nyambuya@nust.ac.zw Received 10 October 2014; accepted 1 August 2015; published 5 August 2015 Copyright © 2015 by author and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract The Poisson-Laplace equation is a working and acceptable equation of gravitation which is mostly used or applied in its differential form in Magneto-Hydro-Dynamic (MHD) modelling of e.g. mole- cular clouds. From a general relativistic standpoint, it describes gravitational fields in the region of low spacetime curvature as it emerges in the weak field limit. For non-static gravitational fields, this equation is not generally covariant. On the requirements of general covariance, this equation can be extended to include a time-dependent component, in which case one is led to the Four Poisson-Laplace equation. We solve the Four Poisson-Laplace equation for radial solutions, and apart from the Newtonian gravitational component, we obtain four new solutions leading to four new gravitational components capable (in-principle) of explaining e.g. the Pioneer anomaly, the Titius-Bode Law and the formation of planetary rings. In this letter, we focus only on writing down these solutions. The task showing that these new solutions might explain the aforesaid gravita- tional anomalies has been left for separate future readings. Keywords Astrometry, Celestial Mechanics, Ephemerides, Planets and Satellites: Formation 1. Introduction “Speculations? I have none. I am resting on certainties. I know whom I have believed and am persuaded that; He is able to keep that which I have committed unto him against that day.” —Michael Faraday (1791-1867) The Azimuthally Symmetric Theory of Gravitation (herafter ASTG-model) set out in [1] [2] and preliminarily