Planetary and Light Motions From Newtoinian Theory: An Amusing Exercise

This document gathers the notes of a 30-hour review course on gravitation, which I delivered in January 2018 and January 2019 at the African Institute for Mathematical Sciences of Cameroon (AIMS-Cameroon). Its main goal is to propose a big picture of gravitation, where Einstein's relativity arises as a natural increment to Newton's theory. It is designed for bachelor/master students who do not necessarily have prior knowledge about relativity. The students are nevertheless ex...

General Relativity is considered to be so far the best gravitation theory. However it is quite hard to use in real situations. The root of these difficulties lays in the non-linearity of the theory. Our aim was not to linearize the theory, but find the source of non-linearity and get rid of it. We found that the resolution can be obtained by defining standards and units properly. We also found that the mathematical method to change the units of General Relativity has been dis...

One of the most subtle points in the modern relativistic models for microarcsecond astrometrical observations is the treatment of the influence of translational motion of gravitating bodies on the light propagation. This paper describes numerical simulations of the light propagation in the gravitational field of moving gravitating bodies as well as summarizes the underlying theory. The simulations include high-precision numerical integrations of both post-Newtonian and post-M...

Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple reconsideration of Newton's figure naturally leads to en explicit expression of the velocity and to the equation of the trajectory. ...

Einstein's general relativity is increasingly important in contemporary physics on the frontiers of both the very largest distance scales (astrophysics and cosmology) and the very smallest(elementary particle physics). This paper makes the case for a `physics first' approach to introducing general relativity to undergraduate physics majors.

Attempts to merge Einsteinian gravity with Newtonian run into inconsistencies because in Newton's gravity time is absolute and the speed of gravity is infinite. Such an assumption was in a focus of attention of scientists in 19th century interested in finding out if the speed of gravity is infinite. By analogy with electrodynamics, some retarded potentials replacing Newtonian were utilized. By using one of such potentials Gerber correctly calculated the perihelion shift for M...

We argue that in the general relativistic calculation of planetary orbits, the choice of a reference frame which is an obligatory condition in the Newtonian approach is replaced by an appropriate boundary condition on the solution of Einstein equation. Implications of this observation on the nature of rotation and the physical interpretation of the metric tensor are discussed.

A simple general relativity theory for objects moving in gravitational fields is developed based on studying the behavior of an atom in a gravitational field. The theory is applied to calculate the satellite time dilation, light deflection by the sun, and Mercury's precession with an error of less than 1%. The approach to the new theory introduced here is radically different from the geometric approach used by Einstein's general relativity. The theory is field based where the...

There are many books on the classical subject of special relativity. However, after having spent a number of years, both in relativistic engineering and research with relativity, I have come to the conclusion that there exist a place for a new book. I do believe that the present book is not quite the same as the others, mainly due to attempt to cast light on dark corners. I should make it clear what this little book is not. It is not a textbook on relativity theory. What the ...

There is proven a theorem, to the effect that a material body in general relativity, in a certain limit of sufficiently small size and mass, moves along a geodesic.