Planetary and Light Motions From Newtoinian Theory: An Amusing Exercise

Although the differential calculus was invented by Newton, Kepler established his famous laws 70 years earlier by using the same idea, namely to find a path in a nonuniform field of force by small steps. It is generally not known that Kepler demonstrated the elliptic orbit to be composed of intelligeable differential pieces, in modern language, to result from a differential equation. Kepler was first to attribute planetary orbits to a force from the sun, rather than giving th...

In this paper we consider the central force problem in the special theory of relativity. We derive the special relativistic version of the Binet equation describing the orbit of a body. Then, the motion of a planet in a solar-like system where the gravitational potential is modified by adding a term that is proportional to the inverse of the square of the radial coordinate is discussed. Using perturbative method, we obtain the explicit orbital function. At the end, the orbita...

Planck's formula and General Relativity indicate that potential energy influences spacetime. Using Einstein's Equivalence Principle and an extension of his Chock Hypothesis, an explicit description of this influence is derived. We present a new relativity model by incorporating the influence of the potential energy on spacetime in Newton's dynamics for motion under a central force. This model extends the model used by Friedman and Steiner to obtain the exact precession of Mer...

This paper has been withdrawn by the author after further work showed the proposed theoretical approach cannot fit planetary perihelion precession data. As presented, the theory doesn't fit gravitational light deflection by the sun either, but a straightforward theoretical change does remedy that; however a proper fit to planetary perihelion precession data is not thus obtained. The author's stated philosophical objections to the Einstein equation can be dealt with in a marke...

We provide an introduction to selected recent advances in the mathematical understanding of Einstein's theory of gravitation.

We give a pedagogical introduction of the essential features of General Theory of Relativity (GTR) in the format of an undergraduate (UG) project. A set of simple MATHEMATICA code is developed which enables the UG students to calculate the tensorial objects without prior knowledge of any package operation. The orbit equations of light and material particle in Minkowski and Schwarzschild spacetime are solved numerically to illustrate the crucial tests of GTR.

In most text books of mechanics, Newton's laws or Hamilton's equations of motion are first written down and then solved based on initial conditions to determine the constants of the motions and to describe the trajectories of the particles. In this essay, we take a different starting point. We begin with the metrics of general relativity and show how they can be used to construct by inspection constants of motion, which can then be used to write down the equations of the traj...

In this article, we review the main results of Volume I of Newton's Principia which relates Kepler's law of planets and universal gravitation. In order to clarify the reasoning of Newton, elementary and simple proofs are given to inspire earnest young students. All proofs are based on either the symmetry of spheres or taking great advantage of Kepler's law of area which also reflects the symmetry of centripedal forces.

This text aims to explain general relativity to geometers who have no knowledge about physics. Using handwritten notes by Michel Vaugon, we construct the bases of the theory.

We develop here a new approach for the relativistic modeling of the photons moving into a quasi-Minkowskian space-time, where the metric is generated by an arbitrary n-body distribution within an isolated Solar System. Our model is built on the prescriptions of the theory of General Relativity and leaves the choices of the metric, as well as that of the motion of the observer, arbitrary. Adopting a quasi-Minkowskian expression of the metric accurate to order (v/c)^2, a thorou...