Planetary and Light Motions From Newtoinian Theory: An Amusing Exercise

A brief outline of the history of the discrepancies within Newtonian mechanics at the end of the nineteenth century is given. The framework of general relativity is described briefly and the famous 'tests' of general relativity are considered and alternative solutions discussed, with particular attention concentrating on the advance of the perihelion of the planet Mercury. The implications for the claims of relativity are discussed, all with reference to both pre and post 191...

In order to test the Einstein gravitation theory (EGT) we compare their predictions with the measured results in the following phenomena: the perihelion advance of planets, deflection of light, radar echo delays around the Sun and an overall planetary motion in Solar System. In our calculation we have used the Schwarzschild metric that is defined in the surrounding vacuum of a spherically symmetric mass distribution, not in rotation. This article was written to graduate and p...

Was Einstein wrong? This paper provides a detailed technical review of Einstein's special and general relativity from an astrophysical perspective, including the historical development of the theories, experimental tests, modern applications to black holes, cosmology and parallel universes, and last but not least, novel ways of expressing their seven most important equations.

In a recent series of papers, the authors introduced a new Relativistic Newtonian Dynamics (RND) and tested its validity by the accurate prediction of the gravitational time dilation, the anomalous precession of Mercury, the periastron advance of any binary and the Shapiro time delay. This dynamics incorporates the influence of potential energy on spacetime in Newtonian dynamics and, unlike Einstein's General Relativity, treats gravity as a force without the need to curve spa...

We provide the differential equations that generalize the Newtonian N-body problem of celestial mechanics to spaces of constant Gaussian curvature, k, for all k real. In previous studies, the equations of motion made sense only for k nonzero. The system derived here does more than just include the Euclidean case in the limit when k tends to 0: it recovers the classical equations for k=0. This new expression of the laws of motion allows the study of the N-body problem in the c...

Einstein's theory of general relativity (GR) provides the best available description of gravity. The recent detection of gravitational waves and the first picture of a black hole have provided spectacular confirmations of GR, as well as arousing substantial interest in topics related to gravitation. However, to understand present and future discoveries, it is convenient to look to the past, to the classical tests of GR, namely, the deflection of light by the Sun, the periheli...

This paper gives a self-contained, elementary, and largely pictorial statement of Einstein's equation.

Modern astrometry is based on angular measurements at the micro-arcsecond level. At this accuracy a fully general relativistic treatment of the data reduction is required. This paper concludes a series of articles dedicated to the problem of relativistic light propagation, presenting the final microarcsecond version of a relativistic astrometric model which enable us to trace back the light path to its emitting source throughout the non-stationary gravity field of the moving ...

Einstein's general relativity is the best available theory of gravity. In recent years, spectacular proofs of Einstein's theory have been conducted, which have aroused interest that goes far beyond the narrow circle of specialists. The aim of this work is to offer an elementary introduction to general relativity. In this first part, we introduce the geometric concepts that constitute the basis of Einstein's theory. In the second part we will use these concepts to explore the ...

Kepler's orbits with corrections due to Special Relativity are explored using the Lagrangian formalism. A very simple model includes only relativistic kinetic energy by defining a Lagrangian that is consistent with both the relativistic momentum of Special Relativity and Newtonian gravity. The corresponding equations of motion are solved in a Keplerian limit, resulting in an approximate relativistic orbit equation that has the same form as that derived from General Relativity...