Relativistic Newtonian Gravitation That Gives the Correct Prediction of Mercury Precession

Espen Gaarder Haug

doi:10.4236/jhepgc.2020.62017

Abstract

In the past, there was an attempt to modify Newton’s gravitational theory, in a simple way, to consider relativistic effects. The approach was “abandoned” mainly because it predicted only half of Mercury’s precession. Here we will revisit this method and see how a small logical extension can lead to a relativistic Newtonian theory that predicts the perihelion precession of Mercury correctly.

Highlights

In 1981 and 1986, Bagge [1] and Phillips [2] each suggested an ad-hoc modification of Newton by replacing the smaller mass in the formula with a relativistic mass Mm F =G − v2 c2 r2 (1)The velocity v is the relative velocity between the two gravitational objects: the velocity of Mercury relative to the Sun, for example
The approach was “abandoned” mainly because it predicted only half of Mercury’s precession. We will revisit this method and see how a small logical extension can lead to a relativistic Newtonian theory that predicts the perihelion precession of Mercury correctly
Phillips initially claimed that his derivation, based on this, led to a prediction of the perihelion precession of Mercury equal to that of Einstein’s general relativity theory [3]

Summary

Introduction

In 1981 and 1986, Bagge [1] and Phillips [2] each suggested an ad-hoc modification of Newton by replacing the smaller mass in the formula with a relativistic mass. The velocity v must be interpreted as the velocity between the large and small masses This extension is, in our view, only valid when the gravity phenomenon is observed from the frame of the large gravitational object, such as predicting the orbital velocity of the moon relative to the Earth, for example. In this case under consideration, the small relativistic mass will fall out and we get the same predictions as in standard Newtonian gravity.

Equivalence Principle

Summary