Derivation of Specific Velocity of Body Moving under Gravity with Zero Total Energy

T V B S Satyanarayana Murthy

doi:10.4236/jamp.2017.51001

Abstract

Mathematical solutions predict abstract conditions that indicate limits or bounds for physical processes. Generally, experimental verifications and physical observations on physical processes validate the mathematical predictions. Sometimes these predictions lead to new theories and concepts that form basis of better understanding of the natural processes. Gravitational interactions between bodies are natural physical processes. A smaller body moves under the influence of gravity, due to the gravitational effect of another large body. Newton’s classical gravitational theory addresses the interactions at low velocities. Einstein’s general relativity provides firm basis for gravitational interactions. Observations over past 100 years prove the mathematical precision and predictions of general relativity. Einstein’s special relativity forms the foundation of quantum physics. In this paper, the author applies concepts of special relativity to classical two body Newtonian gravitational problem. The study predicts a new mathematically viable condition that when a body moves at a specific velocity derived in this paper, the total energy of the moving body is zero. The specific velocity is a constant. At velocities far less than specific velocity, the total energy is negative and is equal to classical value of half the potential energy. At velocities, greater the specific velocity the total energy is positive. The specific velocity condition also enables determination of specific mass of gravitating body, as well as the specific distance of the moving body from gravitating body, at which the total energy of moving body is zero.

Highlights

Equation (17) is the outcome of the present study. It states that the specific velocity is a constant in any gravitational interaction when the total energy of moving body is zero
We can observe from Equation (12), that until the moving body reaches the specific velocity, its total energy is negative, at specific velocity, its total energy is zero and for velocity more than the specific velocity, its total energy is positive
From Equation (12), we get the ratio of total energy to gravitational potential energy as

Summary

Introduction

The study predicts a new mathematically viable condition that when a body moves at a specific velocity derived in this paper, the total energy of the moving body is zero. At velocities far less than specific velocity, the total energy is negative and is equal to classical value of half the potential energy. Substituting for (γ −1) from Equation (7) in Equation (6), we get a new mathematical expression for kinetic energy as where U is the potential energy of the moving body given by [2], U = − GM 0m0 (9)

Results

Conclusion