Revolutionary Motion of a Body under the Action of Resolution of Acceleration Due To Gravity Involved

N.C. PANDEY¹

Section:Research Paper, Product Type: Journal-Paper
Vol.8 , Issue.4 , pp.27-34, Aug-2020

Online published on Aug 31, 2020

Copyright © N.C. PANDEY . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
The revolutionary motion of a body under the force of gravitation is treated in view of its motion in a two dimensional plane. The change in the direction of velocity of the revolving body for going into a circular orbit can be understood on the basis of gravitational force appearing during the motion to act for showing its effect two dimensionally. Therefore, the resolution of force is undertaken to exist along two mutually perpendicular directions. Because, the force causes acceleration to act on velocity. Hence, the horizontal and vertical components of acceleration due to gravity play a dominant role to change the corresponding components of velocity. Newton?s law of motion with regard to the mechanics of accelerating and retarding phenomena is applied by the way. The investigated components of acceleration due to the gravity vary as according to aH = g Sin∆θ and aV = g Cos∆θ, where ∆θ is the measurement of angular displacement of the body during the motion from its initial position. The resultant of these two components is related by g = V? / R with the orbital velocity for providing requisite centripetal force equal to the gravitational force acting towards the centre of the orbit. Because, the involved centripetal acceleration acts normally to orbital velocity V. Therefore, such an acceleration is called a revolutionary normal acceleration. The changing magnitudes of the horizontal and vertical components of velocity is found to be the actual cause for changing the direction of resultant velocity of the body for remaining ever acting towards the orbit during the motion. The revolutionary motion in an elliptical orbit is also tried to understand by the application of such components involved during the motion under the changing magnitude of gravitational force acting towards the focus of the ellipse. The whole motion in an elliptical orbit is simplified by correlating the observations for obtaining the motion in the trajectory of two successive conjugate parabolic envelopes of the same shape

Key-Words / Index Term :
: Gravitational force, centripetal force, revolutionary motion, circular motion, elliptical motion, orbital velocity, acceleration due to gravity, resolution, acceleration & retardation, parabolic motion, enevelopes, perigee & apogee, focus

References :
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