Global Journal of Researches in Engineering, A: Mechanical & Mechanics, Volume 22 Issue 1

Gravitomagnetics a Simpler Approach Applied to Dynamics within the Solar System H. Ron Harrison Abstract- Galileo studied bodies falling under gravity and Tycho Brahe made extensive astronomical observations which led Kepler to formulate his three famous laws of planetary motion. All these observations were of relative motion. This led Newton to propose his theory of gravity which could just as well have been expressed in a form that does not involve the concept of force. The approach in this paper extends the Newtonian theory and the Special Theory of Relativity by including relative velocity by comparison with electromagnetic effects as shown in section 1.4 based on the Lorentz force. It is also guided from the form of measured data. This enables the non-Newtonian effects of gravity to be calculated in a simpler manner than by use of the General Theory of Relativity (GR). Application to the precession of the perihelion of Mercury and the gravitational deflection of light gives results which agree with observations and are identical to those of GR. It also gives the accepted expression for the Schwarzschild Radius. This approach could be used to determine non-Newtonian variations in the trajectories of satellites. An extra term is then added to the initial basic equation which acts in the direction of the relative velocity. The amended basic equation now predicts a change in the speed of light due to gravity and derives the accepted measured result for the Shapiro time delay. It also gives the accepted value for the Last Stable Orbit. Further, it shows that light passing through a gravitational field refracts in accordance with Snell’s Law. It also shows that anti-gravity is possible but only when relative speeds get close to that of light. Because the extra term is a function of (v/c) 4 the previously mentioned predictions are not significantly changed. The prime action in this paper is to show the reasons for creating the form of gravitomagnetics. The applications Keywords: gravity, relativity, lorentz force, speed of light. I. T he B asics a) Newtonian Gravity alileo studied bodies falling to Earth under gravity and concluded that all bodies fell with the same acceleration independent of size and material. Tycho Brahe made extensive astronomical observations which led Kepler to formulate his three famous laws of planetary motion relative to the Sun. All of these observations were of relative motion but the mass of one body was, in each case, much greater than that of the Author: Formerly Senior Lecturer of the Department of Mechanical Engineering and Aeronautics, City, University of London, Ph.D. other. These led Newton to propose his theory of gravity using the concept of force and yielding an equation which gives the acceleration of a body relative to the centre of mass. He could just as well have presented it in the form ( ) 2 / / AB B A AB r mmG a + −= (1) without invoking the concept of force and only requiring one definition of mass. This means that the principal of equivalence does not appear. That is, the acceleration of body B relative to A, in the radial direction, is proportional to the sum of their masses and inversely proportional to the square of their separation. G is the gravitational constant. b) Gravitomagnetics It is now proposed that equation (1) be extended to include the relative velocity. The axioms are. a) It is assumed that in mass-free space light travels in straight lines. This defines a non-rotating frame of reference. b) Because all motion is relative there are no other restrictions on the frame of reference. c) Gravity propagates at the same speed as light. d) Mass, or rest mass, is simply the quantity of matter and is regarded as constant. It could be a count of the number of basic particles. The initial proposed equation is based on comparisons with electromagnetics. This equation gives results which agree with the measured results of the precession of the perihelion of Mercury and with the deflection of light grazing the Sun. Also it gives the correct definition for the Schwarzschild Radius. However, it suggests that the speed of light is constant. As a result it does not predict the Shapiro Time Delay. An extra term is then added which gives agreement with the time delay and also generates the accepted value for the Last Stable Orbit. See equations (2a), (3a), (4a) and (5a). The proposed equation is ( ) 2 1 2 2 2 2 2 r r ev v e a ×× +       − −= cr K c v r K (2) or 2 1 22 2 2 2 v e a cr Kv c v r K r r +       + −= (3) G Global Journal of Researches in Engineering (A ) Volume XxXII Issue I Version I 1 Year 2022 © 2022 Global Journals See section I d for the similarity with the Lorentz force. are discussed to justify the equations. As shown in [32]. e-mail: h.ron.harrison@harmonic.plus.com F.R.Ae.S.

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