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

Figure 1 Equation (4a) may be re-written as ( ) t ev v e a r r 3 2 22 2 2 2 2 2 1       + × × +       − −= c v c v r K cr K c v r K r (2a) or 2 2 1 3 2 22 2 2 2 t v e a       + +       + −= c v c v r K cr Kv c v r K r r r (3a) From which it is seen that the additional term is negligible when (v/c) 4 is small compared to unity Again, noting that v / v t = means that (3a) may be written as v e a r              + +       + −= 2 22 2 2 2 1 2 1 c v cr Kv c v r K r . or v e a r Q cr Kv c v r K r 2 2 2 2 2 2 1 +       + −= . where              + = 2 1 c v Q And ( ) 2 2 1 3 22 22 2 2 2 t ev v e a P r r       + × × +       − −= = c v c v cr mGm cr mGm c v r mGm r B A B A B A µ (5a) where ) /( B A B A m mmm + = µ , the reduced mass. Equations (2 - 5) will account for the precession of the perihelion of Mercury and will predict the observed value for the deflection of light grazing the Sun. These results were heralded as confirmation of Einstein’s General Theory of Relativity. They also give the accepted value for the Schwarzschild Radius. Equations (2a – 5a) will generate the same results as mentioned above but will also give the accepted value for the Shapiro Time Delay because the speed of light is now affected by gravity. Light is slowed down by gravity which is the opposite of mass particles. The value generated for the Last Stable Orbit is the accepted value. d) Lorentz force We shall look at the standard theory of electromagnetism, but this is only to obtain some guidance as to the possible form of a gravitomagnetic theory. The electromagnetic notation is based on reference [7] for SI units. The force on a charge q 2 in an electromagnetic field is B v E F × + = 2 2 2 2 q q (1.4.1) B is the magnetic field and E is the electrostatic field and v 2 is the velocity of the charge. This equation defines the Lorentz force. The magnetic field, due to a length of conductor d l 1 carrying a current i 1 is e r v a V r a N φ 2 φ A B a T Global Journal of Researches in Engineering (A ) Volume XxXII Issue I Version I 3 Year 2022 © 2022 Global Journals Gravitomagnetics a Simpler Approach Applied to Dynamics within the Solar System