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

expected. This equation is applicable to a point mass so for the whole ring we need to integrate for point mass md/2π divided by total mass of the ring m. ∫ �1 + 2 2 � �−1 + 2 � � 2 � Note that the integral of 2 between 0 and 2π equals π. The second term in the square bracket is always positive therefore this term of the acceleration will be radially outwards for all parts of the ring. Integration for all parts of the ring leads to ∙ / 2 = (−1 + 4 ) , where = ⁄ . The value runs from -1, which is the Newtonian, to 0, which means weightless. When the spinning speed is small compared that of light then the chance of a measurable change in gravitational acceleration, or weight, is very unlikely since it depends of the forth power of v/c . If negative gravity ever existed then start with a pool of particles with mixed gravity and electrical charge. Electrical charge is stronger than gravity so the positive electrical charged particles will attract the negative ones and will have zero electrical charge. The particles with gravitational positive charge will repel the negatively charges ones so the groups will separate. IV. D iscussion Equation (4a) is easier to apply than the theory of General Relativity (GR) and therefore leaves less room for misinterpretation. That force is a secondary quantity was strongly advocated by H. R. Hertz who regarded force as “a sleeping partner”. Force is to dynamics as money is to commerce. Once force has been demoted to a defined quantity then force fields and inertia are also defined quantities, similarly for work and energy. Equation (2) is loosely modelled on the Lorentz force but this relationship is for guidance only in the same way that Maxwell used a mechanical model to form his equations. However, he abandoned the reference in his final paper on the subject once he had established that his equations predicted the then known observations. As shown above, when the new approach is applied to two body systems it agrees with the well verified observations of the precession of the perihelion of Mercury, deflection of light passing the Sun and the definition of the Schwarzschild Radius. All agree with the results obtained from the General Theory of Relativity. The third term in equation (4a) was added as it agrees with the measurements of the Shapiro Time Delay and generates a value equal to the accepted value for the Last Stable Orbit. The Gravity Probe B experiment testing the precession of gyroscopes in Earth orbit displays two equations, one for the geodesic term and one for the frame-dragging effect. The geodesic term does not involve the rotation of the Earth but the frame-dragging term does. The same form of equations have been generated algebraically using equation (5). The frame- dragging term is half of the published value, however, the geodesic term is about two thirds of the published value. The de Sitter effect agrees with the accepted results of analysis whether algebraically or by numerical integration for two body systems or large non-rotating bodies. This is true whether using equation (2) or equation (5). However, for the Lense-Thirring terms there is an unresolved factor which affects the periapsis precession. The published nodal precession test on the Earth satellites LAGEOS I & II, see reference [28], appear to agree with the accepted theory. The inclination of the satellites is approximately 90 0 +/- 20 0 . The reason for this is that the accepted Lense-Thirring term does not depend on the inclination but all other effects do and therefore can be cancelled out. See also references [10] and [29]. The gravitational effect on the speed of light is still discussed but apart from the Shapiro Time Delay the effect is negligible when dealing with the motion of bodies. The decrease of the speed of light grazing the Sun is only 4 parts per million. Gravitational Redshift it is sometimes regarded as a proof of GR, however, it can be derived from other fundamental theories. As shown, light passing through a gravitational field refracts in accordance with Snell’s Law. It has proved to be impossible, so far, to find any modification to equation (4) such that it gives the generally accepted value for the Lense-Thirring effect without changing the de Sitter effect applications. The de Sitter results have been obtained by several observations but the Lense-Thirring effect is very small compared to other effects. In the LAGEOS experiments for the precession of the periapsis the Lense-Thirring effect is less than 1% of the de Sitter effect, which makes it more difficult to evaluate. The GP-B test results have recently been published, reference [27]. There are four gyroscopes, two of which have original frame- dragging results which are close to that predicted by the new theory. The geodesic results are, on average, close to those of the accepted value. Nevertheless, over a one month period two of the gyroscopes precess at a rate close to the new theory predictions. It is widely stated that the inward spiralling of a binary star system is due to gravitational radiation. The loss of energy alone is not the cause of this effect. Energy loss can be related to outward spiralling, as is the case for the Earth Moon system. However, radiation pressure could be the cause. When general relativity is applied to multiple body systems several authors have produced slightly different results. Some results even do not return to the © 2022 Global Journals Global Journal of Researches in Engineering (A ) Volume XxXII Issue I Version I 10 Year 2022 Gravitomagnetics a Simpler Approach Applied to Dynamics within the Solar System