Numerical Calculation of the Angle of Displacement of Star Images during Solar Eclipses

A finite differences procedure is presented for calculating the angle of displacement of star images during solar eclipses. It is based on Schiff’s paper in 1960 in which he obtained results using a purely analytical method. A key feature of both methods is the assumption that light follows a strictly straight-line trajectory on its way between a given star and the Earth’s surface, in contradiction to the claim of Einstein’s General Relativity Theory (GRT) that it follows a curved trajectory instead. The calculations described herein make use of a quantity S (r) = (1 + Gm0/c2r)-1 (G is the Universal Gravitation Constant, m0 is the Sun’s mass, c is the speed of light in free space and r is the distance separating the current position of the light from the Sun’s center of mass). The speed of light varies in direct proportion to S (r). The result is that of two light rays moving parallel to the Sun, the one that is farther away moves at a higher average speed and travels further during the same time period. The ratio of the increased distance of travel ΔX to the corresponding distance ΔY separating the two light rays is the displacement angle Θ of the star images from their normal position. The finite differences result for Θ is shown to be in quantitative agreement with Schiff’s analytical value, which in turns agrees very well with the result inferred from the GRT closed formula for Θ. The main point of Schiff’s paper was to show that his method is much easier to apply than GRT, and this assertion is verified by the present finite differences approach. It is also noted that the angle of precession of Mercury’s perihelion, another of Einstein’s great successes, is also predicted to be in quantitative agreement with the GRT value by extending Schiff’s scaling procedure to the acceleration due to gravity g.