The Gravitational Potential for a Moving Observer, Mercury’s Perihelion, Photon Deflection and Time Delay of a Solar Grazing Photon Curtis E Renshaw Tele-Consultants, Inc. 4080 McGinnis Ferry Rd., Suite 902, Alpharetta, GA 30005 crenshaw@teleinc.com

Pound-Rebka Experiment Gravitational Red-Shift v Motion induced Blue-Shift Resolution h Fundamental Result c Pound-Rebka Experiment

General Doppler Shift Equation c’ – takes into account relative motion with respect to source h’ – takes into account effective changes in h with time g’ – takes into account motion induced effects on gravitational potential Fundamental Result General Doppler Shift Equation

v dh h h c + v c Radial Motion

Motion induced Doppler Gravitational Red-Shift Radial motion (along gravitational line) has no effect on the measured gravitational red-shift or on the effective gravitational potential for such motion. Radial Motion

v v c’ c h c’ c Transverse Motion

The Generalized Gravitational Potential for a Relative Motion Motion induced Doppler Gravitational Red-Shift The Generalized Gravitational Potential for a Relative Motion Transverse motion has an effect on the measured gravitational red-shift and on the effective gravitational potential for such motion. The Generalized Potential Transverse Motion

Does the Principle of Equivalence imply that a free-fall observer should see the same gravitational red-shift at a particular point in space as a stationary observer? GPS

LaGrangian Equations of Motion

The Perihelion Shift of Mercury

Photon Deflection

Time Delay of Solar Grazing Photon Irwin Shapiro – 1964 n’ Time Delay of Solar Grazing Photon

Time Delay of Solar Grazing Photon

Time Delay of Solar Grazing Photon

Time Delay of Solar Grazing Photon

Time Delay of Solar Grazing Photon For distances on the order of Earth-Mars, Dd is approximately 19 km, resulting in a time delay of about 250ms, which is what Shapiro observed. d R r Time Delay of Solar Grazing Photon

Using only Newtonian Mechanics and the Principle of Equivalence, a Dynamic Gravitational Potential was developed to account for relative motion between bodies. This modified Newtonian potential has been demonstrated to fully account for three “tests” of general relativity: Mercury’s perihelion shift of 43” per century, The deflection of a solar grazing photon The time delay of a solar grazing photon Conclusion