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Curtis E Renshaw Tele-Consultants, Inc. 4080 McGinnis Ferry Rd., Suite 902, Alpharetta, GA 30005

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. Gravitational Red-Shift. v.

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Curtis E Renshaw Tele-Consultants, Inc. 4080 McGinnis Ferry Rd., Suite 902, Alpharetta, GA 30005

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  1. 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

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

  3. 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

  4. v dh h h c c + v Radial Motion

  5. 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

  6. v v c’ c h c’ c Transverse Motion

  7. 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. Transverse Motion The Generalized Potential

  8. 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

  9. LaGrangian Equations of Motion

  10. The Perihelion Shift of Mercury

  11. Photon Deflection

  12. n d R Irwin Shapiro – 1964 n’ Time Delay of Solar Grazing Photon r

  13. d R Time Delay of Solar Grazing Photon r

  14. d R Time Delay of Solar Grazing Photon r

  15. d R Time Delay of Solar Grazing Photon r

  16. d R 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. Time Delay of Solar Grazing Photon r

  17. 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

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