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 McGinnis Ferry Rd., Suite 902, Alpharetta, GA 30005

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

3. 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

4. v dh h h
c + v c
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. 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

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

13. Time Delay of Solar Grazing Photon

14. Time Delay of Solar Grazing Photon

15. Time Delay of Solar Grazing Photon

16. 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

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