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Curtis E RenshawTele-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
h
c
v
Motion induced Blue-Shift
Gravitational Red-Shift
Pound-Rebka Experiment
Resolution
Fundamental Result
Fundamental Result
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
General Doppler Shift Equation
h h
dhv
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
h
c
v
c’
v
cc’
Transverse Motion
Transverse motion has an effect on the measured gravitational red-shift and on the effective gravitational potential for such motion.
Motion induced Doppler Gravitational Red-Shift
The Generalized Gravitational Potential for a Relative Motion
Transverse MotionThe Generalized Potential
GPSDoes 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?
LaGrangian
Equations of Motion
The Perihelion Shift of Mercury
Photon Deflection
Time Delay of Solar Grazing Photon
Irwin Shapiro – 1964
n
’n
d
Rr
Time Delay of Solar Grazing Photon
d
Rr
Time Delay of Solar Grazing Photon
d
Rr
Time Delay of Solar Grazing Photon
d
Rr
Time Delay of Solar Grazing Photon
d
Rr
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.
Conclusion
• 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