An answer provided by Dr. Sten Odenwald (Raytheon STX) for the NASA Astronomy Cafe, part of the NASA Education and Public Outreach program to the above says ``Special relativity does not enter into the calculation and contributes nothing." (see the link)
But the answer to the same question is quite different as seen in another interpretation of the general relativistic interpretation of the perihelion advance of Mercury as given in a foot-note on page 113 of Thornton-Marion's book (Classical Dynamics of Particles and Systems, 5th edition):
``One half of the relativistic term results from eects understandable in terms of special relativity, viz., time dilation (1/3) and the relativistic momentum effect (1/6); the velocity is greatest at the perihelion and least at aphelion (see Chapter 14). The other half of the term arises from general relativisticeffects and is associated with the nite propagation time of gravitational interactions. Thus, the agreement between theory and experiment confirms the prediction that the gravitational propagation velocity is the same as that for light."
How come, gravitational gravitational propagation velocity in Schwarzschild metric (a static solution of GR, which has the same action-at-a-distance problem as in Newton's law) that one uses to calculate the observed effect?
If we leave aside this finite propagation effect, which other effect nullify the known relativistic contribution to the effect? Does GR nullify the Newtonian contribution to the total precession? I think, any explanation that disregards the special relativistic contribution to the observed effect is faulty.
What the experts think of it?
https://einstein.stanford.edu/content/relativity/q1173.html
Dear Harihar,
Excellent question!
526"/century are explained by the Newtonian gravity of other planets. Only 43"/century of the observed perihelion advance remained unexplained.
This anomaly is perfectly well described/explained by the gravitational induction that the speed of the Sun provides upon the other planets.
Indeed, the Sun moves in the Milky Way with about 350 km/sec, and this gives a gravitational induction, as experimentally proven by the Gravity Probe B experiment. This experiment had gyroscopes in satellites and their axis orientation was altered by the gravitational induction of the spinning Earth.
So, GRT nor special relativity play any role.
Annexed, you find the calculus of Mercury's perihelion advance.
https://en.wikipedia.org/wiki/Gravity_Probe_B
Zero. Global boosts don't introduce pseudoforces, that would imply that a boosted observer would measure non-periodic motion. Once more, one shouldn't mix up invariant with non-invariant quantities.
And there's no such notion as action at a distance in general relativity.
GR doesn't cancel the Newtonian contribution to the precession-since, in Newtonian gravity, the precession is, also, zero, in the 2-body problem-the orbit is closed.
The precession, the fact that the orbit isn't closed, is due to spacetime curvature, that describes the additional forces that imply that the motion isn't periodic.
This is elementary mechanics: the motion in the 1/r potential is periodic-that's another way of expressing the fact that the orbit is closed. In GR the potential isn't 1/r but such that the orbit isn't periodic.
(It's possible to distinguish the forces produced by a non-trivial metric from those produced by a vector field. If ``induction'' effects were present, they would be a strong hint for supergravity. http://inspirehep.net/record/142417 where vector fields appear inevitably. So it is possible to exclude them.)
Dear Harihar,
From the point of view of the special relativity theory, I found a very interesting calculus performed by Oleg Jefimenko, in his book "Gravitation and Cogravitation", which you can find in online bookstores.
In his chapter 20, section 2, he finds the relativistic acceleration of a body according to special relativity.
Then he equals that acceleration to the gravitational force between Mercury and the Sun, while accounting for the relativistic effect by Mercury's speed.
This is the same method as when, in Newtonian physics, one equals the kinetic energy with the gravitational energy.
This equation can be linearized by approaching sqrt(1-v2/c2) by (1-v2/2c2) and the equation splits in a Newtonian term and a relativistic term, which is velocity-dependent and dependent from the angle of the velocity (due to the elliptic path).
The relativistic term is responsible for the perihelihon advance according to Special relativity only.
When the relativistic term is integrated over a whole elliptic orbit, the additional perihelion advance is found.
The result is 14 arc sec per century.
This proves that relativity is plain wrong, since special relativity gives the wrong result and since the superposition of special relativity and general relativity gives the wrong result as well.
Dear Dr. Thierry De Mees,
My main point in the question is that any explanation of "anomalus precession" should take into account the special relativistic contribution unless until one finds some other negative contribution exactly cancelling the special relativistic contribution if any-and it does have.
That is the limited point I wish to draw you attention.
Thanks and regards,
Hari
Dear Hari,
Presicely, the observed, unexplained or anomalous precession is 14 arcsec/cy by special relativity and 43 arcsec/cy by general relativity.
Isn't that amazing? How should this be interpreted according to you?
The claims in Thornton-Marion's book are just a footnote, without any calculus nor proof?
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