From: rsf1@Ra.MsState.Edu (Robert S. Fritzius)
Subject: Re: General Relativity Tests
Keywords: Advancement in Perihelion, Einstein, Ritz, Tolman
Organization: Mississippi State University
Date: Tue, 29 Dec 1992 18:43:29 GMT

In article <rsf1.725556854@Ra.MsState.Edu> I showed one version of
Einstein's approach for calculating the advancement in perihelion
*per revolution* for a planet:
 
		  24 * pi^3 * a^2
	  +  ------------------------                 (1)
	       T^2 * c^2 * (1 - e^2)
 
where  a = semi-major axis of planetary ellipse
       T = period of revolution
       c = speed of light
       e = eccentricity of planetary ellipse
 
then, by using the first order approximation:
 
	 pi^2 * a^2        v^2
	------------  =  -------- ,                   (2)
	  T^2 * c^2        c^2
 
where v is the average speed of the planet in orbit.
 
I simplifed Einstein's expression (1) to:
 
	    24 * pi         v^2
	  -----------  *  --------                    (3)
	   (1 - e^2)        c^2
 
Then I messed up by making this revised expression equal the 43 seconds
of arc advancement *per century* for Mercury instead of its value
(whatever that is) *per revolution.*
 
Egg on my face.  Sorry!
 
Then I said:
 
>It's my understanding that the  c^2 factor relates to Einstein's view that
>gravitational effects (static and dynamic) travel at the speed of light and
>that 'c' in this case represents *the* gravitational propagation speed.
 
In article  <1992Dec29.004800.22768@sfu.ca> Leigh Palmer, palmer@sfu.ca
writes.
 
>You are putting these words into his mouth.  Why is that your under-
>standing?    [Stuff deleted]
 
A couple of years back I was trying to push some of Walter Ritz's ideas
off on a Physics prof at Case Western (CWRU).  In particular, I was
pressing the point that in (1908) Ritz, in principle, beat Einstein to
the punch by suggesting that the larger part of the advancement of
Mercury's perihelion could be solved using Galilean relativity and
retarded speed-of-light (gravitational) potentials.
 
The prof's response (paraphrased here) was, "Any theory that assigns the
speed of light to the speed of gravity will solve the perihelion
advancement problem."   To me, he was saying that the advancement of
perihelion cannot not be a critical test between Ritz and Einstein because
they both have the same speed for the propagation of gravitational
(supposedly static and/or dynamic) fields.
 
Palmer went on to say:
 
>The formula does, indeed refer to a particle moving in a static
>gravitational field, that of the sun, and employs the approximation
>that the sun is stationary.  Thus the question of the speed with which
>the gravitational field "propagates" never arises.
 
Tom Van Flandern, where are you?
 
Last night I checked Tolman's, Relativity Thermodynamics and Cosmology
on the perihelion advancement issue, pp 205-209, (1934).  He arrives at
an *approximate* expression for the advancement *per revolution* of:
 
		      m^2
	   6 * pi * -------   ,    T(83.19)           (4)
		      h^2
 
(This will be compared to the simplified Einstein equation (3), above.)
 
where:  m = mass of sun  (units defined on Tolman's p. 202)
 
		    d(phi)
	h = r^2  * -------         T(83.11)           (5)
		     d(s)
 
       This is relativistic expression almost equal to the swept out
       equal areas in equal  times thing, and:
 
       r = sun-planet  distance   (as defined appropriately)
 
       d(phi) is the differential in longitude of the planet
 
       d(s)   is an element of proper time as measured with a
	      local clock moving with the planet
 
Tolman sets
 
		d(phi)^2        v^2
	 r^2 * ---------   =   -----    T(p.208)      (6)
		 d(s)^2         c^2
 
		      v^2
so     h^2  =  r^2 * ------   from (5) and (6)        (7)
		      c^2
 
If we plug expression (7) for h^2 back into (4) we get:
 
Longitudinal advancement in perihelion per orbit:
 
		   m^2      c^2
	 6 * pi  * ---  *  -----      Tolman          (8)
		   r^2      v^2
 
	    24 * pi         v^2
	  -----------  *   -----     Einstein         (3)
	   (1 - e^2)        c^2
 
 
Note that Tolman's (v^2/c^2) got inverted, as compared to that in the
simplified Einstein expression (3).  Comments?
 
 
Robert S. Fritzius  rsf1@ra.msstate.edu
 
 

Newsgroups: sci.physics,alt.sci.physics.new-theories