From: loose@ramsey.cs.laurentian.ca (Stephen Loose)
Subject: Re: General Relativity Tests
Keywords: Advancement in Perihelion, Einstein, Ritz, Tolman
Organization: Dept. of Computer Science, Laurentian University, Sudbury, ON
Date: Thu, 31 Dec 1992 16:57:51 GMT

In <rsf1.725654609@Ra.MsState.Edu> rsf1@Ra.MsState.Edu (Robert S. Fritzius) writes:

>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
> 
> 

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