From: tjroberts137@sbcglobal.net   
      
   On 4/5/17 4/5/17 - 2:26 AM, Nicolaas Vroom wrote:   
   > On Thursday, 23 March 2017 05:42:39 UTC+1, Tom Roberts  wrote:   
   >> Simply modifying Newtonian gravity with a finite speed   
   >> is a non-starter. You have to use the post-Newtonian approximation   
   >> to GR, which is much more complicated, but accurate.   
   >   
   > The method I used is imo the same as what you call model 2.   
   > For each object involved I saved its path. (At previous calculated moments)   
   > In case you want to calculate the force caused by object n towards object 1,   
   > instead of using the present position of object n, you use the stored path   
   > to calculate its past position.   
   > This calculation involves the speed of gravity.   
      
   You must include the terms related to object n's velocity and   
   acceleration. These are part of the post-Newtonian approximation to GR,   
   but are not in a simplistic extension of Newtonian gravity. These make   
   the force from object n be very, very close to the Newtonian calculation   
   using its current position [#] and infinite "propagation" speed.   
      
   	[#] in suitable coordinates, such as BCRS.   
      
   > In the solar system if you want to simulate the movement of the planet   
   > mercury, you 'must' use the approach explained above.   
      
   Depends on the accuracy you require; for many purposes Newtonian gravity   
   is sufficiently accurate (and A LOT simpler). If going beyond NG, be   
   sure to use the P-N approximation to GR, not a simplistic extension of   
   NG.   
      
   > Imo you also have to take the movement of the sun into account if   
   > you want to simulate for thousands of years.   
      
   OF COURSE! Because you surely will use the Barycentric celestial   
   reference system (BCRS).   
      
   > Sorry but imo in this approach you can not claim that gravity propagate   
   > instantaneously (or behaves as if it propagates instantaneously)   
      
   Sure. In the post-Newtonian approximation to GR, gravity propagates at   
   c; but due to the extrapolation discussed above, results are   
   APPROXIMATELY the same as Newtonian gravity in which it "propagates"   
   instantaneously.   
      
   > My, maybe biased, opinion is, that in case of n-body problem, using GR   
   > is practical 'impossible' when stars are evolved.   
      
   I'm not sure what you mean. The post-Newtonian approximation to GR   
   applies when gravity and speeds are "small", and that can include many   
   (but not all!) systems of stars. As I said before, it is is extremely   
   challenging to apply GR without approximation to an n-body problem.   
      
   > My first suggestion is why not simulate a system in which no moving   
   > clocks are involved?   
      
   Huh? Planets and stars are not clocks.   
      
   > A whole different issue is how important are the Lorentz transformations   
   > in this context ( n-star problem) ?   
      
   The question does not make sense, as only one coordinate system is used.   
   Lorentz transforms are irrelevant in GR, and in the post-Newtonian   
   approximation to GR.   
      
   Tom Roberts   
      
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