From: tjoberts137@sbcglobal.net   
      
   On 5/16/23 2:24 AM, Richard Livingston wrote:   
   > Recently I've been thinking about planetary aberration.  This is the   
   > effect where the finite speed of light causes an orbiting body to see   
   > the opposite body on its past light cone, and thus displaced from its   
   > "now" position directly opposite the center of gravity. The problem   
   > is that if the body it attracted directly towards this displaced   
   > position, there is a torque on the system that would cause it to   
   > speed up.   
   >   
   > This clearly does not happen. [...] My question for this group is why   
   > not?   
      
   In Newtonian mechanics, the gravitational interaction between sun and   
   earth is instantaneous action at a distance, so the force on the earth   
   always points directly to where the sun is now, at each point around the   
   orbit.   
      
   In GR this is different, as there is no instantaneous action at a distance:   
      
   In the full theory, treating the earth as a massless "particle" with   
   negligible effect on the geometry [#], the earth follows a timelike   
   geodesic through spacetime, and that geodesic is completely independent   
   of where the earth is located. No force is involved, the earth just goes   
   as "straight as possible" through the geometry, which is an orbit around   
   the sun [@].   
      
   	[#] This is an excellent approximation, as the earth   
   	mass is just ~ 0.000003 of the sun's mass.   
      
   	[@] Considered in approximately Minkowski coordinates   
   	in which the sun is at rest, this path is an elongated   
   	helix along the time axis, with radius ~ 8 light minutes   
   	and period 1 light year -- just a few parts per million   
   	different from the straight line of the sun.   
      
   In the PPN approximation to GR, one uses a Minkowski metric on spacetime   
   (i.e. flat, with clear simultaneity in the sun's rest frame). One can   
   identify a term in the equation as a force -- this force points not to   
   the current location of the earth, but rather to the 2nd-order   
   extrapolation of where the earth will be when the force (propagated at   
   c) reaches the earth. Remember than an ellipse is a 2nd-order curve, so   
   that extrapolation is extremely good, and the interaction differs by an   
   extremely small amount from the instantaneous interaction of Newtonian   
   mechanics -- the gravitational effects of other planets are enormously   
   larger.   
      
   	[This is reminiscent of classical electrodynamics, in   
   	 which the Lienard-Wiechert potentials perform a   
   	 similar extrapolation to first order.]   
      
   Tom Roberts   
      
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