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Last month I asked here whether there's a consensus about Van Flandern's speculations about the speed of gravity. I quickly learned that he's not well-regarded. Fine. I was hoping to be able to get something out of Steve Carlip's explanation for how GR explains the apparent almost instantaneous speed with which planets know about each other's current positions. (In 1805, Laplace estimated that the speed of Newtonian gravity would have to be at least 7 million c for the moon's orbit to be as stable as it is -- Van Flandern estimated at least 20 billion c, based upon more precise experimental findings.)

Carlip's article is at: http://xxx.lanl.gov/PS_cache/gr-qc/pdf/9909/9909087.pdf

But, sad to say, I find the mathematics impenetrable, and wasn't able to get anything out of the prose, either (although his intro was excellent).

Can anyone here give me a "common sense" explanation of these velocity dependent terms that Carlip talks about, and/or the quadrupole nature of gravity? Here's Carlip's abstract:

"The observed absence of gravitational aberration requires that

“Newtonian” gravity propagate at a speed cg > 2 × 1010c. By

evaluating the gravitational effect of an accelerating mass, I show

that aberration in general relativity is almost exactly canceled by

velocity-dependent interactions, permitting cg = c. This cancella-

tion is dictated by conservation laws and the quadrupole nature of

gravitational radiation."

I guess the level of explanation I'm looking for is, "the gravitational field of an accelerating object [somehow] warps spacetime preferentially in its direction of acceleration, such that its future position seems to be telegraphed ahead, and uniformly accelerating objects such as orbiting planets thereby achieve stable orbits..."

(I've read Purcell's E&M textbook's similar treatment of electrical charges with constant velocity telegraphing their future position, but the gravitational case is different.)

Thanks in advance!

Carlip's article is at: http://xxx.lanl.gov/PS_cache/gr-qc/pdf/9909/9909087.pdf

But, sad to say, I find the mathematics impenetrable, and wasn't able to get anything out of the prose, either (although his intro was excellent).

Can anyone here give me a "common sense" explanation of these velocity dependent terms that Carlip talks about, and/or the quadrupole nature of gravity? Here's Carlip's abstract:

"The observed absence of gravitational aberration requires that

“Newtonian” gravity propagate at a speed cg > 2 × 1010c. By

evaluating the gravitational effect of an accelerating mass, I show

that aberration in general relativity is almost exactly canceled by

velocity-dependent interactions, permitting cg = c. This cancella-

tion is dictated by conservation laws and the quadrupole nature of

gravitational radiation."

I guess the level of explanation I'm looking for is, "the gravitational field of an accelerating object [somehow] warps spacetime preferentially in its direction of acceleration, such that its future position seems to be telegraphed ahead, and uniformly accelerating objects such as orbiting planets thereby achieve stable orbits..."

(I've read Purcell's E&M textbook's similar treatment of electrical charges with constant velocity telegraphing their future position, but the gravitational case is different.)

Thanks in advance!

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