# Special & General Relativity Questions and Answers

## If gravity travels at the speed of light, why don't the equations used in celestial mechanics include time delays?

The standard equations do not worry about this propagation delay effect of gravity because for most ephimerides calculations they are to small to make a difference on the short term. Most sophisticated, relativistic celestial mechanics calculations take this propagation delay into account and the results are in complete accord with the most accurate observations.

Laplace once estimated that the speed of gravity would have to be over a million times that of light to avoid having to include corrections into the Newtonian calculations to account for a finite propagation delay. Even as late as 1959, this estimate by Laplace has still surfaced in works such as the text book by Russian astronomer Y. Ryabov ( An Elementary Survey of Celestial Mechanics", Dover Publications, 1959) page 142. But as long ago as 1920, Sir Arthur Eddington wrote in "Space, Time and Gravitation: An outline of general relativity", page 94, that "Until comparatively recently, it was thought that conclusive proof had been given that the speed of gravitation must be far higher than that of light". A reference to the Laplacian estimate of 1 million times the speed of light. Eddington, and even Einstein before him in 1916, had shown that Laplace's estimate was fallacious because the effect of the propagation delay will actually be different than what Laplace had surmised.

General relativity assumes that gravity propagates at the speed of light, and when a PROPER accounting of forces, times, and positions is made, the end result are predictions that match reality based on this finite propagation speed for gravity.

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All answers are provided by Dr. Sten Odenwald (Raytheon STX) for the NASA Astronomy Cafe, part of the NASA Education and Public Outreach program.