First my statement that Newton was accurate to 1 part in 107 came from Penrose's, The Road to Reality, pg. 390. And second your estimation of accuracy is not very accurate, it would be more accurate (I am fudging a little) if you took into account all the revolutions that Mercury makes in 100 years (apx. 415) and used that to provide a percentage (43/1,494,000= .0000287), not 1 part in 107 but closer.
The problem with that particular example is that because of the mass and proximity of the Sun to Mercury relativistic forces are in play and it was one of the examples that Einstein used to support the Theory of Relativity : )
An interesting web site on the differences and problems with the two theories is, http://www.coolissues.com/gravitation/gmetric.htm
No, it's very nearly right although I guess I should have expressed it as a fraction of the observed value of 5600 seconds of arc per century.
And anyway, you can tell yours is wrong because the value you compute is not dimensionless.
OK, I see kind of what you mean although I think you miscalculated the number of arc seconds in 100 years worth of revolutions. I'll have to think about whether your description is more appropriate for the application at hand.
It seems to me that my expression of the error in this case is better. The calculation is of the rate of precession of the perihelion and it is the observed rate of it that should be the basis for the calculation.
The precession rate is not directly connected to the orbit per se and is, I think, calculated not by dynamically simulating the orbit of Mercury for 100 years from one perihelion to another 415 revolutions later and noting that the position has advanced 5557 arc seconds, but rather by adding together a set of effects and directly obtain an amount of extra turning.
Oh yes, and on that coolissues site. I am not physicist enough to evaluate that page and dispute it point by point but I am very suspicious. For example, he speaks of and stresses certain "ad hoc" equivalences and of course that's not a good description of the way it works in real life. Such things are guided by the very good physical intuition of these scientists and then checked by evaluating the consequences. For another, he speaks favorably of "speed of gravity" skeptics but their claims have been thoroughly debunked. Yet another is I checked out his Precession of Perihelia page. He says in one place
In the 19th century, the French astronomer Le Verrier found that the perihelion of Mercury advanced by 43 arc- seconds/100yand later says
574.1 arcsec/100y, the observed precession of Mercurywhich are not only contradictory but both are wrong and the first mistakes the Newtonian error in the precession for the actual precession.
I think the guy's a crackpot. Like that theorist who's joined the Baghwan and writes his Unified Field papers.