I don't doubt that astronomers have accurately measured the perihelion advance of the planet Mercury. But in order to claim that it is not as would be expected under Newtonian law, we would need to see how this is calculated. And that would have to involve introducing the perturbation effects of the other planets. How is this done with the required degree of accuracy?
Dear Frederick
As far a the Newtonian interaction alone is involved, the first important analytic contributions to perturbation theory are due to Lagrange and Laplace. Then taking more and more terms into account in the development of the perturbing function has been achieved by a series of astronomers, starting with Le Verrier and continuing nowadays with the computer assisted methods. The drawback of the latter is that very often
relativistic effects are included in the mathematical model. I suggest the
book by Morbidelli (Modern Celestial Mechanics) for a first overview of the theory, the fantastic books of Poincaré (Les méthodes nouvelles de le mécanique céleste and Leçons de mécanique céleste) for the beginning of the modern computations on the perturbing functions, and the works by J. Laskar and P. Robutel since the 2000's where the situation is carefully examined.
Hi Jean-Pierre, OK thank you. But the question was "Is Jupiter included in the calculation of Mercury's perihelion advance?" And if the answer is yes, have you ever seen the Newtonian calculation without any GTR involved?
Try this:
http://www.mathpages.com/home/kmath280/kmath280.htm
The table near the end gives the contributions of all the major planets and also includes the asteroid belt.
Collisions, Rings, and Other Newtonian N-Body Problems by Donald G. Saari (Conference Board of the Mathematical Science Regional Conference Series in Mathematics Number 104, American Mathematical Society) addresses Mercury in section 1.2 but does not explicitly mention Jupiter's influence. See also pp. 43-44 and 153 for a force law that approximates relativity to explain the advance of Mercury's perihelion, again without explicit mention of Jupiter.
It's just that if they aren't taking into consideration the irregularities, how can they be so sure that the theoretical prediction is out by 43 seconds of arc per century?