Einstein's Equations vs Precession of Mercury

When Einstein in 1916 presented a new model of gravitation in the form of  Einstein's equations, he desperately needed evidence that his model was better than Newton's. He found this in a back-of-the-envelope computation adding precisely the missing 43 arcseconds in the extra precession of the perihelion of Mercury (slight perturbation of the rotation of the elliptical orbit of Mercury of 5600 arcseconds per century from other planets), to make the prediction by Newton's model of 531 arcseconds/century made by Le Verrier in 1859 to fit exactly with the observed 574 arcseconds/century. 

Einstein thus started from the known results of 531 by Newton and observed 574 and miraculously obtained exactly the missing 43 by a very simple computation which he claimed captured the difference between his and Newton's model.  

If we ask chatGPT about this apparent miracle we get the following information:

1. Le Verrier's 531 has been confirmed to within 1 arcsecond by modern high tech computation and precise data. This is in itself a miracle. No improvement since 1859!
2. It is impossible to directly compute the observed 574 by solving Einstein's equations including in particular the other planets, because the equations are impossible to solve both analytically and computationally. 
3. Computation always start from 531 with Newton's equations and 571 is obtained as a correction of 43 claimed to be based on Einstein's equations, even if they are impossible to solve. This is also a miracle.

To get perspective on these miracles as prime evidence that Einstein's equations are more precise than Newton's, let us note 

• 1 arcsecond/century corresponds to a relative accuracy of about $2\times 10^{-9}$ per revolution of Mercury (415 revolutions/century) if errors add up linearly. 
• Data errors cannot be expected to cancel and so may well add up linearly. 
• A precision of $2\times 10^{-9}$ is thus needed in data such as planet masses, gravitational constant G, initial data, composition of the Sun, tidal motions, other celestial objects than planets, to get the precession right to say 1 arcsecond over 100 year. 
• The gravitational constant is known to at best 6 decimal places, other data with less. 

The conclusion that the desired precision cannot be reached, cannot be avoided. There is factor of 1000 between required and available precision. Yet, the computation of the precession of the perihelion of Mercury by Einstein is still presented as prime evidence that Einstein's equations describe gravitation better than Newton and thus as an undeniable major victory of modern physics over classical physics. 

Check if this is confirmed by chatGPT after careful reading of the literature!

But at his deathbed Einstein begged: "Newton, forgive me!"