Someone tries to redo the Newtonian budget for Mercury's apsidal precession and…
PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Mechanics & Dynamical Systems · Gravitation and central-force motion
Action and Symmetry, Ch Perturbed orbits, precession and the three-body problem
Problem
Someone tries to redo the Newtonian budget for Mercury's apsidal precession and argues: "Venus's mass is mV/M⊙=2.447×10−6, and r/aV=0.3871/0.7233=0.535 where r is Mercury's orbital radius and aV Venus's. Using the ring formula Δωp=23π(mV/M⊙)(r/aV)3 per orbit and Mercury's 415.2 orbits per century, Venus contributes 151.3 arcseconds per century. Adding Earth's 90.0, Jupiter's 153.6, Saturn's 7.3 and the small remaining terms (2.6) gives a planetary total of 404.8 arcseconds per century. Subtracting from the observed 574 arcseconds per century leaves a residual of about 170 arcseconds per century, so whatever produces the anomalous precession must be about four times the standard 43 arcseconds usually quoted."
((a)) Find the error in this working.
((b)) State the corrected planetary total and residual, using the published full-calculation value of 278 arcseconds per century for Venus's contribution alone (the other planets' figures above are correct).