On the first determination of Mercury's perihelion advance

TL;DR

This paper re-evaluates Mercury's perihelion advance using least squares analysis of historical observations, resulting in a value close to Einstein's predictions and refining previous estimates of orbital eccentricity changes.

Contribution

It provides a new calculation of Mercury's perihelion advance and eccentricity correction based on historical data, using the least squares method, improving upon Leverrier's original estimates.

Findings

Perihelion advance: 42.8 arcseconds per century

Eccentricity correction: -0.044 arcseconds per year

Results align closely with general relativity predictions

Abstract

The first determination of the perihelion advance of Mercury's orbit was obtained by Leverrier from the analysis of the transit contacts of the planet on the solar disk. He obtained for the advance the value \delta \pi ' = 38".3/century, considering that the value \delta e', namely the correction of the variation of the planet's orbit eccentricity, is negligible. In this paper \delta \pi ' and \delta e' are calculated by the least squares method, on the basis of the meridian observations used by Leverrier. Thus, we obtain for advance the value \delta \pi ' = 42".8/century, which is close to the one given in the theory of general relativity. The same, we obtained the value \delta e' = -0".044/year, which is lower in absolute value than Leverrier's estimation \delta e' = -0".0806/year.