TITLE:
Annotated Translations of Three of the Euler’s Papers on Celestial Mechanics
AUTHORS:
Sylvio R. Bistafa
KEYWORDS:
Three-Body Problem, Motion of Celestial Bodies, Astronomical Perturbation, Lunar Motion
JOURNAL NAME:
Advances in Historical Studies,
Vol.8 No.5,
December
26,
2019
ABSTRACT: Annotated translations from Latin of three of the
Euler’s papers on celestial mechanics are presented, which fall into the
category of three-body problems. The first translation deals with an exact
solution of three bodies that move around the common center of mass and always
line up. This is considered the first work from which the three collinear
Lagrange points could be obtained. The second translation deals with motions of
Sun, Earth and Moon in syzygy and Moon
libration as well, where, for the first time, Euler introduces an archaic form
of a Fourier sine series expansion to describe the Moon’s wagging motion. The
last translation relates to a paper that was written with the goal of
alleviating astronomical computations of the perturbed motion of the Moon
around the Earth by the Sun, ending up with eight coupled differential
equations for resolving the perturbed motion of this celestial body. Despite
showing great analytical skills, Euler gave no indications on how this system
of equations could be solved, which renders his efforts practically useless in
the determination of the variations of the nodal line and inclination of the
Moon’s orbit.