TITLE:
Euler’s Forgotten Equation of the Center
AUTHORS:
Sylvio R. Bistafa
KEYWORDS:
Euler’s Works on Astronomy, Equation of the Center, History of Orbital Calculations, Investigations on Planets’ Orbits, Astronomical Calculations, Keplerian Orbital Mechanics
JOURNAL NAME:
Advances in Historical Studies,
Vol.10 No.1,
March
15,
2021
ABSTRACT: In a 1778 publication in Latin, titled Nova Methodvs Motvm Planetarvm Determinandi (New method to determine the motion of planets), Euler derives an equation of
the center, which, apparently, has been forgotten. In the present work, the
developments that led to Euler’s equation of the center are revisited, and
applied to three planets of the Solar System. These are then compared with
results obtained from an equation of center that has been proposed, showing
good agreement for planets with not so high eccentricities. Nonetheless,
Euler’s derivation was not influential, and since then, the resulting equation
of the center has been neglected by scholars and by specialized publications
alike.