TITLE:
Revisiting Euler’s Orbital Calculations for the Comet of 1742
AUTHORS:
Sylvio R. Bistafa
KEYWORDS:
Euler’s Works on Astronomy, History of Orbital Calculations, Investigations on Comets Orbits, Astronomical Calculations, Astronomical Observations
JOURNAL NAME:
Advances in Historical Studies,
Vol.10 No.1,
March
25,
2021
ABSTRACT: The calculations made by Euler for the orbital
parameters for the Comet of 1742 are revisited. These calculations were
published in Latin in E58—Determinatio orbitae cometae qui mense Martio huius anni 1742 potissimum fuit observatus (Determination of the orbit of the comet which was clearly observed in the
month of March of 1742). The present work begins by giving some background on
comets before addressing the main topic itself, which consists on the calculation of the orbital parameters for the assumed parabolic and elliptical orbit made by Euler for the Comet, making use of three
observations. Because of the extent of the work, characterized by rather
lengthy and repetitive calculations, only the parabolic orbit case is
considered here. More specifically, the work
addresses the calculations for the standard parameters: longitude of the
ascending node, inclination of the orbit, argument of the perihelion, the
perihelion distance, which, together with the time that the comet is at the
perihelion, make five unknowns that fully characterize the parabolic orbit of a
comet.