Revisiting Euler’s Orbital Calculations for the Comet of 1742

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.