A translation of L. Euler's "Simple determination of the orbit of a comet, when it is possible to observe its passage across the ecliptic twice"

TL;DR

This paper presents a translation of Euler's method for determining a comet's parabolic orbit using only two observations of its crossing across the ecliptic, involving solving a quartic polynomial.

Contribution

It provides a clear translation of Euler's classical approach for orbit determination from minimal observational data, emphasizing the solution of a quartic polynomial.

Findings

Method enables orbit calculation from two observations

Uses solution of a quartic polynomial for orbital parameters

Applicable to comets crossing the ecliptic at two points

Abstract

This is the translation from Latin of E547 'Determinatio facilis orbitae cometae, cuius transitum per eclipticam bis observare licuit', in which Euler addresses the determination of a comet's parabolic orbit, with the Sun at the focus, from two astronomical observations from the earth, when the comet crosses the ecliptic at the ascending and descending nodes. The key point of the calculation is the solution of a fourth degree polynomial, from which the determination of the orbital parameters are determined from one of its roots.