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"

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.