In fact it was his work in calculating the orbits of two comets from observations which had been made in 1532 and 1661 that led to his election to the Académie des Sciences . Méchain's memoir on these comets was presented to the Academy for the Grand Prix of 1782 and in it he showed, unexpectedly, that they were not two appearances of the same comet but indeed different comets.
Sa katunayan, ito ay ang kanyang trabaho sa pagkalkula ng orbits ng dalawang comets mula sa obserbasyon na kung saan nagkaroon na ginawa sa 1532 at 1661 na humantong sa kanyang mga halalan sa Académie des Sciences. Méchain's talaarawan sa mga comets ay ipinapahayag sa Academy para sa grand pri ng 1782 at sa mga ito ay nagpakita siya, biglaan, na sila ay hindi dalawang appearances ng parehong kometa ngunit sa katunayan iba't-ibang mga comets.