Many of the ideas at the heart of our current understanding of the motion of NEOs date back to the XVIIIth and XIXth century, and are based on the study of the orbit of a single, exceptional body, the comet discovered on the night between 14 and 15 June 1770 by Messier, one of the most famous comet hunters of all times (click here to know more about comets). The comet was heading right towards the Earth; within a few days, starting from 21 June, it became visible to the naked eye, reaching the second magnitude three days later. The minimum distance from the Earth was reached on 1 July, at about six times the lunar distance, and in a few more days the comet became not visible due to its proximity to the Sun; Pingré computed an ephemeris for its recovery based on a parabolic orbit, as it was then customary, and Messier was able to see the comet again starting from the beginning of August.

Charles Messier

The comet was then observed until the first days of October. A serious problem soon became clear to astronomers: although the ephemeris by Pingre' had allowed the recovery of the comet in August, it was clearly incapable of accounting for the entire set of observations. Prosperin tried to use three parabolas to fit separately the observations of June, August, and September, but this was evidently unsatisfactory, and unjustifiable from the point of view of celestial mechanics.
It was Lexell who gave the right answer: he showed that the comet was on an elliptical orbit with a period of five and a half years, far shorter than the 76 years of the only other case then known, that of comet Halley; his solution accounted very well for the entire set of observations. But Messier then asked why the comet had not been observed before, given its short orbital period and its small perihelion distance; the answer by Lexell was that in May 1767 the comet and Jupiter had been very close to each other, and the action of the gravity of the giant planet had greatly transformed the orbit of the comet. In fact, before 1767 the comet had a much larger perihelion distance, which meant that it could not become very bright, thus explaining the fact that it had not been observed before.
Lexell did not content himself with these findings; he went on to say that the orbit of the comet in 1770, after the 1767 encounter, was nearly resonant with that of Jupiter, since in the time it took the comet to make two revolutions about the Sun the giant planet would make one revolution. As a consequence, in 1779 the comet would encounter Jupiter again, at an even closer distance than in 1767, and would be expelled from the inner solar system into an orbit of large perihelion distance and period, that would make it invisible again for the telescopes then available The comet, in fact, was not observed again in 1782, as it should have been if it had remained in its 1770 orbit. Lexell reconstruction of what had happened in 1767, as well as his prediction of what would happen in 1779, became generally accepted and the comet, although discovered by Messier, now brings Lexell's name. The studies of the dynamics of small solar system bodies had entered the modern era.
But this is not the end of the story: in less than a century from then, Le Verrier would have completed the picture by exploring what could have happened if ... (the history of Lexell comet will be continued in the next number).

Anders Lexell (sometimes known by the Russian version of his name, Andrei Ivanovich Lexell) was born on 24, December 1740 in Sweden and died on 11 December 1784. He studied and graduated in Sweden, where he first became appointed professor of mathematics. He was then invited to the St Petersburg Academy of Science, where he started working from 1769 with Euler and other high quality scientists, becoming appointed professor of astronomy in 1771.
Lexell stayed in St. Petersburg until his death, working mainly in the area of analysis and geometry (working with Euler, Lexell made a detailed investigation of exact equations of differential equations).
In astronomy, Lexell is famous for having calculated the orbits of several comets, including the comet of 1770, that was named after him. Lexell is also famous for having recognized planet Uranus (that was named Uranus only afterwards): in fact, when William Herschel discovered a new body on 13 March 1781, he computed its orbit showing that, rather than a comet as had been thought at first, this object had to be a planet twice as far from the sun as Saturn. Although he did not predict the position of Neptune (as did Adams and Le Verrier) Lexell's initial calculations of the orbit of Uranus showed that it was being perturbed and he deduced that these perturbations were due to another more distant planet.

The name comet comes from the greek word kometes, meaning "head of hair". Comets have been known for thousand of years. Some of them appeared so bright, that they could be seen during the day. Others had beautiful tails that could stretch halfway across the sky. In the antiquity, comets were seen as bad signs that seemed to announce future disasters. In particular, Halley’s comet has been associated with the destruction of Jerusalem and the Norman Invasion of England in 1066.

But exactly, what is a comet? Nowadays, comets are seen as dirty snowballs (or icy mudballs). In fact, comets are thought to be made of a mixture of ices and dust that wasn't incorporated into the planets when the solar system was formed. This is the main reason why they are believed to share the same composition of the primordial solar system, having formed essentially form the same material. Click here to know more about comets' composition