It was not long after Nicole-Reine married that Jérôme Lalande, who was at that time a law student, became fascinated by astronomy and was given a room above the porch of the Palais du Luxembourg to use as an observatory. Lalande quickly became a friend of Nicole-Reine and Jean-Andre Lepaute. He was sent to the Cape of Good Hope to make astronomical observations and, returning to Paris in 1753 after a very successful trip, he was elected to the Academy of Sciences. Jean-Andre Lepaute had designed a clock with a new type of escapement and Lalande was asked by the Academy to evaluate it for astronomical use. This prompted Jean-Andre Lepaute to become interested in building astronomical clocks and he published Traité d'Horlogerie contenant tout ce qui est nécessaire pour bien connoître et pour régler les pendules et les montres Ⓣ in Paris in 1755. This work contains the first mathematical work by Nicole-Reine Lepaute who calculated the tables of oscillations of a pendulum which were contained in her husband's work.
In June 1757 Lalande decided that he would like to attempt to calculate a precise date for the return of Halley's comet. It was known to have been seen in 1305, 1380, 1456, 1531, 1607 and 1682 and Halley, taking into account perturbations to the orbit caused by the gravitational effects of Jupiter, had predicted that the comet would return reaching perihelion in December 1758. However the only way to get a more accurate prediction of its date of return was to calculate the perturbations to the orbit caused by the gravitational effects of both Jupiter and Saturn. Lalande approached Alexis Clairaut for help and Clairaut provided a basic programme of work requiring an extraordinary amount of computation. Lalande then asked Nicole-Reine Lepaute to assist him in the computations. Lalande wrote in Bibliographie Astronomique (1803) (see for example ):-
During six months we calculated from morning to night, sometimes even at meals. ... The assistance of Mme Lepaute was such that, without her I should never have been able to undertake the enormous labour, in which it was necessary to calculate the distance of each of the two planets Jupiter and Saturn from the comet, separately for each successive degree for 150 years.On 14 November 1758 Clairaut reported to the Academy of Sciences that they predicted the comet would reach perihelion by mid-April 1759. In fact the team had completed the calculations just in time for, on 25 December 1758, the comet was sighted. It actually reached perihelion on 13 April 1759, within the margin of error given for the prediction. Clairaut published Théorie des comètes Ⓣ (Paris, 1760) describing how the calculations had been carried out. He listed those who had assisted in the computations but did not put Nicole-Reine Lepaute's name on the list. It has been claimed that this deliberate omission was to please his girlfriend Mademoiselle Goulier who was jealous of Lepaute. Whatever the reason, the omission caused a rift between Lalande and Clairaut, and the two men never again collaborated on an astronomical project. Lalande gave Nicole-Reine Lepaute the credit she deserved in his own publication; see the quote above.
In 1759 Lalande was asked if he would take over the editorship of the astronomical almanac Connaissance des temps. He was editor from 1760 until 1776, and Nicole-Reine Lepaute assisted him in computing the tables in this annual publication of the Academy of Sciences. Although her contributions are thought to have been substantial, we do not have any precise details of which part of the work she undertook. There are, however, many areas where we do know of her contributions. The Ephémérides des mouvements célestes Ⓣ gave tables of the sun, the moon and planets covering a period of ten years. Lepaute was the main person responsible for producing Volume VII, covering the period 1775-1784, and Volume VIII, covering the period 1783-1792. Alic writes :-
For this last volume she alone made all the computations for the positions of the sun, moon and planets.Alic also claims in  that Lepaute published a memoir containing observations of the transit of Venus across disk of the sun in 1761. This may have been one of the memoirs which Lalande says that she wrote for the l'Académie de Béziers but these have not been found. Since she was elected a member of l'Académie de Béziers around this time it is likely that this information is correct. The letter confirming her election the this Academy was published in . Other specific tasks carried out by Lepaute that are specified by Lalande include calculations for elements of the comet observed in 1762.
Another piece of work which is certainly due to Lepaute is the calculation concerning the annular eclipse of the sun on 1 April 1764. She produced a chart giving the path of the eclipse across Europe which was published in the Jesuit journal the Mémoires de Trévoux in June 1762. Alic writes :-
Her calculations required that she prepare a table of parallactic angles (the angle of displacement of an object caused by a change in the observer's position), her extended version of which was published by the French government.Thousands of copies of Lepaute's chart were distributed in Paris.
Finally we mention that a crater on the moon has been named in honour of Lepaute.
Article by: J J O'Connor and E F Robertson