His main job at the observatoire was that of performing a series of routine observations and of helping Carlini with the compilation of the ephemerides. There were standard calculation procedures to the compilation of the ephemerides, but in 1804 Carlini started to work on new, more efficient methods. In 1810 he published the Esposizione di un nuovo metodo di costruire le Tavole Astronomiche. When Mossotti worked with Carlini, he did not limit himself to the mere application of Carlini's methods, but he also tried to tackle some theoretical problems of the method. His papers on the subject were published in 1816 and 1817 as appendices to the ephemerides, with the title of Nuova analisi del problema di determinare le orbite dei corpi celesti. The rigorous solution of the problem of determining the motion of a celestial body by means of three observations led to insoluble equations. The approximated solution that was known withstood the efforts of famous geometers, among which Olbers and Gauss, as it produced a polinomial equation of high degree which was impossible to solve algebraically. Mossotti introduced a simplification based on the hypothesis that the three observations be made at such short intervals one from the other, that the segments subtending the partial orbital arcs defined by the times of the observations could be considered proportional to the time lapse between the observations themselves, i.e. he approximated the ellipse of rotation to a circle. He also took into account a fourth observation and repeated the calculations with the second, third and fourth observations. So he obtained two simpler equations defining the constants of the orbital plane.