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.

Thu Feb 26 22:27:51 CET 1998