Sur le problème des retours périodiques de la Terre et des autres planètes dans des situations identiques.

The reoccurrence of a particular planetary alignment in the solar system, i.e., the sun-earth-other planet, is considered algebraically, with attention given to a return to an identical position. The planets are assumed to follow circular, concentric, and coplanar orbits. A formulation is developed for obtaining the synodic revolution of the planet into a conjunction, and it is shown that a multiple of the synodic revolution can be defined that quantifies the time before the same positions are repeated. Examples are furnished in terms of earth-sun conjunctions with Mercury and Mars.