Planetary configurations and periods

The sidereal period T is the time a planet takes to go once round the Sun relative to the stars. The synodic period S is the interval between successive repeats of the same configuration (for example opposition or inferior conjunction); it can be observed from the Earth. Because the Earth also moves, they are related: for an inner planet 1/S = 1/T – 1/T_E, for an outer planet 1/S = 1/T_E – 1/T, where T_E = 365.25 days. For example Venus has T ≈ 224.7 days and S ≈ 584 days; Mars has T ≈ 687 days and S ≈ 780 days (about 2 years 2 months); Jupiter’s S ≈ 399 days. Finding T from observed synodic periods was the oldest way of determining planetary periods.