The synodic period is the time required for a planet to return to a similar alignment with the Earth. If the length of the Earth's year is 365.24 days, and Venus's year is 224.7 days, the synodic period is
1 1 1
------ = ----- - -----
P 224.7 365.24
so that P = 583.92 days. For Mars and other 'Superior' planets as seen from
Earth, the martian year is 686.9 days long so
1 1 1
------ = ----- - -----
P 365.24 686.9
so P = 779.9 days. This means that mars comes closest to the Earth every
779.9 days. The synodic periods of the other planets from Earth are:
Mercury 115.9 days Venus 583.9 Earth ..... Mars 779.9 Jupiter 398.9 Saturn 378.1 Uranus 369.7 Neptune 367.5 Pluto 366.7