How do I figure out how long it takes a planet to orbit?

[go.lag]

Venus passes earth every 583.  Is there a formula that I can use to calculate how many days it takes Venus to orbit the sun?

[curlz]

583 days is the synodic period (S) of Earth and Venus. The formula you need is 1/S = 1/V - 1/E where V is the orbital period of Venus and E is the orbital period of the Earth. Rearrange to get: 1/V = 1/S + 1/E