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A short check on Kepler's 3rd Law: P2 α a3 We have just found out that the orbital period of Mercury is 88 days, and Venus is 225 days. We can use Kepler's 3 rd law to figure out their distances from the Sun. First, we have to recall that the “α” in that equation means “proportional to”. There is a constant in that equation to make the formula actually work: P2 = k a3 We could go find out what “k” actually is, but there is a better way, simply use the ratio of two equations, one where you know “P” and “a”: PP2 = k ap3 --------------------------- PE2 = k aE3 The subscript “E” is for the Earth. We know the orbital period of the Earth (PE = 1 year = 365 day) and we know its distance from the sun (aE = 1 AU), so the equation becomes: PP2/12 = ap3 /13 (the “k” divides out!) For Mercury: (88/365)2 = 0.0581 = a3 so a = (0.0581)1/3 = 0.387AU For Venus: (225/365)2 = 0.380 = a3 , a = 0.72 AU As you can see, these are the actual numbers for the mean distances from the Sun for Mercury and Venus.