Let m and M be the masses of the planet and the star respectively Let F be the force between the planet and the star F=GmM/a2 Let v be the average vel. of the planet around the sun. F=mv2/a Equating both, v=(GM/a)1/2 T = distance covered in 1 revolution / average speed of plate = 2a/v T=2(GM)-1/2 (a) 3/2 = (GM)-1/2 (a) 3/2 where = 2
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a/v 
(GM)-1/2 (a) 3/2 where 
