Q.3:- Suppose there existed a planet that went around the sun twice as fast as the earth.What would be its orbital size as compared to that of the earth?
Time taken by the Earth to complete one revolution around the Sun,
Te = 1 year
Orbital radius of the Earth in its orbit, Re = 1 AU
Time taken by the planet to complete one revolution around the Sun, TP = ½Te = ½ year
Orbital radius of the planet = Rp
From Kepler’s third law of planetary motion, we can write:
(Rp / Re)3 = (Tp / Te)2
(Rp / Re) = (Tp / Te)2/3
= (½ / 1)2/3 = 0.52/3 = 0.63
Hence, the orbital radius of the planet will be 0.63 times smaller than that of the Earth.