Question

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?​

Answer 1

Explanation:

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.