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

Lesser by a factor of 0.63

Time taken by the Earth to complete one revolution around the Sun,

T_e = 1 year
Orbital radius of the Earth in its orbit, R_e = 1 AU

Time taken by the planet to complete one revolution around the Sun, 

Orbital radius of the planet = R_p

From Kepler’s third law of planetary motion, we can write:

Hence, the orbital radius of the planet will be 0.63 times smaller than that of the Earth.