Gravitation NCERT Solutions Class 11 Physics - Solved Exercise Question 8.3

Question 8.3:

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?

Solution:

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, T_P = ½T_e = ½ year
Orbital radius of the planet = R_p
From Kepler’s third law of planetary motion, we can write:
(R_p / R_e)³ = (T_p / T_e)²
(R_p / R_e) = (T_p / T_e)^2/3
= (½ / 1)^2/3  =  0.5^2/3  =  0.63
Hence, the orbital radius of the planet will be 0.63 times smaller than that of the Earth.