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? | Learn NCERT solution | Education portal Class 11 Physics | Study online Unit-8 Gravitation



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?

 

Answer:-



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.