Assume that the earth moves around the sun in a circular orbit of radius R and there exists a planet which also move around the sun in a circular orbit with an angular speed twice as large as that of the earth. The radius of the orbit of the planet is

Step-by-step solution

According to the Kepler's third law T² r³ where, T= time period of revolution r= radius Now, ( T_ E T_ P )²= ( r_ E r_ P )³= r_ E r_ P = ( T_ E T_ P )^ 2 / 3 r_ E r_ P = ( 2 / _ E 2 / _ P )^ 2 / 3 [ T= 2 ] r_ E r_ P = ( _ P _ E )^ 2 / 3 According to the question, _ P =2 _ E and r_ E =R R r_ P = ( 2 _ E _ E )^ 2 / 3 array l R r_ P =(2)^ 2 / 3 r_ P = R (2)^ 2 / 3 =R(2)^ -2 / 3 array