Two satellites A and B are orbiting a planet in circular orbits. The time period of revolution of satellite B is 8 times that of satellite A. If the orbital radius of satellite A is R , what is the orbital radius of satellite B?

Step-by-step solution

According to Kepler's Third Law, the square of the time period is proportional to the cube of the orbital radius, i.e., T^2 r^3 . This can be rearranged to find the radius dependence on the time period: r T^ 2/3 . Taking the ratio for satellites B and A: r_B r_A = ( T_B T_A )^ 2/3 Given T_B = 8 T_A and r_A = R : r_B R = (8)^ 2/3 = (2^3)^ 2/3 = 2^2 = 4 Therefore, r_B = 4R . Answer: 4R