A satellite is revolving in a circular orbit around a massive planet. If it is transferred to another circular orbit such that its areal velocity about the center of the planet becomes twice its initial value, then its new time period of revolution will be:

Step-by-step solution

The areal velocity of a satellite in a circular orbit is given by: dA dt = L 2m = mvr 2m = vr 2 For a circular orbit, the orbital speed is v = GM r . Substituting v into the areal velocity expression: dA dt = 1 2 GM r r = 1 2 GM r This shows that the areal velocity is proportional to r . If the areal velocity becomes twice its initial value, the new radius r' must be 4 times the initial radius r (since 4r = 2 r ). According to Kepler's third law, the time period T is related to the orbital radius r by: T r^ 3/2 For