A satellite orbits Planet A in a circular path of radius \(r_A\) with an orbital period \(T_A\). A second satellite orbits Planet B in a circular path of radius \(r_B = 4r_A\) with an orbital period \(T_B = 2T_A\). The physical radius of Planet B is twice the physical radius of Planet A (\(R_B = 2R_A\)). What is the ratio of the gravitational field strength at the surface of Planet B to the gravitational field strength at the surface of Planet A, \(\dfrac{g_B}{g_A}\)?