Two spheres of identical shape and size, Sphere 1 of mass \(m\) and Sphere 2 of mass \(2m\), fall vertically through the atmosphere where each experiences a resistive drag force modeled by \(F_D = bv^2\), with \(b\) being a positive constant. Let \(v_{T,1}\) and \(v_{T,2}\) represent the terminal speeds of Sphere 1 and Sphere 2, respectively. Both spheres are launched vertically downward with the same initial speed \(v_0 = v_{T,1}\). What are the initial acceleration \(a_0\) of Sphere 2 immediately after launch and the ratio \(\dfrac{v_{T,2}}{v_{T,1}}\) of their terminal speeds?