A satellite moves around the Earth in a circular orbit of radius r. (utilize G for the universal gravitation constant, M for the mass of the Earth, and r, as appropriate, when answering parts (a), (b), and (c) below.)
(a) What is the speed v0 of the satellite? (Use G, M, and r, as necessary.)
(b) Abruptly, an explosion breaks the satellite into two pieces, by masses m and 4m. Immediately after the explosion the smaller piece of mass m is stationary by respect to the Earth and falls directly toward the Earth. What is the speed vi of the larger piece immediately after the explosion? (Use G, M, and r, as needed.)
(c) Because of the increase in its speed, this larger piece of mass4m now moves in a new elliptical orbit. Discover its distance away from the center of the Earth when it reaches the other end of the ellipse. (Use G, M, and r, as necessary.)