Extra Credit. A rocket ship is initially going in a circular orbit close to Earth. It's desired to put the ship on a new orbit such that it's apogee (furthest) distance is equal to the radius of the moon's orbit about the Earth. (a) If a single thrust from the rocket engines is used to do this, determine the ratio of the nal to initial speeds. Assume the radius of the initial orbit is 1/60 that of the distance to the moon. (Near earth orbit is negligibly larger than earth's radius compared to the moon's distance from the center of the earth which is 60 times earth's radius.) (Hint: make use the of the formulas you derived in the homework problem 68(a) from the text. With a little algebra, you can derive a formula for the ratio of the velocities in terms of the T1 and r2. Note, for this problem r1 /r2 = 1/60.) (b) Find the new orbit if the speed ratio is 1% too great. To do this solve the equation you I derived in part (a) for the ratio 171/ 121 in terms of r1 /r2. This problem illustrates the extreme accuracy needed to achieve a circumlunar orbit