Halliday, Resnick & Walker — Gravitation: Problem Problem_83

In a shuttle craft of mass \( m = 3000 \text{ kg} \), Captain Janeway orbits a planet of mass \( M = 9.50 \times 10^{25} \text{ kg} \), in a circular orbit of radius \( r = 4.20 \times 10^7 \text{ m} \). What are (a) the period of the orbit and (b) the speed of the shuttle craft? Janeway briefly fires a forward-pointing thruster, reducing her speed by 2.00%. Just then, what are (c) the speed, (d) the kinetic energy, (e) the gravitational potential energy, and (f) the mechanical energy of the shuttle craft? (g) What is the semimajor axis of the elliptical orbit now taken by the craft? (h) What is the difference between the period of the original circular orbit and that of the new elliptical orbit? (i) Which orbit has the smaller period?