Question

In a shuttle craft of mass m = 3100 kg, Captain Janeway orbits a planet of mass M = 8.50 ✕ 10²⁵ kg, in a circular orbit of radius r = 4.70 ✕ 10⁷ m.

(a) What is the period of the orbit?
26887 s

(b) What is the speed of the shuttle craft?
10983 m/s

Janeway briefly fires a forward-pointing thruster, reducing her speed by 1.70%.

(c) Just then, what is the speed of the shuttle craft?
10763 m/s

(d) What is the kinetic energy of the shuttle craft at that moment?
1.795e11 J

(e) What is the gravitational potential energy of the shuttle craft at that moment?
-3.7e11 J

(f) What is the mechanical energy of the shuttle craft at that moment?
-1.943e11 J

(g) What is the semimajor axis of the elliptical orbit now taken by the craft?
45209695 m

(h) What is the difference between the period of the original circular orbit and that of the new elliptical orbit (T_new − T_old)? Note which orbit has the smaller period.
-1521 s

All my answers are correct except h and I'm not sure why.

Answer 1