Question

Question 4 20 pts A probe is orbiting a distant moon. The moon has a mass of M = 5.0 x 1022 kg and a radius of R= 1.5 x 106m. The probe makes one revolution every 6 hours. a) Find the distance the probe is above the surface of the moon. b) At what minimum velocity would would a rocket launched from the surface of the moon be able to reach a distance of 2.2 x 10m from the center of the moon. Neglect any non-gravitational effects.

Answer 1

(a) The probe is revolving around the moon and hence, the gravitational force exerted by the moon on the probe is equal to the centripetal force by the probe as follows: The expression for gravitational force acting on the moon and probe is as follows: GMm F (R+h) The expression for centripetal force is as follows: F my? (R+h) mo(R+h) (R+h) 21 (R+h) I (R+h) m = m ( 21 т (R+h) From above expressions we get, GMn (R+h) -m (397(R=h)

Simplifying we get GM (R+h) 277 т (R+h)= GM 21 (6.67x10-'N-m®/C)(5x10kg) 21 (6)(3600)s = 3.4x10 m h=3.4x10 m-1.5x10m =1.9x10 m

(b) The expression for escape velocity given below: 2GM 7" Substituting we get V= (2) (6.67x10 "N-m*/C*)(5x10% kg) (1.5x10^m+22x106m = 1.3 x10 m/s