Question

Upon arrival, the spacecraft is first put into a circular orbit around Mars. The period of the orbit is 119 minutes. Calculate the altitude of the orbit in km.

Answer 1

The period is 119 minutes.
the acceleration of the spacecraft due to gravity is equal to the centripetal acceleration, giving us
Gc*M/r^2 = V^2/r
Gc*M / r^3 = V^2 / r^2
V/r = angular velocity
T = 2pi*r/v =======> V/r = 2 pi /T

Gc*M/r^3 = 4 pi^2/T^2
( Gc*M*T^2 / (4*pi^2) )^(1/3)= r = 3.27 ×10^6 meters from center of the Mars.

3.27 ×10^6 meters - radius of Mars = 3.27 ×10^6 - 3.39*10^6 = 1.2 *10^5 meters altitude

Hope it is correct.