Answer:
The period of orbit of Phobos around Mars can be calculated using Kepler's third law, which relates the period of an object's orbit to its distance from the central body:
T^2 = (4π^2/GM)r^3
Where T is the period of the orbit, G is the gravitational constant, M is the mass of Mars, and r is the distance between the centers of Mars and Phobos.
Plugging in the values given, we get:
T^2 = (4π^2/6.6743 x 10^-11 m^3/kg s^2)(6.42 x 10^23 kg)(9.38 x 10^6 m)^3
T^2 = 27,647,801,632 s^2
Taking the square root of both sides, we get:
T = 1669.7 seconds or approximately 27.83 minutes
Therefore, the period of orbit of Phobos around Mars is approximately 27.83 minutes.