Question

Pls do it ASAP

4. We are planning a human exploration mission to Mars. We will first place our spacecraft into a circular around Mars and then send down a lander. a) If we want the spacecraft to orbit at an altitude of 170 km above the Martian surface, what will the velocity and orbital period of the spacecraft? b) When we land astronauts on the surface of Mars, what acceleration due to gravity in terms of g’s (i.e. as a fraction of the Earth’s gravitational acceleration) will the astronauts experience? You are permitted to use an online resource (e.g. Google) to find the necessary information about Mars that you might need in solving this problem.

Answer 1

a)

h = altitude = 170 km = 0.170 x 106 m

R = radius of mars = 3.389 x 106 m

r = orbital radius = R + h = 3.389 x 106 + 0.170 x 106 = 3.559 x 106 m

M = mass of mars = 6.39 x 1023 kg

orbital velocity is given as

v = sqrt(GM/r)

v = sqrt((6.67 x 10-11)(6.39 x 1023)/(3.559 x 106))

v = 3460.6 m/s

Using Kepler's third law

T2 = 4 pi2 r3 /(GM)

T2 = 4 (3.14)2 (3.559 x 106 )3 /((6.67 x 10-11)(6.39 x 1023))

T = 6458.6 sec

b)

acceleration due to gravity is given as

a = GM/R2 = (6.67 x 10-11)(6.39 x 1023) /(3.389 x 106)2

a = 3.71 m/s2