Question

The Moon has a mass of M = 7.3 · 1022 kg, a radius of R = 1.7 · 106 m and a rotation period of
T = 27.3 days. Scientists are planning to place a satellite around the Moon that always remains
above the same position (geostationary).
(a) Calculate the distance from the Moon’s surface to this satellite.
(b) Explain if such a Moon satellite is possible in reality.

Answer 1

Hey Dear,

◆ Answer -

h = 2.98×10^8 m

◆ Explanation -

# Given -

M = 7.3×10^22 kg

R = 1.7×10^6 m

T = 27.3 days = 2.36×10^6 s

# Solution -

(a)

Time period of geostationary satellite is given by -

T^2 = (R+h)^3 / GM

(2.36×10^6)^2 = (R+h)^3 / (6.67×10^-11 × 7.3×10^22)

(R+h)^3 = 5.57×10^12 × 4.87×10^12

(R+h)^3 = 2.712×10^25

R+h = 3×10^8 m

Distance of satellite from surface -

h = 3×10^8 - 1.7×10^6

h = 2.98×10^8 m

Therefore, distance of satellite from moons surface is 2.98×10^8.

(b)

Till date, no such geosynchronous satellite revolves around moon in reality.

Hope this helps..