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

Answer:

Explanation:

The rotational period of the moon t1 is equal to rotational period of a satellite t2. So t1 = t2

Now α = 4 π^2 r / t2^2 here r is the distance from moon’s surface to satellite.

According to Newton’s second law of motion we have

          m α = GmM / r^2

Substituting α we get

    m 4 π^2 r / t2^2 = GmM /r^2

  Using t1 = t2 we get

   r = cube root of GMt1^2 / 4 π^2

  r = cube root  9.8 x 7.3 x 10^22 x 27.3^2 / 4 x 3.14^2

 r = 1.9 x 10^7 m

b) here gravitational force of earth is greater than that of moon. Also, mass of earth is 81 times greater than mass of moon. So moon satellite is not possible in reality.