The distance between the moon and the earth is 384,403 km and the masses of the

Question

The distance between the moon and the earth is 384,403 km and the masses of the moon and the earth are

Msub moon = 7.35 x 10^22 kg and Msub earth = 5.97 x 10^24 kg, respectively.

a. The orbital period of the moon is about 27.32 days. Calculate the average orbital speed in m/s of the moon.

b. Calculate the centripetal acceleration of the rotation of the moon, both the magnitude and direction.

c. Calculate the centripetal force, needed to keep moon in the ratational motion around earth.

d. Calculate the gravitational force between the moon and the earth by using Newtons univeral gravitation and compare it with the centripetal force estimated in (C)

Explanation / Answer

a) Speed = distance / time = 2*pi*384403000/(27.32*86400)

= 1023.23 m/s

(b) v^2 /r = 2.72*10^-3 m/s^2, towards the earth

(c) F = m*a = 7.35*10^22 * 2.72*10^-3 = 2*10^20 N

(d) Fg = GMm/R^2

= 1.98*10^20 N

Almost equal to centripetal force

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