The moon's mass is 7.35 × 1022 kg, and it moves around the earth approximately in a circle or radius 3.82 × 105 km. the time required for one revolution is 27.3 days. calculate the centripetal force that must act on the moon. how does this compare to the gravitational force that the earth exerts on the moon at that same distance?

Explanation:

It is given that,

Mass of moon,

Radius of circle,

The time required for one revolution is 27.3 days, t = 27.3 days

1 day = 86400 seconds

27.3 days = 2358720 seconds

Let v is the speed of moon around the circular path. It is given by :

v = 1017.57 m/s

Let F is the centripetal force acting on the moon. It is given by :

So, the centripetal force that must act on the moon is . The gravitational force that the earth exerts on the moon at that same distance is also equal to . Hence, this is the required solution.

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