The moon is in a nearly circular orbit of radius r = 384000000 meters
and has a period of 27.32 days. What is the centripetal acceleration of
the moon toward the earth?

Explanation:

The centripetal acceleration of an object in circular motion is the acceleration with which the object is attracted towards the center of the circular orbit. Mathematically, it is given by

where

v is the speed of the object

r is the radius of the orbit

The speed of the object is also given by the ratio between the circumference of the orbit and the orbital period, T:

Substituting into the previous equation, we find a new expression for the centripetal acceleration:

In this problem:

- The radius of the orbit of the Moon is

- The period of the orbit is

Therefore, the centripetal acceleration is:

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