Deimos completes one (circular) orbit of Mars in 1.26 days. The distance from Mars to Deimos is 2.35×107m. What is the centripetal acceleration of Deimos?

The centripetal acceleration of Deimos is .

Explanation:

The centripetal acceleration is defined as:

  (1)

Where v is the velocity of Deimos and r is the orbital distance.        

Notice that is necessary to determine the velocity first.

The speed of the Deimos can be found by means of the Universal law of gravity:

 (2)

Then, replacing Newton's second law in equation 2 it is gotten:

 (3)

However, a is the centripetal acceleration since Deimos almost describes a circular motion around Mars:

 (4)

Replacing equation 4 in equation 3 it is gotten:

 (5)

Where v is the orbital speed, G is the gravitational constant, M is the mass of Mars, and r is the orbital radius.    

Finally, equation 4 can be used:

Hence, the centripetal acceleration of Deimos is  .

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