Solve part (b) of Example 6.6 using a_c = v² /r.

Data given in Example 6.6

(a) Find the acceleration due to Earth’s gravity at the distance of the Moon.

(b) Calculate the centripetal acceleration needed to keep the Moon in its orbit (assuming a circular orbit about a fixed Earth), and compare it with the value of the acceleration due to Earth’s gravity that you have just found.

Strategy for (a)

This calculation is the same as the one finding the acceleration due to gravity at Earth’s surface, except that r is the distance from the center of Earth to the center of the Moon. The radius of the Moon’s nearly circular orbit is 3.84 × 10⁸ m.

Strategy for (b)

Centripetal acceleration can be calculated using either form of

where ω is the angular velocity of the Moon about Earth.

We choose to use the second form: ac ac = rw _ro, acro