Centripetal acceleration of the Moon

Data

• Period T = 27.32 days =  27.32 · 24 hours/day · 60 minutes/hour · 60 seconds/minute = 2360448 s
• Radius R = 384000 km = 3.84·10⁸ m 

Preliminary considerations

Normal or centripetal acceleration is responsible for the change of direction of the velocity vector. It is the only type of acceleration in uniform circular motion.

Resolution

Applying the expression of normal or centripetal acceleration, we get the value we are looking for:

$$a_n=\frac{v^2}{R}={\omega }^2·R={\left(\frac{2·\mathrm{\pi }}{T}\right)}^2·R={\left(\frac{2·\mathrm{\pi }}{2360448}\right)}^2·{\mathrm{384·10}}^6=\boxed{2.72·{10}^{-3} m/s^2}$$