## Statement

difficulty

Determine the centripetal acceleration of the Moon knowing that a complete orbit around the Earth takes 27.32 days (sidereal period) and the average distance is 384000 km.

## Solution

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:

## Formulas worksheet

These are the main formulas that you must know to solve this exercise. If you are not clear about their meaning, we recommend you to check the theory in the corresponding sections. Furthermore, you will find in them, under the Formulas tab, the codes that will allow you to integrate these equations in external programs like Word or Mathematica.

Formulas
Related sections
${a}_{n}=\frac{{v}^{2}}{R}={\omega }^{2}·R$