Question

The moon revolves around the earth in 2.36 into 10 to the power 6 seconds in a circular orbit of radius 3.85 into 10 to the power 5 kilometre calculate the acceleration of the moon towards the earth​

Answer 1

Answer:

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:

an=v2R=ω2⋅R=(2⋅πT)2⋅R=(2⋅π2360448)2⋅384⋅106=2.72⋅10−3 m/s2