Question

An object at the Moon’s equator travels once around the Moon’s circumference after one full rotation. The radius of the Moon is about 1,700 km, and it takes about 27 days to complete one rotation. How fast is the Moon rotating? Give your answer in miles per hour, and show your work.

Answer 1

The speed of the rotation of the Moon is 10.24 miles per hour.

Given the data in the question;

Radius of the Moon; $r = 1700km = 1056.331 miles\ [ convert kilometer to miles]$Since it takes the object 27 days to complete one rotation;

Time; $t = 27days = 27\ * \ 24hrs = 648hrs$

Now we calculate the the circumference of the moon ( i.e distance )

Circumference of Moon $= 2\pi r$

Where r is the radius

So we substitute in the value of r

Circumference of Moon $= 2\pi ( 1056.331 miles )$

Circumference of Moon $= 6637.1234 miles$

Now, we find the speed ( velocity ) of the moon

We know that; Velocity is distance divided by time

$Velocity = \frac{Distance}{Time} = \frac{Circumference}{Time}$

We substitute in the value of the circumference and time to get our speed

$Velocity = \frac{6637.1234 miles}{648hrs}$

$Velocity = 10.24 mile/hr$

Therefore, the speed of the rotation of the Moon is 10.24 miles per hour

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