Q. 105 - Precalculus Enhanced with Graphing Utilities

Question

The mean distance of the moon from Earth is $2.39 \times {10}^5$ miles. Assuming that the orbit of the moon around Earth is circular and that 1 revolution takes 27.3 days, find the linear speed of the moon. Express your answer in miles per hour. 

Step-by-Step Solution

Answer

The linear speed of the moon is 2290.781 miles per hour.

Step 1: Given information.

Let us consider that, the earth is the center and the moon is revolving around the earth in a circular shape.

So that, radius of the circular path $\left(r\right)=2.39\times {10}^5 \mathrm{miles}$.

And  1 revolution takes 27.3 days.

Step 2: Calculate the linear speed.

We have to find how many miles the moon needs to go to make a whole circle, that means the perimeter of the circle.

$\mathrm{Circumference}=2\mathrm{\pi r}=2\times 3.14\times 2.39\times {10}^5=1500920 \mathrm{miles}$ 

Thus, the moon travels 1500920 miles, and given that makes a revolution in 27.3 days.

Since $\mathrm{Linear} \mathrm{speed}=\frac{\mathrm{Distance}}{\mathrm{time}}$

$27.3 \mathrm{days} =27.3\times 24= 655.2 \mathrm{hours}$ 

Therefore, the linear speed is computed as,

$$\begin{gathered} \mathrm{Linear} \mathrm{speed}=\frac{1500920}{655.2} \\ \mathrm{Linear} \mathrm{speed}=2290.781 \mathrm{miles} \mathrm{per} \mathrm{hour} \end{gathered}$$