Q. 106 - Precalculus Enhanced with Graphing Utilities

Question

The mean distance of Earth from the Sun is $9.29 \times {10}^7$ miles. Assuming that the orbit of Earth around the Sun is circular and that 1 revolution takes 365 days, find the linear speed of Earth. Express your answer in miles per hour .

Step-by-Step Solution

Answer

The linear speed of the earth is 66,599.54 miles per hour.

Step 1: Given

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

So, the radius of the circular path $\left(r\right)=9.29 \times {10}^7 \mathrm{miles}$and  1 revolution takes 365 days.

Step 2: Calculate the linear speed.

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

$\mathrm{Circumference}=2\mathrm{\pi r}=2\times 3.14\times 9.29\times {10}^7=583,412,000 \mathrm{miles}$

Thus, the moon travels 583,412,000 miles, and given that makes a revolution in 365 days.

Since

$365 \mathrm{days}= 365\times 24=8760 \mathrm{hours}$ 

Therefore, the linear speed is computed as,

          $$\begin{gathered} \mathrm{Linear} \mathrm{speed}=\frac{583412000}{8760} \\ \mathrm{Linear} \mathrm{speed}=66,599.54 \mathrm{miles} \mathrm{per} \mathrm{hour} \end{gathered}$$