Chapter 1.1, Problem 27PPS

(a)

To determine

To find: the circumference of Earth’s orbit assuming that the orbit is a circle.

Answer to Problem 27PPS

The circumference of the Earth’s orbit is 584336233.6 miles.

Explanation of Solution

Given information:

The radius of Earth’s orbit is 93000000 miles.

Formula Used:

The formula for the circumference of a circle is $2\pi r$ .

Calculation:

Consider the given formula

  $C=2\pi r$

Now, substitute the radius of Earth’s orbit in the given formula,

  $\begin{array}{c}C=2\pi r\\ C=\left(2\right)\left(\pi \right)\left(93000000\right)\\ =584336233.6\end{array}$

Hence, the circumference of the Earth’s orbit is 584336233.6 miles.

(b)

To determine

To find: the number of hours it takes Earth to revolve around the sun.

Answer to Problem 27PPS

The Earth takes to revolve around the sun is 8761 hours.

Explanation of Solution

Given information:

Earth travels at a speed of 66.698 miles per hour around the sun.

Formula Used:

The formula $T=\frac{C}{V}$ , where $T$ is time in hours, $C$ is circumference, and $V$ is velocity.

Calculation:

Consider the given formula

  $T=\frac{C}{V}$

Now, substitute the radius of Earth’s circumference into the equation.

  $\begin{array}{c}T=\frac{584336233.6}{66698}\\ =8761\end{array}$

Hence, The Earth takes to revolve around the sun is 8761 hours.

(c)

To determine

To prove: that the Earth takes 1 year to go around the sun.

Explanation of Solution

Given information:

The radius of Earth’s orbit is 93000000 miles.

Calculation:

The number of hours in an orbit divided by the number of hours in a day should will equal the number of days in an orbit.

The number of days in an orbit

  $\begin{array}{c}\frac{8761}{24}\\ =365\end{array}$

Hence, proved.