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Expert-verified Found in: Page 480 ### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508 # Orbit of the Earth Find the distance that the earth travels in one day in its path around the sun. Assume that a year has 365 days and that the path of the earth around the sun is a circle of radius 93 million miles. [Note: The path of the earth around the sun is actually an ellipse with the sun at one focus (see Section 11.2). This ellipse, however, has verysmall eccentricity, so it is nearly circular] The final distance that the earth travels in one day in its path around the sun is approximate 1.6 million miles.

See the step by step solution

## Step 1. Given information

Radius of the sun $\left(r\right)=93$ million miles.

## Step 2. Write the concept.

One full revolution ($2\pi$ rad) of the earth around the sun is a year, so in one day is equal to be central angle $\theta$ which is:

$\theta =\frac{2\pi }{365}$ radians

Now to find the distance that the earth travels in one day in its path around the sun, we can use below formula:

$s=r\theta$

Where:

$s=$distance that the earth travels in one day

$r=$radius of earth

$\theta =$central angle

## Step 3. Determining the value.

The distance that the earth travels in one day in its path around the sun is:

$s=r\theta$

Put the given values in the formula:

$s=\frac{93×2×\pi }{365}$

Put $\pi =3.14$, we get

role="math" localid="1648643379162" $s=\frac{93×2×3.14}{365}\phantom{\rule{0ex}{0ex}}s=\frac{584.04}{365}\phantom{\rule{0ex}{0ex}}=1.60092\phantom{\rule{0ex}{0ex}}=1.6\text{million miles}\phantom{\rule{0ex}{0ex}}$ ### Want to see more solutions like these? 