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Q79.

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Precalculus Mathematics for Calculus

Found in: Page 480

Book edition 7th Edition

Author(s) James Stewart, Lothar Redlin, Saleem Watson

Pages 948 pages

ISBN 9781337067508

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Short Answer

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 very
small 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 by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

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

Step 2. Write the concept.

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

$θ = \frac{2 π}{365}$ radians

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

$s = r θ$

Where:

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

$r =$ radius of earth

$θ =$ central angle

Step 3. Determining the value.

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

$s = r θ$

Put the given values in the formula:

$s = \frac{93 \times 2 \times π}{365}$

Put $π = 3.14$ , we get

role="math" localid="1648643379162" $s = \frac{93 \times 2 \times 3.14}{365} s = \frac{584.04}{365} = 1.60092 = 1.6 million miles$

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