Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

(a) How far is the center of mass of the Earth–Moon system from the center of Earth? (Appendix C gives the masses of Earth and the Moon and the distance between the two.) (b) What percentage of Earth’s radius is that distance?

Position of center of mass of the Earth-Moon system, $X_{c o m} is 4.6 \times 10^{3} km$ .
Percentage of that distance with Earth’s radius is 73% .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Understanding the given information

Appendix C in the book gives the masses of Earth, Moon and distance between them.

Step 2: Concept and formula used in the given question

Use the concept of center of mass. Using the equation of center of mass of position you find the position of center of mass of Earth –Moon system from the center of earth. Then find that distance in terms of Earth’s radius. The formula used is given below.

$X_{c o m} = \frac{(m_{1} x_{1} + m_{2} x_{2})}{m_{1} + m_{2}}$

Step 3: (a) Calculate the how far is the center of mass of the Earth–Moon system from the center of Earth

Consider origin at the center of earth and write as:

$X_{c o m} = \frac{M x_{1} + M x_{2}}{M + m}$

Where M is the mass of Earth and m is the mass of the moon.

$X_{c o m} = \frac{(5.98 \times 10^{24}) (0) + (7.36 \times 10^{22}) (3.82 \times 10^{8})}{(5.98 \times 10^{24}) + (7.36 \times 10^{22})} = 4.64 \times 10^{6} m = 4.6 \times 10^{3} km$

Step 3: (b) Calculate the percentage of Earth’s radius to that distance

Consider radius of earth is $r_{E} = 6.37 \times 10^{6} m$

We get,

$\frac{(4.64 \times 10^{6})}{6.37 \times 10^{6}} = 0.73 = 73 %$

So, the percentage of distance is 73% of radius of earth.

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Fundamentals Of Physics

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Short Answer

(a) How far is the center of mass of the Earth–Moon system from the center of Earth? (Appendix C gives the masses of Earth and the Moon and the distance between the two.) (b) What percentage of Earth’s radius is that distance?

Step by Step Solution

Step 1: Understanding the given information

Step 2: Concept and formula used in the given question

Step 3: (a) Calculate the how far is the center of mass of the Earth–Moon system from the center of Earth

Step 3: (b) Calculate the percentage of Earth’s radius to that distance

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Fundamentals Of Physics

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Short Answer

(a) How far is the center of mass of the Earth–Moon system from the center of Earth? (Appendix C gives the masses of Earth and the Moon and the distance between the two.) (b) What percentage of Earth’s radius is that distance?

Step by Step Solution

Step 1: Understanding the given information

Step 2: Concept and formula used in the given question

Step 3: (a) Calculate the how far is the center of mass of the Earth–Moon system from the center of Earth

Step 3: (b) Calculate the percentage of Earth’s radius to that distance

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