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Chapter 9: Q109P (page 255)

(a) How far is the center of mass of the Earth鈥揗oon 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鈥檚 radius is that distance?

Short Answer

Expert verified
  1. Position of center of mass of the Earth-Moon system,Xcomis4.6脳103km.
  2. Percentage of that distance with Earth鈥檚 radius is 73% .

Step by step solution

01

Understanding the given information

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

02

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 鈥揗oon system from the center of earth. Then find that distance in terms of Earth鈥檚 radius. The formula used is given below.

Xcom=(m1x1+m2x2)m1+m2

03

(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:

Xcom=Mx1+Mx2M+m

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

Xcom=(5.98脳1024)(0)+(7.36脳1022)(3.82脳108)(5.98脳1024)+(7.36脳1022)=4.64脳106m=4.6脳103km

04

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

Consider radius of earth isrE=6.37脳106m

We get,

(4.64脳106)6.37脳106=0.73=73%

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

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