What is the center of mass location for the Earth-Moon system?

[profuse007]

nedd help w/ this one: gravitational force

the spatial average distance b/t the Earth and the moon, center to center, is about 3.84x10^8m. the mass of the Earth is 80 times the masss of the moon. determine the location of the center of mass of the earth-moon system: A)relatives to the center of mass of the earth; B)relative to the surface of the earth.
______________________
"The two most common elements in the universe are H+ and stupidity"

 

[Philcorp]

I think what you need to know has less to do with gravitation and more with whayt the centre of mass is.

A coordinate (say x) of the centre of mass is given by:

$x_{cm}=\frac{\sum_i x_i m_i}{\sum_i m_i}$

by choosing your coordinate system and using these relations you should be able to answer the problem.
Hope this helps

And I am so glad you guys finally allow tex :p

 

[profuse007]

i haven't learn that stuff yet that you just mentioned. this is chapter 6. the top of the book says grativational force and field.

we use these eq.
$$F=ma$$ and $$F=\frac{GMm}{r^2}$$

 

[outandbeyond2004]

profuse007, you haven't gotten any explanation of what center of mass is yet?

 

[profuse007]

thats the whole question.

 

[HallsofIvy]

No, that's not the whole question. The "whole question" was asking you to find the center of mass in this particular situation.
No one is going to ask you to find "asfdwefs" with first defining "asfdwefs"! Even if your instructor has not given you the definition in class, it is surely in your textbook. In any case, Philcorp has given you the formula: $x_{cm}=\frac{\sum_i x_i m_i}{\sum_i m_i}$.

In this particular case, there are only two masses, the Earth and the moon. Take the mass of the moon, m₁ to be 1 and the mass of the earth, m₂, to be 80 (since the Earth is 80 times the mass of the moon). To find the center of mass of the earth-moon system "relative to the center of mass of the earth", A, take x₁ to be 0 (take the center of mass of the Earth to be the 0 point) and x₂ to be 3.84x10^8m. To find the center of mass of the earth-moon system "relative to the center of mass of the moon", B, take x₂ to be 0 (take the center of mass of the moon to be the 0 point) and x₁ to be 3.84x10^8m.

Finally, as Philcorp also told you, this problem has nothing whatever to do with "gravitational force". They may be using it to make the point that although the Earth and moon both rotate around their common center of mass, that is so close to the center of the Earth that it appears that the moon is rotating around the earth.

 

[Philcorp]

Perhaps i should have been more explicit...