# Center of mass for earth-moon system

1. Oct 31, 2005

### Punchlinegirl

The ratio of the mass of the earth to the mass of the moon is 77.6. Assume that the radius of the earth is about 6404.0 km and that the distance between the center of the earth and the moon is 380604.0 km. Determine the distance of the center of mass of the earth-moon system from the center of the earth.
I got this.. it was 4840 km.
The second part of the problem says, The earth-moon system moves in a circular orbit around the sun. How far from the circular orbit does the center of the earth move radially (i.e. toward or away from the sun) during the lunar month?
Since the center of mass never changes I used
4840= m1 x1 + m2 x2 / m1 + m2
4840= 77.6( x + 6404) + x / 78.6
Solving for x gave me -1482 km.. which wasn't right..
Any help?

2. Oct 31, 2005

### whozum

Someone asked htis a few days ago, look around

3. Nov 1, 2005

### Punchlinegirl

I was the one that asked this a few days ago without realizing that it had a second part.. which I don't know how to do.

4. Apr 3, 2009

### jbsalzbe

i think your approach is wrong

5. Apr 3, 2009

### jbsalzbe

Assuming: the website isn't allowing for proper formating of the coordinate system

particle ; mass(kg) ; x(km) ; y(km)
--------------------------------------------------------------------
M_1(earth) ; 5.98x10^24 ; 0 ; 0

M_2(moon) ; 7.36x10^22 ; 3.82x10^5 ; 0

-----------------------------------------------------------------------------------
X_cm=((5.98x10^24kg)(0) + (7.36x10^22kg)(3.82x10^5km))/(5.98x10^24kg + 7.36x10^22kg)

X_cm= 4644.38km