Center of mass for earth-moon system

AI Thread Summary
The ratio of the Earth's mass to the Moon's mass is 77.6, with the Earth’s radius at approximately 6404 km and the distance to the Moon at 380604 km. The calculated distance of the center of mass from the Earth's center is 4840 km. For the second part of the problem, the user attempted to calculate the radial movement of the Earth's center during a lunar month but arrived at an incorrect value of -1482 km. A different approach using the center of mass formula yielded a new position of approximately 4644.38 km. The discussion highlights the complexity of calculating the center of mass in the Earth-Moon system.
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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?
 
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Someone asked htis a few days ago, look around
 
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.
 
i think your approach is wrong
 
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
 
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