What is the centroid of the earth-moon system and how is it calculated?

[Ry122]

How do you calculate the centroid of the earth-moon system?
Is it this exact point that the moon-earth system orbits? Is it an elliptical or circular orbit?

 

[BobG]

Center of mass:
Pick a reference point (the center of the Earth is a good reference point, since that's the origin for you geocentric equatorial coordinate system). You measure all distances from your reference point.

Multiply the distance of object 1 (Earth?) by its mass.

Multiply the distance of object 2 (Moon?) by its mass.

Add the results together.

Divide the total mass (sum of the Earth's mass and Moon's mass).

That gives you the center of mass relative to your reference point.

If you're using the center of Earth as your reference, then its distance is zero, making your calculation even easier. It's just the Moon's distance times its mass divided by the total mass of the Earth and Moon.

And this is the exact point that both the Earth and Moon orbit around. The orbit could be either circular or elliptical as long as the total energy for both orbits stays constant (with the total energy being the sum of kinetic energy and potential energy). The angular momentum of the two body system also has to stay constant, so the orbit of one will affect the orbit of the other.

 

[Ry122]

thanks. I got 4768km so I take it the Earth revolves around a point below its surface.

 

[phinds]

thanks. I got 4768km so I take it the Earth revolves around a point below its surface.

Would you consider that to be a problem? Consider a system in which we had no moon but just one artificial satellite, say the International Space Station. The space station and the Earth would mutually rotate around a point somewhere pretty much exactly at the center of the Earth (off by a very small amount).

 

[Gannet]

thanks. I got 4768km so I take it the Earth revolves around a point below its surface.

At a instant in time it is a "point" but over the lunar month it is an oscillating elliptical spiral because of the Earth's rotation and the moon's elliptical orbit