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## Homework Statement

Locate the center of the mass of the Earth-moon system with respect to the center of the Earth, and then find the orbital velocity of the Earth about this center of mass

## Homework Equations

R_G = (m1R1 + m2R2) / (m1 + m2)

V_circ = sqrt ( μ / r )

M_E = 5.974 * 10 ^24 kg

M_m = 73.48 * 10^21 kg

Moon semi-major axis of orbit = 384,400 km

## The Attempt at a Solution

So, I went ahead and calculated the center of mass of the system. I found that along a straight line connecting the center of the Earth to the center of the Moon, the center of mass was located 4671 km from the center of the Earth.

So now, I need to find the orbital velocity of the Earth about this COM. Using

V_circ = √( μ / r ), I know that I will be able to do so.

I know that in this case, r = 4671 m, as this is the distance from the COM to the center of the Earth. However, I'm having trouble determining the gravitational paramater μ.

In a case like this, is the gravitational parameter of the COM simply μ = G (m_E + m_M)?

This is the first problem that I've had to do that measures velocities in reference to a COM.

Any help would be appreciated