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Two masses \(m_1\) and \(m_2\) attract each other with the gravitational force \(F_{\text g}\) and are at the distance \(r\) to each other. The masses rotate around the common center of mass C.M. The mass \(m_1\) is at the distance \(r_1\) to the center of mass and the mass \(m_2\) is at the distance \(r_2\) to the center of mass.
To reduce this two-body problem to a one-body problem, the reduced mass \(\mu\) is introduced:$$ \mu ~=~ \frac{ m_1 \, m_2 }{ m_1 ~+~ m_2 } $$