# Illustration Reduced mass and center of mass of a two-body system

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:$$\mu ~=~ \frac{ m_1 \, m_2 }{ m_1 ~+~ m_2 }$$