Skip to main content

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

Reduced mass and center of mass of a two-body system
Reduced mass and center of mass of a two-body system
Download illustration

Share — copy and redistribute the material in any medium or format

Adapt — remix, transform, and build upon the material for any purpose, even commercially.

Sharing and adapting of the illustration is allowed with indication of the link to the illustration.

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