Reduced Mass

$\mu =\frac{m_1{m}_2}{m_1+m_2}$

• Reduces two body problem into a one body problem
• Always smaller than or equal to $m_1$ or $m_2$ because $m_1=\frac{m_1}{1}\left(\frac{m_1+m_2}{m_1+m_2}\right)=\frac{m_1^2}{m_1+m_2}+\mu \ge \mu$

${\vec{F}}_{21}=\mu {\vec{a}}_{\text{rel}}$

• This is the force object 2 exerts on object 1
• ${\vec{a}}_{\text{rel}}$ is ${\vec{a}}_1-{\vec{a}}_2$
• Here, we fix the position of object 2 and treat object 1 as the object moving
• See Wikipedia article for derivation