Reduced mass is a concept that allows one to solve the two-body problem of mechanics as if it were a one body problem. Given two bodies, one with mass $m\_\{1\}$ and the other with mass $m\_\{2\}$, they will orbit the barycenter of the two bodies. The equivalent one-body problem, with the position of one body with respect to the other as the unknown, is that of a single body of inertial mass

$m\_\{red\}\; \backslash equiv\; \{1\; \backslash over\; \}\; =$

Applying the gravitational formula we get that the position of the first body with respect to the second is governed by the same differential equation as the position of a very small body orbiting a body with a mass equal to the sum of the two masses, because $\}=m\_1+m\_2$.

The reduced mass is always less than the mass of each body.

External links

• Reduced Mass on HyperPhysics

Mechanics | Mass

Reduzierte Masse | Masa reducida | Redukuota masė