Reduced mass

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} \equiv {1 \over {{1 \over m_1} + {1 \over m_2}}} = {{m_1 m_2} \over {m_1 + m_2}}

with the force the actual one. 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} \over {m_{red}}}=m_1+m_2

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

Reduced mass

I guss a picture of the two-body system would be a good idea?

See other meanings of words starting from letter:

R

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Words begining with Reduced_mass:

Reduced_mass
Reduced_mass