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# Jeans mass

**Jeans mass** and **Jeans length** are related criteria in the gravitational collapse of gas clouds in the study of how stars might form. These criteria were discovered by James Jeans in 1910. Jeans was an astronomer, mathematician and physicist.

Jeans length is the critical radius of a gas cloud or a part of one where the force of gravity overcomes the expansion forces of the cloud. A cloud larger than then Jeans length is unstable while one smaller is stable and will not collapse without further forces applied.

Jeans mass is the mass of the gas cloud used to determine the gravitational force and is the value at which the forces of expansion is in equilibrium with the force of gravity. Greater masses will collapse and lower masses will not unless another force is applied.

The equation starts with the virial theorem which describes equilibrium. E = 1/2U where E is the total energy (potential and kinetic) of the system and U is the gravitational potential.

if 3NkT < 3/5 * (GM^{2})/R the force of gravity exceeds the expansion force and collapse will occur.

This can be expanded until the Jeans mass equation is derived (see references).

Mj = ((5kT)/(Gm))^{3/2} *(3/4*pi*p)^{^1/2} where Mj is the jeans mass.

These formula use a spherical mass of gas to simplify the calculations.