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Jeans Length

(critical radius below which gravity will collapse a cloud)

The Jeans Length is James Jeans' calculation of the radius of a cloud at which pressure balances Gravity.

λJ = √ —————


This equation, as written, is a form of a relationship called the Jeans Criterion, a limit, which if exceeded, results in the collapse of a cloud, due to gravity overcoming pressure, a condition called a Jeans Instability. Basically, it means the sum of the Kinetic Energy and Gravitational Potential energy (the latter of which is negative) is less than zero. The above equation essentially states when that sum equals zero (i.e., the limit beyond which a Jeans instability occurs) given the characteristics of gases. Solving the equation for mass indicates the Jeans Mass (given values for the other parameters) and solving for the density similarly yields the Jeans Density.


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