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The **Jeans length** is James Jeans's calculation of
the radius of a cloud at which pressure balances gravity.

15k_{B}T λ_{J}= √ ————— 4πGμρ

Where:

- λ
_{J}is the Jeans length. - k
_{B}the is Boltzmann constant. - T is the temperature of the cloud.
- ρ is the mass density of the cloud.
- μ is the mass per molecule.
- G is the gravitational constant.

If a cloud with the given temperature, density and molecular mass
has less than this radius, it collapses (and the same goes
for any sub-region of the cloud).
This 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**.

The name **Jeans swindle** has been coined for an apparent flaw in
Jeans's derivation, that ignored some effects by dropping a term in the
underlying equation that would account for the surrounding density.
While simplification is necessary and ubiquitous in astrophysical
equations, this absence appears to be required to produce the
instability. However Jeans's model apparently works and effort has
been expended on explaining why Jeans's model appears to work despite
the flaw.

https://en.wikipedia.org/wiki/Jeans_instability#Jeans'_length

http://scienceworld.wolfram.com/physics/JeansLength.html

ftp://ftp.hs.uni-hamburg.de/pub/outgoing/abonafede/ASTRO1/astro1.11.pdf

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