What is the significance of the Jeans length in cloud collapse?

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The discussion focuses on the Jeans length formula, which is crucial for understanding cloud collapse in astrophysics. The formula incorporates variables such as temperature, gravitational constant, and pressure to determine stability. It is clarified that the mass per particle, denoted as μ, is an average derived from the composition of the gas, primarily hydrogen and helium. The conversation highlights the necessity of approximating particle masses to achieve a numerical solution in n-body problems. Understanding these concepts is essential for analyzing the dynamics of interstellar clouds.
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Hello,

As I understand, the following formula describes the Jeans length.

\lambda_j = \sqrt\frac{15k_BT}{4\pi G \mu P}

Where \mu is the mass per particle.

Forgive me if this question may come across as relatively stupid, I imagine that each of the particles within the cloud should have different masses. Is \mu an average of the masses?
 
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Yeah it is, but since most gas is generally ~75% H and ~25% He or something close to that, it's easy to figure out the average mass per particle.
 
It's one of those n-body things where you must approximate to get a numerical solution.
 
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