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Jeans Analysis
A uniform cloud of gas will collapse under gravity if its gravitational timescale is shorter than its thermal timescale. That is, if the freefall time of the gas,
is less than the time it would take for sound waves to attempt to equilibrate the matter distribution, or the sound-crossing time, , where R is the radius of the cloud and Cs is its sound speed.The problem
Case 1 - Increase in Mass
Case 2 - Decrease in Radius
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