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# Jeans Analysis

A uniform cloud of gas will collapse under gravity if its gravitational timescale (the freefall time,

) is shorter than its thermal timescale (sound crossing time, ). That is, if is less than , where R is the radius of the cloud and Cs is its sound speed, a cloud is unstable to collapse. Setting these equal and solving for r gives an estimate of the Jeans length,# The problem

# Case 1 - Increase in Mass

# Case 2 - Decrease in Radius

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