The Jeans Mass
The Jeans mass is determined by asking when the magnitude of the
gravitational potential energy exceeds the magnitude of the gas kinetic energy.
It is given by
M_{J} = 3kTR / 2Gm
where k is the Boltzmann constant, T the temperature, R
the radius of the
cloud, G the gravitational constant, and m the average mass of a gas
particle. If the cloud's mass exceeds this value, gravity can overcome the
gas kinetic energy and initiate collapse. The corresponding Jeans density is
D_{J} = constant
x (T^{ 3} /
m^{ 3}M^{ 2})
where constant = 81k^{3} / 32πG^{3} and
M is the mass of the cloud.
If the cloud is compressed so that its density exceeds this value, it can begin to collapse.
