Jeans' length is the critical radius of a cloud (typically a cloud of interstellar dust) where thermal energy, which causes the cloud to expand, is counteracted by gravity, which causes the cloud to collapse. It is named after the British astronomer Sir James Jeans, who concerned himself with the stability of spherical nebula in the early 1900s.
The formula for Jeans Length is:
where is Boltzmann's constant, is the temperature of the cloud, is the radius of the cloud, is the mass per particle in the cloud, is the Gravitational Constant and is the cloud's mass density (i.e. the cloud's mass divided by the cloud's volume).
Perhaps the easiest way to conceptualize Jeans' Length is in terms of a close approximation, in which we discard the factors and and in which we rephrase as . The formula for Jeans' Length then becomes:
It follows immediately that when i.e. the cloud's radius is the Jeans' Length when thermal energy per particle equals gravitational work per particle. At this critical length the cloud neither expands nor contracts. It is only when thermal energy is not equal to gravitational work that the cloud either expands and cools or contracts and warms, a process that continues until equilibrium is reached.
Read more about this topic: Jeans Instability
Other articles related to "jeans length, jeans, length":
... Jeans' length is the critical radius of a cloud (typically a cloud of interstellar dust) where thermal energy, which causes the cloud to expand, is ... It is named after the British astronomer Sir James Jeans, who concerned himself with the stability of spherical nebula in the early 1900s ... The formula for Jeans Length is where is Boltzmann's constant, is the temperature of the cloud, is the radius of the cloud, is the mass per particle in the cloud ...
... The Jeans mass is named after the British physicist Sir James Jeans, who considered the process of gravitational collapse within a gaseous cloud ... The approximate value of the Jeans mass may be derived through a simple physical argument ... collapse is therefore The resultant Jeans length is approximately This length scale is known as the Jeans length ...
... Jeans instability can also give rise to fragmentation in certain conditions ... processes, For an ideal gas, Polytropic equation of state, Jeans mass, Thus, If adiabatic index, Jeans mass increases with increasing density while if Jeans mass decreases with increasing density ... always increases, thus in the second case Jeans mass will decrease during collapse allowing smaller overdense regions to collapse leading to fragmentation of the giant molecular cloud ...
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