Jeans length

Jeans length

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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
Gravitational constant
The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...

 and is the cloud's mass density (i.e. the cloud's mass divided by the cloud's volume).http://scienceworld.wolfram.com/physics/JeansLength.html

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 is then immediately obvious 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.

Jeans' Length as oscillation wavelength


The Jeans' Length is the oscillation wavelength below which stable oscillations rather than gravitational collapse will occur.


Where G is the gravitational constant
Gravitational constant
The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...

, is the sound speed
Speed of sound
The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....

, and is the enclosed mass density.

It is also the distance a sound wave would travel in the collapse time
Jeans instability
In physics, the Jeans instability causes the collapse of interstellar gas clouds and subsequent star formation. It occurs when the internal gas pressure is not strong enough to prevent gravitational collapse of a region filled with matter...

.