| MadSci Network: Astronomy |
No. The Jeans velocity of a perturbation and the Jeans escape are two unrelated concepts named in honor of the same mathematician and astronomer at the turn of the XX century, who was also known for his popular works on astronomy.
If there is a density fluctuation in a gas immersed in a
gravitational field of force due to, say, a nearby explosion or
a collision with another cloud, this perturbation will cause
waves or ripple in the gas. The velocity of motion of this
perturbation throughout the cloud is called the "Jeans velocity" in
honor of Sir James Hopwood Jeans, who developed the theory. He
discovered that if the amplitude of the fluctuation is larger
than a certain length that depends on the temperature and density
of the gas, called the Jeans length of course, the fluctuation
grows rapidly in time. A cloud bigger than this length is
unstable and can collapse into a star. A nice computer simulation
of a Jeans instability is at
http://astro.uchicago.edu/Computing/Science/cosmology.html
But this is not what you are looking for. The Jeans escape was also named after Jeans as a mechanism of evaporation of planetary atmospheres. When the molecules of a certain chemical species in the upper atmosphere achieve speeds greater than the escape velocity of the planet, they get lost in space. When the most probable velocity of those molecules is about 6 times less than the escape velocity, the chemical species can evaporate completely in a billion years (a significant time in geological terms). This is often used to explain why the atmosphere of Earth has so little hydrogen and helium. Hydrogen and helium molecules are the lightest species, and thus their molecules have higher speeds than other species.
Vladimir Escalante Ramirez
[Moderator's Note: For the gory mathematical details of the Jeans escape mechanism, see http://www.treasure-troves.com/physics/JeansEscape.html.]
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