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Jeans Length Using Temperature

The Jeans length is the critical radius for the instability of a collapsing thermalized cloud of self­gravitating gas.

Jeans length is proportional to the square root of the temperature divided by the mean mass per particle and the mass density.

Formula

QuantityVariable[Subscript["R", "J"], "Length"] == (Sqrt[15/Pi]*Sqrt[(Quantity[1, "BoltzmannConstant"/"GravitationalConstant"]*QuantityVariable["T", "Temperature"])/(QuantityVariable["μ", "Mass"]*QuantityVariable["ρ", "MassDensity"])])/2

symbol description physical quantity
RJ Jeans length "Length"
T temperature "Temperature"
μ mean mass per particle "Mass"
ρ mass density "MassDensity"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Jeans Length Using Temperature"]
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Get the formula:

In[2]:=
FormulaData[ResourceObject["Jeans Length Using Temperature"]]
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Use some values:

In[3]:=
FormulaData[ ResourceObject["Jeans Length Using Temperature"], {QuantityVariable[ \!\(\*SubscriptBox[\("R"\), \("J"\)]\),"Length"] -> Quantity[2.624`4.*^14, "Kilometers"], QuantityVariable["\[Rho]","MassDensity"] -> Quantity[6.69489`6.*^-24, ("Kilograms")/("Centimeters")^3]}]
Out[3]=

Source Metadata

  • Creator:
  • Date: 1902

Publisher Information