Editing Dynamical friction (section)

===Maxwell's distribution===

A commonly used special case is where there is a uniform density in the field of matter, with matter particles significantly lighter than the major particle under consideration i.e., <math>M\gg m</math> and with a [[Maxwell–Boltzmann distribution|Maxwellian distribution]] for the velocity of matter particles i.e.,
<math display="block">f(v) = \frac{N}{(2\pi\sigma^2)^{3/2}}e^{-\frac{v^2}{2\sigma^2}}</math>
where <math>N</math> is the total number of stars and <math>\sigma</math> is the dispersion. In this case, the dynamical friction formula is as follows:<ref>{{Citation | last = Merritt | first = David | author-link = David Merritt | title = Dynamics and Evolution of Galactic Nuclei | publisher = [[Princeton University Press]] | date = 2013 | bibcode = 2013degn.book.....M | isbn = 9781400846122 | url = https://openlibrary.org/works/OL16802359W/Dynamics_and_Evolution_of_Galactic_Nuclei }}</ref>

<math display="block"> \frac{d\mathbf{v}_M}{dt} = -\frac{4\pi \ln (\Lambda) G^2  \rho M}{v_M^3}\left[\mathrm{erf}(X)-\frac{2X}{\sqrt{\pi}}e^{-X^2}\right]\mathbf{v}_M</math>
where
* <math> X = v_M/(\sqrt{2} \sigma) </math> is the ratio of the velocity of the object under consideration to the modal velocity of the Maxwellian distribution. 
* <math> \mathrm{erf}(X) </math> is the [[error function]].
* <math> \rho= mN </math> is the density of the matter field.

In general, a simplified equation for the force from dynamical friction has the form

<math display="block">F_\text{dyn} \approx C \frac{G^2 M^2 \rho}{v^2_M}</math>

where the [[dimensionless]] numerical factor <math> C </math> depends on how <math>v_M</math> compares to the velocity dispersion of the surrounding matter.<ref>{{Citation
  | last1 = Carroll | first1 = Bradley W. 
  | last2 = Ostlie | first2 = Dale A. 
  | title = An Introduction to Modern Astrophysics
  | publisher = [[Weber State University]]
  | date = 1996
  | bibcode = 1996ima..book.....C 
 | isbn = 0-201-54730-9 }}</ref>
But note that this simplified expression diverges when <math> v_M \to 0 </math>; caution should therefore be exercised when using it.