Editing Magnetopause (section)

==Estimating the standoff distance to the magnetopause==
If the pressure from particles within the magnetosphere is neglected, it is possible to estimate the distance to the part of the magnetosphere that faces the [[Sun]].  The condition governing this position is that the dynamic [[ram pressure]] from the [[solar wind]] is equal to the magnetic pressure from the Earth's [[magnetic field]]:<ref group="note">The reason for the factor of 4 is because the magnetic field strength just inside the magnetopause is twice the dipole value for a planar magnetopause</ref>
<math display="block">(\rho v^2)_{sw}\approx \left( \frac{4 B(r)^2}{2\mu_0} \right) _m</math>
where <math>\rho</math> and  <math>v</math> are the [[density]] and [[velocity]] of the [[solar wind]], and
{{math|''B''(''r'')}} is the [[Magnetic field|magnetic field strength]] of the planet in [[SI]] units ({{math|''B''}} in [[Tesla (unit)|T]], [[Permeability constant|{{math|''μ''<sub>0</sub>}}]] in [[Henry (unit)|H]]/m).

Since the [[dipole]] magnetic field strength varies with distance as <math>1/r^3</math> the magnetic field strength can be written as <math>B(r) = {\mu_0 m \over 4\pi r^3}</math>, where <math>m</math> is the planet's magnetic moment, expressed in <math>A \cdot m^2</math>.
<math display="block">\rho v^2 \approx \frac{\mu_0 m^2}{8\pi^2r^6}.</math>
Solving this equation for r leads to an estimate of the distance
<math display="block">r \approx \sqrt[6]{\frac{\mu_0 m^2}{8\pi^2 \rho v^2}}</math>

The distance from Earth to the subsolar magnetopause varies over time due to solar activity, but typical distances range from 6–15 [[Earth radius|R<math>_{\oplus}</math>]]. Empirical models<ref>{{Cite journal |last=Roelof |first=E. |last2=Sibeck |first2=D. |year=1993 |title=Magnetopause shape as a bivariate function of interplanetary magnetic field Bz and solar wind Dynamic pressure |journal=J. Geophys. Res. |volume=98 |issue=A12 |page=A12 |bibcode=1993JGR....9821421R |doi=10.1029/93JA02362}}</ref><ref>{{Cite journal |last=Shue |first=H. |last2=Chao |first2=J. |last3=Fu |first3=H. |last4=Russell |first4=C. |last5=Song |first5=P. |last6=Khurana |first6=K. |last7=Singer |first7=H. |year=1997 |title=A new functional form to study the solar wind control of the magnetopause size and shape |journal=J. Geophys. Res. |volume=102 |issue=A5 |page=A5 |bibcode=1997JGR...102.9497S |doi=10.1029/97JA00196}}</ref> using real-time [[solar wind]] data can provide a real-time estimate of the magnetopause location.  A [[bow shock]] stands upstream from the magnetopause.  It serves to decelerate and deflect the solar wind flow before it reaches the magnetopause.<ref>{{Cite book |last=De Pater |first=Imke |title=Planetary sciences |last2=Lissauer |first2=Jack J. |publisher=Cambridge University Press |year=2001 |isbn=0-521-48219-4 |location=Cambridge |pages=261 |oclc=45283049 |author-link=Imke de Pater}}</ref>