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[[File:EarthAtmosphereBig.jpg|thumb|80px|right|Earth atmosphere diagram showing the exosphere and other layers. The layers are to scale. From Earth's surface to the top of the stratosphere (50km) is just under 12% of Earth's radius.]]
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.
The '''exosphere''' ({{lang-grc|ἔξω}} {{lang|grc-Latn|''éxō''}} "outside, external, beyond", {{lang-grc|σφαῖρα}} {{lang|grc-Latn|''sphaĩra''}} "sphere") is a thin, atmosphere-like volume surrounding a planetary body where [[molecule]]s are gravitationally bound to that body, but where the density is too low for them to behave as a gas by [[particle collision|colliding]] with each other. In the case of bodies with substantial atmospheres, such as the [[Atmosphere of Earth|Earth's atmosphere]], the exosphere is the uppermost layer, where the atmosphere thins out and merges with interplanetary space. It is located directly above the [[thermosphere]].


Several moons, such as [[Earth's moon]] and the [[Galilean moons|Galilean satellites]], have exospheres without a denser atmosphere underneath. Here molecules are ejected from surface rocks and follow independent [[parabolic trajectory|parabolic trajectories]] until they collide with the surface. Authors differ as to whether such moons are considered to have atmospheres or not. Smaller bodies such as asteroids, in which the molecules emitted from the surface escape to space, are not considered to have exospheres.
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
* Only registered users will be able to execute this rendering mode.
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


==Earth's exosphere==
Registered users will be able to choose between the following three rendering modes:
The main gases within the Earth's exosphere are the lightest atmospheric gases, mainly [[hydrogen]], with some [[helium]], [[carbon dioxide]], and [[atomic oxygen]] near the base of the exosphere. Since there is no clear boundary between outer space and the exosphere,  the exosphere is sometimes considered a part of [[outer space]].


===Lower boundary===
'''MathML'''
{{Main|Thermopause}}
:<math forcemathmode="mathml">E=mc^2</math>
The lower boundary of the exosphere is known as ''exopause''; it is also called the ''[[exobase]]'', as in Earth's atmosphere the atmospheric temperature becomes nearly a constant above this altitude. Before the term exobase was established the boundary was also called the ''critical altitude'' where [[Barometric formula|barometric conditions]] no longer apply.<ref>Bauer & Lammer, Planetary Aeronomy: Atmosphere Environments in Planetary Systems, [[Springer Publishing|Springer]], 2004.</ref> The altitude of the exobase ranges from about {{convert|500|to|1000|km|lk=on}} depending on solar activity. {{Citation needed|date=January 2009}}


The exobase can be defined in one of two ways:  
<!--'''PNG'''  (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


If we define the exobase as the height at which upward-traveling molecules experience one collision on average, then at this position the [[mean free path]] of a molecule is equal to one pressure [[scale height]]. This is shown in the following. Consider a volume of air, with horizontal area <math>A</math> and height equal to the mean free path <math>l</math>, at pressure <math>p</math> and temperature <math>T</math>. For an [[ideal gas]], the number of molecules contained in it is:
'''source'''
: <math> n = \frac{pAl} {RT} </math>
:<math forcemathmode="source">E=mc^2</math> -->


where <math>R</math> is the universal [[gas constant]]. From the requirement that each molecule traveling upward undergoes on average one collision, the pressure is:
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


: <math> p = \frac{m_{A}ng} {A} </math>
==Demos==


where <math>m_{A}</math> is the mean molecular mass of the gas. Solving these two equations gives:
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:


: <math> l = \frac{R T} {m_{A}g} </math>


which is the equation for the pressure scale height. As the pressure scale height is almost equal to the density scale height of the primary constituent, and since the [[Knudsen number]] is the ratio of mean free path and typical density fluctuation scale, this means that the exobase lies in the region where <math>\mathrm{Kn}(h_{EB}) \simeq 1</math>.
* accessibility:
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


The fluctuation in the height of the exobase is important because this provides atmospheric drag on satellites, eventually causing them to fall from [[orbit]] if no action is taken to maintain the orbit.
==Test pages ==


===Upper boundary===
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
In principle, the exosphere covers all distances where particles are still [[Gravity|gravitationally]] bound to [[Earth]], i.e. particles still have ballistic orbits that will take them back towards Earth. Theoretically, the upper boundary of the exosphere can be defined as the distance at which the influence of solar [[radiation pressure]] on atomic [[hydrogen]] exceeds that of the Earth’s gravitational pull. This happens at half the distance to the Moon ({{convert|190000|km}}). The exosphere observable from space as the [[geocorona]] is seen to extend to at least {{convert|10,000|km}} from the surface of the Earth. The exosphere is a transitional zone between Earth’s atmosphere and [[interplanetary space]].
*[[Displaystyle]]
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]


{{-}}
*[[Inputtypes|Inputtypes (private Wikis only)]]
 
*[[Url2Image|Url2Image (private Wikis only)]]
==References==
==Bug reporting==
{{portal|Atmospheric sciences}}
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .
{{reflist}}
{{-}}
==External links==
* Gerd W. Prolss: ''Physics of the Earth's Space Environment: An Introduction''. ISBN 3-540-21426-7
 
{{Earth's atmosphere}}
 
[[Category:Atmosphere]]
[[Category:Atmosphere of Earth]]

Latest revision as of 23:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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