View source for Kármán line

{{Short description|Conventional definition of the edge of space}}
{{about|the concept in aviation and aerospace|other uses|Karman Line (disambiguation)}}
[[File:ISS043-E-143486 - View of Earth.jpg|thumb|upright=1.5|Earth's atmosphere photographed from the [[International Space Station]]. The orange and green line of [[airglow]] is at roughly the altitude of the Kármán line.<ref name="NASA Earth Observatory 2020 c617">{{cite web | title=Airglow Over the Indian Ocean | publisher=NASA Earth Observatory | date=2020-10-08 | url=https://earthobservatory.nasa.gov/images/147367/airglow-over-the-indian-ocean | access-date=2024-04-20}}</ref>]]

The '''Kármán line''' (or '''von Kármán line''' {{IPAc-en|v|ɒ|n|_|ˈ|k|ɑr|m|ɑː|n}})<ref>{{cite Dictionary.com|von-karman}}</ref> is a conventional definition of the [[Outer space#Boundary|edge of space]]; it is widely but not universally accepted. The international record-keeping body [[Fédération Aéronautique Internationale|FAI]] (Fédération aéronautique internationale) defines the Kármán line at an altitude of {{convert|100|km|nmi mi ft|abbr=off}} above [[above mean sea level|mean sea level]]. 

While named after [[Theodore von Kármán]], who calculated a theoretical limit of altitude for aeroplane flight at {{Convert|83.8|km|mi|sigfig=3|abbr=on}} above Earth, the later established Kármán line is more general and has no distinct physical significance, in that there is a rather gradual difference between the characteristics of the atmosphere at the line, and experts disagree on defining a distinct boundary where the atmosphere ends and space begins. It lies well above the altitude reachable by conventional aeroplanes or [[high-altitude balloon]]s, and is approximately where satellites, even on very eccentric trajectories, will [[Orbital decay|decay]] before completing a single orbit.

The Kármán line is mainly used for legal and regulatory purposes of differentiating between [[aircraft]] and [[spacecraft]], which are then subject to different jurisdictions and legislations. While [[international law]] does not define the edge of space, or the limit of national airspace,<ref name="ScienceJul2018" /><ref>Harwood, William; [https://www.cbsnews.com/news/space-launch-richard-branson-virgin-galactic-watch-live-2021-07-11/ "Richard Branson and Virgin Galactic complete successful space flight"], ''CBS News'', 2021-07-12</ref> most international organizations and regulatory agencies (including the United Nations) accept the FAI's Kármán line definition or something close to it.<ref>{{Cite web|url=https://astronomy.com/news/2021/03/the-krmn-line-where-does-space-begin|title = The Kármán Line: Where does space begin?| date=5 March 2021 }}</ref> As defined by the FAI, the Kármán line was established in the 1960s.<ref name="Dr. S. Sanz Fernández de Córdoba">{{cite web |first=Dr. S. |last=Sanz Fernández de Córdoba |date=2004-06-24 |title=The 100&nbsp;km Boundary for Astronautics |url=https://www.fai.org/page/icare-boundary |access-date=28 December 2020 |publisher=Fédération aéronautique internationale }}</ref> Various countries and entities define space's boundary differently for various purposes.<ref>{{Cite web |last=Drake |first=Nadia |author-link=Nadia Drake |date=2018-12-20 |title=Where, exactly, is the edge of space? It depends on who you ask. |url=https://www.nationalgeographic.com/science/article/where-is-the-edge-of-space-and-what-is-the-karman-line |archive-url=https://web.archive.org/web/20210304132146/https://www.nationalgeographic.com/science/article/where-is-the-edge-of-space-and-what-is-the-karman-line |url-status=dead |archive-date=March 4, 2021 |access-date=2021-07-14 |website=National Geographic |language=en }}</ref><ref name="ScienceJul2018">{{cite journal |last=Voosen |first=Paul |date=2018-07-24 |title=Outer space may have just gotten a bit closer |url=https://www.science.org/content/article/outer-space-may-have-just-gotten-bit-closer |journal=[[Science (journal)|Science]] |doi=10.1126/science.aau8822 |s2cid=126154837 |access-date=April 1, 2019 }}</ref><ref>{{Cite web |date=2021-05-27 |title=Air Force Guidance Memorandum to AFMAN 11-402 |url=https://static.e-publishing.af.mil/production/1/af_a3/publication/afman11-402/afman11-402.pdf |access-date=July 13, 2021 |website=Department of the Air Force }}</ref>

== Definition ==
[[File:Atmosphere layers.svg|thumb|upright|alt=A dark blue shaded diagram divided by horizontal lines, with the names of the five atmospheric regions arranged along the left. From bottom to top, the troposphere section shows [[Mount Everest]] and an airplane icon, the stratosphere displays a weather balloon, the mesosphere shows meteors, and the thermosphere includes an aurora and the Space Station. At the top, the exosphere shows only stars.|The layers of Earth's atmosphere with the Kármán line indicated (not to scale)<ref>[https://www.weather.gov/jetstream/layers Layers of the Atmosphere], National Weather Service JetStream – Online School for Weather</ref>]]The FAI uses the term Kármán line to define the boundary between aeronautics and astronautics:<ref name="Dr. S. Sanz Fernández de Córdoba"/>

{{Quotation|
* [[Aeronautics]]: For FAI purposes, aerial activity, including all air sports, within 100&nbsp;km of Earth's surface.
* [[Astronautics]]: For FAI purposes, activity more than 100&nbsp;km above Earth's surface.}}

== {{anchor|Edge of space}}Interpretations of the definition ==
The expressions "'''edge of space'''" or "near space" are often used (by, for instance, the FAI in some of their publications)<ref name="FAI_Statement" /> to refer to a region below the boundary of Outer Space, which is often meant to include substantially lower regions as well. Thus, certain [[balloon (aircraft)|balloon]] or [[airplane]] flights might be described as "reaching the edge of space". In such statements, "reaching the edge of space" merely refers to going higher than average aeronautical vehicles commonly would.<ref name=wings>{{cite web |first=Jay |last=Levine |url=http://www.nasa.gov/centers/dryden/news/X-Press/stories/2005/102105_Wings.html |title=A long-overdue tribute |publisher=NASA |date=2005-10-21 |access-date=2006-10-30 }}</ref><ref>{{cite web|url=http://www.nasa.gov/worldbook/astronaut_worldbook.html |title=World Book @ NASA |publisher=NASA |access-date=2006-10-18 |url-status=dead |archive-url=http://webarchive.loc.gov/all/20090504022327/http://www.nasa.gov/worldbook/astronaut_worldbook.html |archive-date=May 4, 2009 }}</ref>

There is still no international legal definition of the demarcation between a country's air space and outer space.<ref>[https://books.google.com/books?id=NR7mFXCB-wgC&dq=legal+boundary+of+space&pg=PA239 ''International Law: A Dictionary''], by Boleslaw Adam Boczek; Scarecrow Press, 2005; page 239: "The issue whether it is possible or useful to establish a legal boundary between airspace and outer space has been debated in the doctrine for quite a long time. … no agreement exists on a fixed airspace – outer space boundary …"</ref> In 1963, [[Andrew G. Haley]] discussed the Kármán line in his book ''Space Law and Government''.<ref name=AGH>[[Andrew G. Haley|Haley, Andrew G.]]; (1963) ''Space Law and Government'', [[Appleton-Century-Crofts]]</ref> In a chapter on the limits of national [[sovereignty]], he made a survey of major writers' opinions.<ref name=AGH />{{rp|82–96}} He indicated the inherent imprecision of the Line:
<blockquote>
The line represents a [[mean]] or [[median]] measurement. It is comparable to such measures used in the law as [[mean sea level]], [[meander]] line, [[tide]] line; but it is more complex than these. In arriving at the von Kármán jurisdictional line, myriad factors must be considered – other than the factor of aerodynamic lift. These factors have been discussed in a very large body of literature and by a score or more of commentators. They include the physical constitution of the [[air]]; the biological and physiological viability; and still other factors which logically join to establish a point at which air no longer exists and at which [[airspace]] ends.<ref name=AGH />{{rp|78,9}}
</blockquote>

== Kármán's comments ==
In the final chapter of his autobiography, Kármán addresses the issue of the edge of [[outer space]]:
<blockquote>
Where space begins ... can actually be determined by the speed of the space vehicle and its altitude above the Earth. Consider, for instance, the record flight of Captain [[Iven Carl Kincheloe Jr.]] in an [[Bell X-2|X-2 rocket plane]]. Kincheloe flew 2000 miles per hour (3,200&nbsp;km/h) at 126,000 feet (38,500&nbsp;m), or 24 miles up. At this altitude and speed, [[aerodynamic lift]] still carries 98 percent of the weight of the plane, and only two percent is carried by inertia, or [[Kepler problem|Kepler force]], as space scientists call it. But at 300,000 feet (91,440&nbsp;m) or 57 miles up, this relationship is reversed because there is no longer any air to contribute lift: only inertia prevails. This is certainly a physical boundary, where [[aerodynamics]] stops and [[astronautics]] begins, and so I thought why should it not also be a jurisdictional boundary? [[Andrew G. Haley]] has termed it the Kármán Jurisdictional Line. Below this line, space belongs to each country. Above this level there would be free space.<ref>[[Theodore von Kármán|von Kármán, Theodore]]; Edson, Lee (1967). ''The Wind and Beyond'', p. 343</ref></blockquote>

== Technical considerations ==
An atmosphere does not abruptly end at any given height but becomes progressively less dense with altitude. Also, depending on how the various layers that make up the space around the [[Earth]] are defined (and depending on whether these layers are considered part of the actual atmosphere), the definition of the edge of space could vary considerably: If one were to consider the [[thermosphere]] and [[exosphere]] part of the atmosphere and not of space, one might have to extend the boundary of space to at least {{convert|10,000|km|mi|abbr=in}} above sea level. The Kármán line thus is a largely arbitrary definition based on some technical considerations.

An aircraft can stay aloft only by constantly traveling forward relative to the air (rather than the ground), so that the wings can generate aerodynamic lift. The thinner the air, the faster the plane must go to generate enough lift to stay up.<ref>{{Cite web |url=http://www.grc.nasa.gov/WWW/k-12/airplane/lifteq.html |title=The Lift Equation |date=2014-06-12 |access-date=2015-03-14 |website=[[Glenn Research Center]] |publisher=[[National Aeronautics and Space Administration]] |editor-last=Benson |editor-first=Tom |archive-url=https://web.archive.org/web/20150317073931/http://www.grc.nasa.gov/WWW/k-12/airplane/lifteq.html |archive-date=2015-03-17 |url-status=dead }}</ref> At very high speeds, centrifugal force (Kepler force) contributes to maintaining altitude. This is the virtual force that keeps satellites in circular orbit without any aerodynamic lift.

As altitude increases and air density decreases, the speed to generate enough aerodynamic lift to support the aircraft weight increases until the speed becomes so high that the centrifugal force contribution becomes significant. At a high enough altitude, the centrifugal force will dominate over the lift force and the aircraft would become effectively an orbiting spacecraft instead of an aircraft supported by aerodynamic lift. 

In 1956, von Kármán presented a paper in which he discussed aerothermal limits to flight. The faster aircraft fly, the more heat they would generate due to [[aerodynamic heating]] from friction with the atmosphere and [[adiabatic process]]es. Based on the current [[state of the art]], he calculated the speeds and altitudes at which continuous flight was possible—fast enough that enough lift would be generated and slow enough that the vehicle would not overheat.<ref>Theodore von Kármán, ''Aerodynamic Heating{{snd}} The Temperature Barrier in Aeronautics'', PROC. HIGH-TEMPERATURE SYMPOSIUM, BERKELEY, CALIFORNIA (1956).</ref> The chart included an inflection point at around {{convert|275,000|ft|mi km|sigfig=4}}, above which the minimum speed would place the vehicle into [[orbit]].<ref name=":0">{{Cite journal |last=Gangale |first=Thomas |date=2017 |title=The Non Kármán Line: An Urban Legend of the Space Age |url=https://airandspace.confit.dev/wp-content/uploads/2020/07/JSL-41.2.pdf |journal=Journal of Space Law |volume=41 |issue=2 |page=155 |url-status=dead|archive-url=https://web.archive.org/web/20210524005008/https://airandspace.confit.dev/wp-content/uploads/2020/07/JSL-41.2.pdf|archive-date=24 May 2021}}</ref><ref>{{cite news |title=Why defining the boundary of space may be crucial for the future of spaceflight |first=Loren |last=Grush |date=2018-12-13 |access-date=April 1, 2019 |work=[[The Verge]] |url=https://www.theverge.com/2018/12/13/18130973/space-karman-line-definition-boundary-atmosphere-astronauts }}</ref>

The term "Kármán line" was invented by [[Andrew G. Haley]] in a 1959 paper,<ref>Andrew G. Haley, ''Space Exploration: The Problems of Today, Tomorrow and in the Future'', 2 PROC. ON THE L. OF OUTER SPACE 49 (1959).</ref> based on the chart in von Kármán's 1956 paper, but Haley acknowledged that the {{convert|275,000|ft|mi km|sigfig=4}} limit was theoretical and would change as technology improved, as the minimum speed in von Kármán's calculations was based on the speed-to-weight ratio of current aircraft, namely the [[Bell X-2]], and the maximum speed based on current cooling technologies and heat-resistant materials.<ref name=":0" /> Haley also cited other technical considerations for that altitude, as it was approximately the altitude limit for an [[airbreathing jet engine]] based on current technology. In the same 1959 paper, Haley also referred to {{convert|295,000|ft|mi km}} as the "von Kármán Line", which was the lowest altitude at which [[free-radical]] [[atomic oxygen]] occurred.<ref name=":0" />

== Alternatives to the FAI definition ==
[[File:Top of Atmosphere.jpg|thumb|upright=1.5|Atmospheric gasses scatter the blue wavelengths, thus giving the Earth a blue arc. As the altitude increases the atmosphere decreases such that by several criteria it ceases to exist. Optically the atmospheric halo here gradually fades into the blackness of space.]]

The [[U.S. Armed Forces]] definition of an [[astronaut]] is a person who has flown higher than {{convert|50|mi|km}} [[above mean sea level]], approximately the line between the [[mesosphere]] and the [[thermosphere]]. [[NASA]] formerly used the FAI's {{convert|100|km|mi|adj=on|abbr=off}} figure, though this was changed in 2005 to eliminate any inconsistency between military personnel and civilians flying in the same vehicle.<ref name="Schneider">{{cite web |first=Dennis R. |last=Jenkins |title=NASA – Schneider walks the Walk [A word about the definition of space] |date=2005-10-21 |url=https://www.nasa.gov/centers/dryden/news/X-Press/stories/2005/102105_Schneider.html |website=www.nasa.gov |access-date=19 October 2018 |language=en |publisher=[[NASA]] }}</ref> Three veteran NASA [[North American X-15|X-15]] pilots ([[John B. McKay]], [[William H. Dana]] and [[Joseph Albert Walker]]) were retroactively (two [[posthumous award|posthumously]]) awarded their [[Astronaut Badge|astronaut wings]], as they had flown between {{convert|90|km|mi|abbr=in}} and {{convert|108|km|mi|abbr=in}} during the 1960s, but at the time had not been recognized as astronauts.<ref name="wings" /> The latter altitude, achieved twice by Walker, exceeds the modern international definition of the boundary of space.

The United States [[Federal Aviation Administration]] also recognizes this line as a space boundary:<ref>[https://www.faa.gov/space/licenses/human_spaceflight/ "Space: Commercial Space Transportation Licenses: Human Spaceflight (also referred to as crewed spaceflight)"], [US] Federal Aviation Administration, 2021-03-16</ref>

{{quotation|Suborbital Flight: Suborbital spaceflight occurs when a spacecraft reaches space but its velocity is such that it cannot achieve orbit. Many people believe that in order to achieve spaceflight, a spacecraft must reach an altitude higher than 100 kilometers (62 miles) above sea level.}}

Works by [[Jonathan McDowell]] (Harvard-Smithsonian Center for Astrophysics)<ref>{{cite journal|title = The edge of space: Revisiting the Karman Line|first = Jonathan C.|last = McDowell|author-link = Jonathan McDowell|journal = [[Acta Astronautica]]|year = 2018|volume = 151|pages = 668–677|doi = 10.1016/j.actaastro.2018.07.003|doi-access = free|bibcode = 2018AcAau.151..668M|arxiv = 1807.07894}}</ref> and [[Thomas Gangale]] (University of Nebraska-Lincoln) in 2018<ref name=":0" /><ref>{{cite book |title=How High the Sky? The Definition and Delimitation of Outer Space and Territorial Airspace in International Law |series=Studies in Space Law |volume=13 |first=Thomas |last=Gangale |year=2018 |isbn=978-90-04-36602-2 |doi=10.1163/9789004366022 |publisher=[[Koninklijke Brill NV]] |location=Leiden, The Netherlands |s2cid=135092905 }}</ref> advocate that the demarcation of space should be at {{convert|80|km|mi ft|abbr=in}}, citing as evidence von Kármán's original notes and calculations (which concluded the boundary should be 270,000&nbsp;ft), confirmation that orbiting objects can survive multiple perigees at altitudes around 80 to 90&nbsp;km, plus functional, cultural, physical, technological, mathematical, and historical factors.<ref name = ScienceJul2018 /><ref>{{cite news |url=https://www.livescience.com/63166-outer-space-border-karman-line.html |title=The Edge of Space Just Crept 12 Miles Closer to Earth |first=Brandon |last=Specktor |date=2018-07-25 |access-date=April 1, 2019 |work=[[Live Science]] }}</ref> More precisely, the paper summarizes:

{{Blockquote|text=To summarize, the lowest possible sustained circular orbits are at of order 125 km altitude, but elliptical orbits with perigees at 100 km can survive for long periods. In contrast, Earth satellites with perigees below 80 km are highly unlikely to complete their next orbit. It is noteworthy that meteors (travelling much more quickly) usually disintegrate in the 70–100 km altitude range, adding to the evidence that this is the region where the atmosphere becomes important.}}

These findings prompted the FAI to propose holding a joint conference with the [[International Astronautical Federation]] (IAF) in 2019 to "fully explore" the issue.<ref name="FAI_Statement">{{cite web |title=Statement about the Karman Line|url=https://www.fai.org/news/statement-about-karman-line |date=2018-11-30 |access-date=April 1, 2019 |publisher=[[Fédération Aéronautique Internationale|Fédération aéronautique internationale (World Air Sports Federation)]] }}</ref>

Another definition proposed in [[international law]] discussions defines the lower boundary of space as the lowest perigee attainable by an orbiting space vehicle, but does not specify an altitude.<ref name=Army>{{cite book|year = 2000|access-date=April 24, 2012 |chapter = Space Environment and Orbital Mechanics|title = Army Space Reference Text|chapter-url = https://fas.org/spp/military/docops/army/ref_text/chap5im.htm|url-status = dead |archive-date=April 18, 2012 |archive-url = https://web.archive.org/web/20120418231343/https://fas.org/spp/military/docops/army/ref_text/chap5im.htm|publisher = [[United States Army]]|quote = '''Where Space Begins''': There is no formal definition of where space begins. International law, based on a review of current treaties, conventions, agreements and tradition, defines the lower boundary of space as the lowest perigee attainable by an orbiting space vehicle. A specific altitude is not mentioned. By international law standards aircraft, missiles and rockets flying over a country are considered to be in its national airspace, regardless of altitude. Orbiting spacecraft are considered to be in space, regardless of altitude. <br />'''U.S. definition''': The U.S. government defines space in the same terms as international law.}}</ref>  This is the definition adopted by the U.S. military.<ref>{{cite book|title = U.S. Military Space Reference Text|year = 2006|publisher = [[National Security Space Institute]]|author = [[National Security Space Institute]] in conjunction with [[U.S. Army Command and General Staff College]] |access-date=April 1, 2019 |url = https://www.hsdl.org/?view&did=724066|via = [[Homeland Security Digital Library]]}}</ref>{{rp|13}}  Due to atmospheric drag, the lowest altitude at which an object in a circular orbit can complete at least one full revolution without propulsion is approximately {{convert|150|km|mi|abbr=in}},<ref>{{cite conference |url=https://aerospace.csis.org/wp-content/uploads/2019/09/Where-is-Space_-And-Why-Does-That-Matter_.pdf |title=Where is Space? And Why Does That Matter?  |last1=Lal |first1=Bhavya |last2=Nightingale |first2=Emily |date=November 5, 2014 |publisher=Aerospace.csis.org |page=6 |conference=Space Traffic Management Conference}}</ref> whereas an object can maintain an [[elliptic orbit]] with [[perigee]] as low as about {{convert|90|km|mi|abbr=in}} without propulsion.{{Citation needed |date=August 2019 }} The U.S. government is resisting efforts to specify a precise regulatory boundary.<ref>{{cite journal |first=Matthew T. |last=King |year=2016 |title=Sovereignty's Gray Area: The Delimitation of Air and Space in the Context of Aerospace Vehicles and the Use of Force |journal=Journal of Air Law and Commerce |volume=81 |issue=3 |pages=377–497 [p. 432] |url=https://scholar.smu.edu/jalc/vol81/iss3/3 }}</ref><ref>{{cite web |quote=With respect to the question of the definition and delimitation of outer space, we have examined this issue carefully and have listened to the various statements delivered at this session. Our position continues to be that defining or delimiting outer space is not necessary. No legal or practical problems have arisen in the absence of such a definition. On the contrary, the differing legal regimes applicable in respect of airspace and outer space have operated well in their respective spheres. The lack of a definition or delimitation of outer space has not impeded the development of activities in either sphere. |title=Delegation of the U.S., Statement on the Definition and Delimitation of Outer Space and the Character and Utilization of the Geostationary Orbit, to the Comm. on the Peaceful Uses of Outer Space, Legal Subcomm. of Its Fortieth Session (Apr. 2–13, 2001) |url=https://2009-2017.state.gov/s/l/22718.htm |archive-date=2020-03-28 |archive-url=https://web.archive.org/web/20200328061029/https://2009-2017.state.gov/s/l/22718.htm |access-date=2019-11-21 |url-status=live }}</ref>

== For other planets ==
While the Kármán line is defined for Earth only, several scientists have estimated the corresponding figures for [[Mars]] and [[Venus]]. Isidoro Martínez arrived at {{convert|80|km|mi|abbr=in}} and {{convert|250|km|mi|abbr=in}} high, respectively,<ref>Martínez, Isidoro; [http://webserver.dmt.upm.es/~isidoro/tc3/Space%20environment.pdf ''Space Environment''] {{Webarchive|url=https://web.archive.org/web/20210709182530/http://webserver.dmt.upm.es/~isidoro/tc3/Space%20environment.pdf |date=2021-07-09 }}, 2021</ref> while Nicolas Bérend arrived at {{convert|113|km|mi|abbr=in}} and {{convert|303|km|mi|abbr=in}}.<ref>A variant of the Kármán line theory facilitating the identification of a precise altitude boundary. International Astronautical Congress 2022,Nicolas Bérend, Sep 2022, Paris, France. [https://hal.science/hal-03798830v2 HAL Id:hal-03798830]</ref>

==In popular culture==
In 2014, Oscar Sharp directed ''The Kármán Line'', a British live-action drama short film starring [[Olivia Colman]] as Sarah, a wife and mother who suddenly starts levitating until she slowly and eventually crosses the eponymous Kármán line and into outer space.<ref>{{cite magazine | url=https://www.newyorker.com/culture/sarah-larson/the-screening-room-the-karman-line | title=The Screening Room: "The Kármán Line" | magazine=The New Yorker | date=7 May 2015 | last1=Larson | first1=Sarah }}</ref>

== See also ==
* {{annotated link|Armstrong limit}}
* {{vimeo|457049772|The Kármán Line - starring Olivia Colman}}

== References ==
{{reflist|30em}}

== External links ==
* [https://web.archive.org/web/20110809093537/http://www.fai.org/astronautics/100km.asp Article on the Kármán line] at the FAI website
* [http://www.srh.noaa.gov/srh/jetstream/atmos/layers.htm Layers of the Atmosphere – NOAA] {{Webarchive|url=https://web.archive.org/web/20051219190158/http://www.srh.noaa.gov/srh/jetstream/atmos/layers.htm |date=2005-12-19 }}
* [https://www.youtube.com/watch?v=ztjYDHO6HVU "The Kármán Line"] music video featuring NASA footage
* [http://www.fxsolver.com/browse/formulas/Karman+line+%28lift+force%29 Kármán line calculator]
{{Portal bar|Spaceflight|Outer space |Ecology|Solar System|World }}
{{Earth's atmosphere}}
{{Extreme motion}}

{{DEFAULTSORT:Karman line}}
[[Category:Aerospace]]
[[Category:Atmospheric boundaries]]
[[Category:Eponyms]]
[[Category:Outer space]]
[[Category:Eponymous border lines]]