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{{short description|Highly elliptical and highly inclined synchronous orbit}}
{{good article}}
[[File:Animation of Tundra orbit.gif|thumb|300px|Animation of two Tundra orbits with inclination of 63.4° and different eccentricities. The apparent loop is due to the use of an [[ECEF|Earth fixed frame]], co-rotating during [[diurnal motion]]; the Tundra orbits are simple ellipses in an [[Earth-centered inertial]] frame. {{legend2|Cyan|0.2 eccentricity}}{{·}}{{legend2|OrangeRed|0.3 eccentricity}}{{·}}{{legend2|RoyalBlue|Earth}}]]

A '''Tundra orbit''' ({{langx|ru|орбита «Тундра»}}) is a [[highly elliptical orbit|highly elliptical]] [[geosynchronous orbit]] with a high [[inclination]] (approximately 63.4°), an [[orbital period]] of one [[sidereal day]], and a typical [[orbital eccentricity|eccentricity]] between 0.2 and 0.3. A [[satellite]] placed in this orbit spends most of its time over a chosen area of the [[Earth]], a phenomenon known as [[Apsis|apogee dwell]], which makes them particularly well suited for [[Communications satellite|communications satellites]] serving high-latitude regions. 

The Tundra orbit, like the Molniya orbit, was developed by Soviet scientists. The Molniya orbit was specifically designed in the 1960s to provide better communication coverage for high-latitude regions, which geostationary satellites struggled to cover effectively. The Tundra orbit, while similar in its high inclination and elliptical shape, was developed later to offer continuous coverage over specific areas by having satellites spend most of their time over a chosen region. Both orbits were innovative solutions to the unique challenges posed by the Soviet Union's geographical location and the need for reliable communication and surveillance capabilities.

The [[ground track]] of a satellite in a Tundra orbit is a closed figure 8 with a smaller loop over either the northern or southern hemisphere.<ref name="fortescue">{{cite book |first1= P. W. |last1= Fortescue |first2= L. J. |last2= Mottershead |first3= G. |last3= Swinerd |first4= J. P. W. |last4= Stark |title= Spacecraft Systems Engineering |publisher= John Wiley and Sons |date= 2003 |chapter= Section 5.7: highly elliptic orbits |isbn= 978-0-471-61951-2}}</ref><ref>{{Cite book |url=https://books.google.com/books?id=s2FgDwAAQBAJ&pg=PT203 |title=The Universe Today Ultimate Guide to Viewing The Cosmos: Everything You Need to Know to Become an Amateur Astronomer |last=Dickinson |first=David |date=2018 |publisher=Page Street Publishing |isbn=9781624145452 |pages=203 |language=en}}</ref> This differentiates them from [[Molniya orbit]]s designed to service high-latitude regions, which have the same inclination but half the period and do not loiter over a single region.<ref name="jenkin">{{cite conference |title=Tundra Disposal Orbit Study |surname1=Jenkin |given1=A. B. |surname2=McVey |given2=J. P. |surname3=Wilson |given3=J. R. |surname4=Sorge |given4=M. E. |date=2017 |publisher=ESA Space Debris Office |conference=7th European Conference on Space Debris |url=https://conference.sdo.esoc.esa.int/proceedings/sdc7/paper/328 |access-date=2017-10-02 |archive-url=https://web.archive.org/web/20171002121240/https://conference.sdo.esoc.esa.int/proceedings/sdc7/paper/328 |archive-date=2017-10-02 |url-status=dead}}</ref><ref name="flower-constellations">{{cite report |url=http://aeweb.tamu.edu/mortari/pubbl/2004/The%20Flower%20Constellations.pdf |title=The Flower Constellations |date=2004 |page=4 |surname1=Mortari |given1=D. |surname2=Wilkins |given2=M. P. |surname3=Bruccoleri |given3=C. |access-date=2017-10-02 |archive-url=https://web.archive.org/web/20170809032805/http://aeweb.tamu.edu/mortari/pubbl/2004/The%20Flower%20Constellations.pdf |archive-date=2017-08-09 |url-status=dead }}</ref>

==Uses==
Tundra and [[Molniya_orbit|Molniya]] orbits are used to provide high-[[latitude]] users with higher [[elevation (astronomy)|elevation]] angles than a [[geostationary orbit]]. This is desirable as broadcasting to these latitudes from a geostationary orbit (above the Earth's [[equator]]) requires considerable power due to the low [[angle of incidence (optics)|elevation angles]], and the extra distance and atmospheric attenuation that comes with it. Sites located above 81° latitude are unable to view geocentric satellites at all, and as a rule of thumb, elevation angles of less than 10° can cause problems, depending on the communications frequency.<ref name="gsmo">{{cite book|url=https://books.google.com/books?id=K9Q5DwAAQBAJ&pg=PA57|title=Global Satellite Meteorological Observation (GSMO) Theory|volume=1|publisher=Springer International Publishing|isbn=978-3-319-67119-2|first=Stojče Dimov |last=Ilčev|page=57|date=2017|access-date=16 April 2019|bibcode=2018gsmo.book.....I}}</ref>{{rp|499}}<ref>{{cite journal|url=http://www.ngs.noaa.gov/CORS/Articles/SolerEisemannJSE.pdf|page=123|title=Determination of Look Angles To Geostationary Communication Satellites|first1=Tomás|last1=Soler|first2=David W.|last2=Eisemann|journal=Journal of Surveying Engineering|volume=120|date=August 1994|issue=3|issn=0733-9453|access-date=16 April 2019|doi=10.1061/(ASCE)0733-9453(1994)120:3(115)|archive-url=https://web.archive.org/web/20160304084630/http://www.ngs.noaa.gov/CORS/Articles/SolerEisemannJSE.pdf|archive-date=4 March 2016|url-status=live}}</ref>

Highly elliptical orbits provide an alternative to geostationary ones, as they remain over their desired high-latitude regions for long periods of time at the apogee. Their convenience is mitigated by cost, however: two satellites are required to provide continuous coverage from a Tundra orbit (three from a Molniya orbit).<ref name="jenkin"/> 

A ground station receiving data from a satellite constellation in a highly elliptical orbit must periodically switch between satellites and deal with varying signal strengths, latency and [[Doppler shift]]s as the satellite's range changes throughout its orbit. These changes are less pronounced for satellites in a Tundra orbit, given their increased distance from the surface, making tracking and communication more efficient.<ref name="scs"/> Additionally, unlike the Molniya orbit, a satellite in a Tundra orbit avoids passing through the [[Van Allen belts]].<ref name=satellites>{{cite book|url=https://books.google.com/books?id=BAihdjtLZXcC&q=tundra+&pg=PA189 |page=228|title=Satellites|isbn=9782287213175|last1=Capderou|first1=Michel|year=2005|publisher=Springer }}</ref>

Despite these advantages the Tundra orbit is used less often than a Molniya orbit<ref name=satellites/> in part due to the higher launch energy required.<ref name="fortescue"/> 

===Proposed uses===
In 2017 the [[ESA]] Space Debris office released a paper proposing that a Tundra-like orbit be used as a disposal orbit for old high-inclination geosynchronous satellites, as opposed to traditional [[graveyard orbit]]s.<ref name="jenkin"/>

==Properties==
A typical<ref name="scs">{{cite book|url=https://books.google.com/books?id=PEsmLaDXzvsC&q=perturbations+and+control+of+tundra+orbits&pg=PT110 |section=2.2.1.2 Tundra Orbits |isbn=9781119965091 |title=Satellite Communications Systems: Systems, Techniques and Technology|last1=Maral |first1=Gerard |last2=Bousquet |first2=Michel |date=2011-08-24 |publisher=John Wiley & Sons }}</ref> Tundra orbit has the following properties:

* Inclination: 63.4°
* Argument of perigee: 270°
* Period: 1436 minutes
* Eccentricity: 0.24–0.4
* Semi-major axis: {{Convert|42164|km|mi|abbr=on}}

===Orbital inclination===
In general, the [[oblate spheroid|oblateness]] of the Earth perturbs a satellite's [[argument of perigee]] (<math>\omega</math>) such that it gradually changes with time.<ref name="fortescue"/> If we only consider the first-order coefficient <math>J_2</math>, the perigee will change according to equation {{EquationNote|1}}, unless it is constantly corrected with station-keeping thruster burns.

{{NumBlk|:|<math>\dot{\omega} = \frac{3}{4} n J_2\left(\frac{R_E}{a}\right)^2 \frac{4 - 5\sin^2 i}{(1 - e^2)^2},</math>|{{EquationRef|1}}}}

where <math>i</math> is the orbital inclination, <math>e</math> is the eccentricity, <math>n</math> is mean motion in degrees per day, <math>J_2</math> is the perturbing factor, <math>R_E</math> is the radius of the Earth, <math>a</math> is the semimajor axis, and <math>\dot{\omega}</math> is in degrees per day.

To avoid this expenditure of fuel, the Tundra orbit uses an inclination of 63.4°, for which the factor <math>(4 - 5\sin^2 i)</math> is zero, so that there is no change in the position of perigee over time.<ref name="art">{{cite journal |page=517 |date=18 August 1989 |journal=Journal of Atmospheric and Oceanic Technology |volume=7 |title=On the Use of Satellites in Molniya Orbits of Meteorological Observation of Middle and High Latitudes |first1=Stanley Q. |last1=Kidder |first2=Thomas H. |last2=Vonder Haar |issue=3 |doi=10.1175/1520-0426(1990)007<0517:OTUOSI>2.0.CO;2 |bibcode=1990JAtOT...7..517K |doi-access=free }}</ref><ref name="smad">{{cite book |title=Space Mission Analysis and Design |publisher=Microcosm Press and Kluwer Academic Publishers |editor1-first=Wiley J. |editor1-last=Larson |editor2-first=James R. |editor2-last=Wertz |bibcode=1999smad.book.....W |last1=Wertz |first1=James Richard |last2=Larson |first2=Wiley J. |year=1999 |isbn=978-1-881883-10-4}}</ref>{{rp|143}}<ref name="scs"/> This is called the critical inclination, and an orbit designed in this manner is called a [[frozen orbit]].

===Argument of perigee===
An [[argument of perigee]] of 270° places apogee at the northernmost point of the orbit. An argument of perigee of 90° would likewise serve the high southern latitudes. An argument of perigee of 0° or 180° would cause the satellite to dwell over the equator, but there would be little point to this as this could be better done with a conventional [[geostationary orbit]].<ref name="scs"/>

===Period===
The period of one sidereal day ensures that the satellites follows the same ground track over time. This is controlled by the semi-major axis of the orbit.<ref name="scs"/>

===Eccentricity===
The eccentricity is chosen for the dwell time required, and changes the shape of the ground track. A '''Tundra''' orbit generally has an eccentricity of about 0.2; one with an eccentricity of about 0.4, changing the ground track from a figure 8 to a teardrop, is called a '''Supertundra''' orbit.<ref>{{cite book|url=http://fgg-web.fgg.uni-lj.si/~/mkuhar/Pouk/SG/Seminar/Vrste_tirnic_um_Zemljinih_sat/Orbit_and_Ground_Track_of_a_Satellite-Capderou2005.pdf|page=224|isbn=978-2-287-27469-5|title=Satellites: Orbits and Missions|last1=Capderou|first1=Michel|date=2006-01-16|publisher=Springer |access-date=2019-04-30|archive-url=https://web.archive.org/web/20180517031908/http://fgg-web.fgg.uni-lj.si/~/mkuhar/Pouk/SG/Seminar/Vrste_tirnic_um_Zemljinih_sat/Orbit_and_Ground_Track_of_a_Satellite-Capderou2005.pdf|archive-date=2018-05-17|url-status=live}}</ref>

===Semi-major axis===
The exact height of a satellite in a Tundra orbit varies between missions, but a typical orbit will have a perigee of approximately {{Convert|25,000|km|mi}} and an apogee of {{Convert|39700|km|mi}}, for a semi-major axis of {{Convert|46,000|km|mi}}.<ref name="scs"/>

==Spacecraft using Tundra orbits==
[[File:Qzss-45-0.09.jpg|thumb|upright|The groundtrack of [[QZSS]] orbit, which has similar characteristics to a Tundra orbit, but a lower inclination]]

Russia currently uses satellites in the Tundra orbit. The EKS (Edinaya Kosmicheskaya Sistema) or Kupol system, which is part of Russia's early warning satellite network, includes satellites that operate in Tundra orbits. These satellites are designed to detect and track ballistic missile launches and provide early warning of potential missile attacks.

From 2000 to 2016, [[Sirius Satellite Radio]], now part of [[Sirius XM Holdings]], operated a [[satellite constellation|constellation]] of three satellites in Tundra orbits for [[satellite radio]].<ref name="Sirius Launch">{{cite web
  |title=Sirius Rising: Proton-M Ready to Launch Digital Radio Satellite Into Orbit
  |url=http://www.americaspace.com/2013/10/18/sirius-rising-proton-m-ready-to-launch-digital-radio-satellite-into-orbit/
  |website=AmericaSpace
  |access-date=8 July 2017
  |date=2013-10-18
  |archive-url=https://web.archive.org/web/20170628043459/http://www.americaspace.com/2013/10/18/sirius-rising-proton-m-ready-to-launch-digital-radio-satellite-into-orbit/
  |archive-date=28 June 2017
  |url-status=live
  }}</ref><ref name="hso">{{cite book|url=https://books.google.com/books?id=1_68BAAAQBAJ&q=+tundra+&pg=PA395|page=290|title=Handbook of Satellite Orbits: From Kepler to GPS|isbn=9783319034164|last1=Capderou|first1=Michel|date=2014-04-23|publisher=Springer |bibcode=2014hso..book.....C}}</ref> The [[Longitude of the ascending node|RAAN]] and [[mean anomaly]] of each satellite were offset by 120° so that when one satellite moved out of position, another had passed perigee and was ready to take over. The constellation was developed to better reach consumers in far northern latitudes, reduce the impact of [[urban canyons]] and required only 130 repeaters compared to 800 for a geostationary system. After Sirius' merger with [[XM]] it changed the design and orbit of the FM-6 replacement satellite from a tundra to a geostationary one.<ref>{{Cite web|url=https://spacenews.com/sirius-xm-needs-install-600-new-ground-repeaters/|first=Peter B. de|last=Selding|title=Sirius XM Needs To Install 600 New Ground Repeaters|date=October 5, 2012|website=SpaceNews.com}}</ref><ref>{{Cite web|url=https://www.smithsonianmag.com/smithsonian-institution/sirius-satellite-comes-to-udvar-hazy-91167868/|title=Sirius Satellite Comes to Udvar-Hazy|first=Leah|last=Binkovitz|website=Smithsonian|date=24 October 2012|access-date=8 May 2019|archive-url=https://web.archive.org/web/20190508135434/https://www.smithsonianmag.com/smithsonian-institution/sirius-satellite-comes-to-udvar-hazy-91167868/|archive-date=8 May 2019|url-status=live}}</ref> This supplemented the already geostationary FM-5 (launched 2009),<ref>{{Cite web|url=https://www.space.com/6909-sirius-xm-radio-satellite-launches-orbit.html|title=New Sirius XM Radio Satellite Launches to Orbit|first=Stephen|last=Clark|date=30 June 2009|website=Space.com|access-date=8 May 2019|archive-url=https://web.archive.org/web/20190508135437/https://www.space.com/6909-sirius-xm-radio-satellite-launches-orbit.html|archive-date=8 May 2019|url-status=live}}</ref> and in 2016 Sirius discontinued broadcasting from tundra orbits.<ref>{{Cite report
  |url=http://licensing.fcc.gov/myibfs/download.do?attachment_key=782032
  |title=Application for Modification
  |publisher=[[Federal Communications Commission]]
  |author=Wiley Rein
  |date=19 November 2009
  |access-date=2 February 2017
  |archive-url=https://web.archive.org/web/20171002123032/http://licensing.fcc.gov/myibfs/download.do?attachment_key=782032
  |archive-date=2 October 2017
  |url-status=live
  }}</ref><ref>{{Cite report |url=http://d1lge852tjjqow.cloudfront.net/CIK-0000908937/57ed9586-d67e-45d0-b999-a358fe698edb.pdf |title=Sirius XM Holdings 10-K 2015 Annual Report |publisher=Sirius XM Holdings |editor-first=James E. |editor-last=Meyer |editor2-first=David J. |editor2-last=Frear |date=2 February 2016 |access-date=2 February 2017 |archive-url=https://web.archive.org/web/20160829021731/http://d1lge852tjjqow.cloudfront.net/CIK-0000908937/57ed9586-d67e-45d0-b999-a358fe698edb.pdf |archive-date=29 August 2016 |url-status=live }}</ref><ref>{{Cite report|url=https://seekingalpha.com/filing/3381845|title=Sirius XM Holdings Inc. 10-K Feb. 2, 2017 11:57 AM|website=Seeking Alpha |publisher=Sirius XM Holdings Inc. |date=2 February 2017|editor-first=James E. |editor-last=Meyer |editor2-first=David J. |editor2-last=Frear}}</ref> The Sirius satellites were the only commercial satellites to use a Tundra orbit.<ref>{{Cite journal |doi = 10.2514/1.7765|title = Tundra Constellation Design and Stationkeeping|journal = Journal of Spacecraft and Rockets|volume = 42|issue = 5|pages = 902–912|year = 2005|last1 = Bruno|first1 = Michael J.|last2 = Pernicka|first2 = Henry J.|bibcode = 2005JSpRo..42..902B|url = https://scholarworks.sjsu.edu/cgi/viewcontent.cgi?article=3538&context=etd_theses}}</ref>

The Japanese [[Quasi-Zenith Satellite System]] uses a geosynchronous orbit similar to a Tundra orbit, but with an inclination of only 43°. It includes four satellites following the same ground track. It was tested from 2010 and became fully operational in November 2018.<ref name=QZSO>{{Cite web |url=http://qzss.go.jp/en/technical/technology/orbit.html |title=Quasi-Zenith Satellite Orbit (QZO) |access-date=2018-03-10 |archive-url=https://web.archive.org/web/20180309194252/http://qzss.go.jp/en/technical/technology/orbit.html |archive-date=2018-03-09 |url-status=live }}</ref>

===Proposed systems===
The Tundra orbit has been considered for use by the [[ESA]]'s Archimedes project, a broadcasting system proposed in the 1990s.<ref name="hso"/><ref>{{Cite book |doi = 10.1007/978-1-4471-1516-8_13|chapter = Digital Audio Broadcasting (DAB) via Archimedes/Media ''Star'' HEO-Satellites|title = Mobile and Personal Satellite Communications 2|pages = 150–161|year = 1996|last1 = Hoeher|first1 = P.|last2 = Schweikert|first2 = R.|last3 = Woerz|first3 = T.|last4 = Schmidbauer|first4 = A.|last5 = Frank|first5 = J.|last6 = Grosskopf|first6 = R.|last7 = Schramm|first7 = R.|last8 = Gale|first8 = F. C. T.|last9 = Harris|first9 = R. A.|isbn = 978-3-540-76111-2}}</ref>

{{multiple image
| align = left
| direction = horizontal
| width = 240
| header = Comparison of Tundra orbit, [[Quasi-Zenith Satellite System|QZSS orbit]] and [[Molniya orbit]] - equatorial view
| image1 = Animation of Tundra and QZSS orbit - front view.gif
| caption1 = Front view
| image2 = Animation of Tundra and QZSS orbit - side view.gif
| caption2 =  Side view
| image3 = Animation of Tundra and QZSS orbit - ECEF - front view.gif
| caption3 = Front view, [[ECEF|Earth fixed frame]]
| image4 = Animation of Tundra and QZSS orbit - ECEF - side view.gif
| caption4 =  Side view, [[ECEF|Earth fixed frame]]
| footer = {{legend2| OrangeRed | Tundra orbit}}{{·}}{{legend2|Lime| QZSS orbit}}{{·}}{{legend2|Cyan|Molniya orbit}}{{·}}{{legend2|RoyalBlue|Earth}}}}
{{clear}}

==See also==
* [[Elliptic orbit]]
* [[List of orbits]]
* [[Molniya orbit]]
{{clear}}

==References==
{{Reflist}}

{{orbits}}
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