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A tundra orbit (Russian: Тундра) is a highly elliptical geosynchronous orbit with a high inclination (usually near 63.4°) and an orbital period of one sidereal day. A satellite placed in this orbit spends most of its time over a chosen area of the Earth, a phenomenon known as apogee dwell. The ground track of a satellite in a Tundra orbit is a closed figure-eight with a smaller loop over either the northern or southern hemisphere. Tundra orbits have moderate eccentricity, typically between 0.2 and 0.3. These orbits are conceptually similar to Molniya orbits, which have the same inclination but half the period.^[1]^[2]^[3]

Uses

Tundra and Molniya orbits are used to provide high-latitude users with higher 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 elevation angles, and the extra distance and atmospheric attenuation that comes with it. Sites located about 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.^[4]^: 499^[5]

These orbits remain over their desired high-latitude regions for long periods of time due to their elliptical orbits. They have a slow movement at apogee, which reduces the time that the satellite is away from its service area.^[1]

A groundstation recieving data from a satellite constellation in a Tundra orbits must periodically switch between satellites and deal with varying signal strengths, latency and doppler shifts as the satellites range changes throughout its orbit.^[6]

Two spacecraft in Tundra orbits are able to provide continuous coverage over an area, as opposed to three for a Molniya orbit.^[2] Unlike the Molniya orbit, it avoids passing through the Van Allen belts, but at the expense of a higher launch energy.^[1]

Properties

A typical Tundra orbit has the following properties:

Inclination: 63.4°
Period: 1436 minutes
Eccentricity: 0.24 - 0.4
Semi-major axis: 42,164 km (26,199 mi)
Perigee: 25,000 km
Apogee: 46,000 km^[6]

Orbital inclination

In general, the oblateness of the Earth perturbs the argument of perigee ( $\omega$ ), so that it gradually changes with time.^[1] If we only consider the first-order coefficient $J_{2}$ , the perigee will change according to equation 1, unless it is constantly corrected with station-keeping thruster burns.

{\dot {\omega }}={\frac {3}{4}}\;nJ_{2}({\frac {R_{E}}{a}})^{2}{\frac {(4-5\sin ^{2}{i})}{(1-e^{2})^{2}}}

(1)

where $i$ is the orbital inclination, $e$ is the eccentricity, $n$ is mean motion in degrees per day, $J_{2}$ is the perturbing factor, $R_{E}$ is the radius of the earth, $a$ is the semimajor axis, and ${\dot {\omega }}$ is in degrees per day.

To avoid this expenditure of fuel, the Tundra orbit uses an inclination of 63.4°, for which the factor $(4-5\sin ^{2}{i})$ is zero, so that there is no change in the position of perigee over time.^[7]^[8]^: 143^[6] 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.

Spacecraft using Tundra orbits

Until 2016, Sirius Satellite Radio, now part of Sirius XM Holdings, operated a constellation of three satellites in Tundra orbits for satellite radio.^[9] The 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 three satellites were launched in 2000 and moved into circular disposal orbits in 2016; Sirius XM now broadcasts only from geostationary satellites.^[10]^[11]^[12]

In November 2018, Russian Glonass announced plans to launch six Glonass-V satellites into two Tundra orbits in 2023-2025 timeframe.

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 forming a single ground track. It was tested from 2010 and became fully operational in November 2018.

References

^ ^a ^b ^c ^d Fortescue, P.W.; Mottershead, L.J.; Swinerd, G.; Stark, J.P.W. (2003). "Section 5.7: highly elliptic orbits". Spacecraft Systems Engineering. John Wiley and Sons. ISBN 0-471-61951-5.
^ ^a ^b Jenkin, A.B.; McVey, J.P.; Wilson, J.R.; Sorge, M.E. (2017). Tundra Disposal Orbit Study. 7th European Conference on Space Debris. ESA Space Debris Office.
^ Mortari, D.; Wilkins, M.P.; Bruccoleri, C. (2004). "The Flower Constellations" (PDF): 4. {{cite journal}}: Cite journal requires |journal= (help)
^ Ilčev, Stojče Dimov (2017). Global Satellite Meteorological Observation (GSMO) Theory. Vol. 1. Springer International Publishing. p. 57. ISBN 3-319-67119-7. Retrieved 16 April 2019.
^ Template:Cite article
^ ^a ^b ^c "2.2.1.2 Tundra Orbits". Satellite Communications Systems: Systems, Techniques and Technology. ISBN 9781119965091.
^ Template:Cite article
^ Wertz, James Richard; Larson, Wiley J. (1999). Larson, Wiley J.; Wertz, James R. (eds.). Space Mission Analysis and Design. Microcosm Press and Kluwer Academic Publishers. Bibcode:1999smad.book.....W. ISBN 1-881883-10-8.
^ "Sirius Rising: Proton-M Ready to Launch Digital Radio Satellite Into Orbit". AmericaSpace. Retrieved 8 July 2017.
^ "Application for Modification". Federal Communications Commission.
^ "Sirius XM Holdings 10-K 2015 Annual Report" (PDF).
^ "Sirius XM Holdings 10-K 2016 Annual Report".

[fortescue-1] Fortescue, P.W.; Mottershead, L.J.; Swinerd, G.; Stark, J.P.W. (2003). "Section 5.7: highly elliptic orbits". Spacecraft Systems Engineering. John Wiley and Sons. ISBN 0-471-61951-5.

[jenkin-2] Jenkin, A.B.; McVey, J.P.; Wilson, J.R.; Sorge, M.E. (2017). Tundra Disposal Orbit Study. 7th European Conference on Space Debris. ESA Space Debris Office.

[flower-constellations-3] Mortari, D.; Wilkins, M.P.; Bruccoleri, C. (2004). "The Flower Constellations" (PDF): 4. {{cite journal}}: Cite journal requires |journal= (help)

[gsmo-4] Ilčev, Stojče Dimov (2017). Global Satellite Meteorological Observation (GSMO) Theory. Vol. 1. Springer International Publishing. p. 57. ISBN 3-319-67119-7. Retrieved 16 April 2019.

[5] Template:Cite article

[scs-6] "2.2.1.2 Tundra Orbits". Satellite Communications Systems: Systems, Techniques and Technology. ISBN 9781119965091.

[art-7] Template:Cite article

[smad-8] Wertz, James Richard; Larson, Wiley J. (1999). Larson, Wiley J.; Wertz, James R. (eds.). Space Mission Analysis and Design. Microcosm Press and Kluwer Academic Publishers. Bibcode:1999smad.book.....W. ISBN 1-881883-10-8.

[Sirius_Launch-9] "Sirius Rising: Proton-M Ready to Launch Digital Radio Satellite Into Orbit". AmericaSpace. Retrieved 8 July 2017.

[10] "Application for Modification". Federal Communications Commission.

[11] "Sirius XM Holdings 10-K 2015 Annual Report" (PDF).

[12] "Sirius XM Holdings 10-K 2016 Annual Report".

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@@ Line 11: / Line 11: @@
 }}</ref>
+==Uses==
-Two spacecraft in Tundra orbits are able to provide continuous coverage over an area.<ref name="fortescue"/><ref name="jenkin"/>
+Tundra and 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 about 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=3-319-67119-7|first=Stojče Dimov |last=Ilčev|page=57|date=2017|access-date=16 April 2019}}</ref>{{rp|499}}<ref>{{cite article|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|issn=0733-9453|access-date=16 April 2019|doi=10.1061/(ASCE)0733-9453(1994)120:3(115)}}</ref>
+These orbits remain over their desired high-latitude regions for long periods of time due to their elliptical orbits. They have a slow movement at apogee, which reduces the time that the satellite is away from its service area.<ref name="fortescue"/>
-Tundra and Molniya orbits are used to provide high-[[latitude]] users with higher [[elevation (astronomy)|elevation]] angles than a geostationary orbit.  These orbits remain over their desired high-latitude regions for long periods of time due to their slow movement at apogee.<ref name="fortescue"/>  Neither the Tundra nor Molniya orbit is geostationary because that is possible only over the equator, so both orbits are elliptical to reduce the time that the satellite is away from its service area. 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]].
+A groundstation recieving data from a satellite constellation in a Tundra orbits must periodically switch between satellites and deal with varying signal strengths, latency and doppler shifts as the satellites range changes throughout its orbit.<ref name="scs"/>
-The Tundra and Molniya orbits use a {{math|sin<sup>−1</sup> {{radical|4/5}} ≈ 63.4°}} inclination to null the [[orbital perturbation analysis (spacecraft)|secular perturbation]] of the argument of perigee caused by the Earth's equatorial bulge. With any inclination other than 63.4° or its supplement, 116.6°, the argument of perigee would change steadily over time, and apogee would occur either before or after the highest latitude is reached.<ref name="fortescue"/>
+Two spacecraft in Tundra orbits are able to provide continuous coverage over an area, as opposed to three for a Molniya orbit.<ref name="jenkin"/> Unlike the Molniya orbit, it avoids passing through the [[Van Allen belts]], but at the expense of a higher launch energy.<ref name="fortescue"/>
-==Users==
-Tundra orbit can be used by global navigation systems to improve regional availability. The Japanese [[Quasi-Zenith Satellite System]] includes four satellites forming a single ground track. It was tested from 2010 and became fully operational in November 2018. The same November 2018, Russian [[Glonass]] announced plans to launch six [[Glonass-V]] satellites into two Tundra orbits in 2023-2025 timeframe.
+==Properties==
+A typical Tundra orbit has the following properties:
+* Inclination: 63.4°
+* Period: 1436 minutes
+* Eccentricity: 0.24 - 0.4
+* Semi-major axis: {{Convert|42164|km|mi|abbr=on}}
+* Perigee: 25,000 km
+* Apogee: 46,000 km<ref name="scs">{{cite book|url=https://books.google.com.au/books?id=PEsmLaDXzvsC&pg=PT110&dq=perturbations+and+control+of+tundra+orbits&hl=en&sa=X&ved=0ahUKEwiUiYCr2OXhAhVMWisKHUt2D68Q6AEIPjAE#v=onepage&q=perturbations%20and%20control%20of%20tundra%20orbits&f=false |section=2.2.1.2 Tundra Orbits |isbn=9781119965091 |title=Satellite Communications Systems: Systems, Techniques and Technology}}</ref>
+===Orbital inclination===
+In general, the [[oblate spheroid|oblateness]] of the Earth [[Orbital perturbation analysis|perturbs the argument of perigee]] (<math>\omega</math>), so 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(\frac{R_E}{a})^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 article|url=https://journals.ametsoc.org/doi/pdf/10.1175/1520-0426%281990%29007%3C0517%3AOTUOSI%3E2.0.CO%3B2 |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|doi=10.1175/1520-0426(1990)007<0517:OTUOSI>2.0.CO;2}}</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=1-881883-10-8}}</ref>{{rp|143}}<ref name="scs"/> 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]].
+==Spacecraft using Tundra orbits==
 Until 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
@@ Line 35: / Line 58: @@
   |title=Sirius XM Holdings 10-K 2016 Annual Report
 }}</ref>
+In November 2018, Russian [[Glonass]] announced plans to launch six [[Glonass-V]] satellites into two Tundra orbits in 2023-2025 timeframe.
+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 forming a single ground track. It was tested from 2010 and became fully operational in November 2018.
 ==See also==