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Tundra orbit

## Summary

Animation of Tundra orbit. inclination = 63.4°
Eccentricity: 0.2 ·    Eccentricity: 0.3 ·   Earth

A Tundra orbit (Russian: Орбита «Тундра») is a highly elliptical geosynchronous orbit with a high inclination (approximately 63.4°), an orbital period of one sidereal day, and a typical 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 apogee dwell, which makes them particularly well suited for communications satellites serving high latitude regions. 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.[1][2] This differentiates them from Molniya orbits designed to service high-latitude regions, which have the same inclination but half the period and do not loiter over a single region.[3][4]

## 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 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.[5]:499[6]

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).[3]

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 shifts as the satellites 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.[7] Additionally, unlike the Molniya orbit, a satellite in a Tundra orbit avoids passing through the Van Allen belts.[8]

Despite these advantages the Tundra orbit is used less often than a Molniya orbit[8] in part due to the higher launch energy required.[1]

### 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 orbits.[3]

## Properties

A typical[7] Tundra orbit has the following properties:

• Inclination: 63.4°
• Argument of perigee: 270°
• Period: 1436 minutes
• Eccentricity: 0.24–0.4
• Semi-major axis: 42,164 km (26,199 mi)

### Orbital inclination

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

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

(1)

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

To avoid this expenditure of fuel, the Tundra orbit uses an inclination of 63.4°, for which the factor ${\displaystyle (4-5\sin ^{2}{i})}$ is zero, so that there is no change in the position of perigee over time.[9][10]:143[7] 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.[7]

### 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.[7]

### 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.[11]

### 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 25,000 kilometres (16,000 mi) and an apogee of 39,700 kilometres (24,700 mi), for a semi-major axis of 46,000 kilometres (29,000 mi).[7]

## Spacecraft using Tundra orbits

The groundtrack of QZSS orbit, which has similar characteristics to a Tundra orbit, but a lower inclination

From 2000 to 2016, Sirius Satellite Radio, now part of Sirius XM Holdings, operated a constellation of three satellites in Tundra orbits for satellite radio.[12][13] 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 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.[14][15] This supplemented the already geostationary FM-5 (launched 2009),[16] and in 2016 Sirius discontinued broadcasting from tundra orbits.[17][18][19] The Sirius satellites were the only commercial satellites to use a Tundra orbit.[20]

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.[21]

### Proposed systems

The Tundra orbit has been considered for use by the ESA's Archimedes project, a broadcasting system proposed in the 1990s.[13][22]

Comparison of Tundra orbit, QZSS orbit and Molniya orbit - equatorial view
Front view
Side view
Earth fixed frame, Front view
Tundra orbit ·    QZSS orbit ·   Molniya orbit ·   Earth

## References

1. ^ a b c 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 978-0-471-61951-2.
2. ^ Dickinson, David (2018). The Universe Today Ultimate Guide to Viewing The Cosmos: Everything You Need to Know to Become an Amateur Astronomer. Page Street Publishing. p. 203. ISBN 9781624145452.
3. ^ a b c 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. Archived from the original on 2017-10-02. Retrieved 2017-10-02.
4. ^ Mortari, D.; Wilkins, M.P.; Bruccoleri, C. (2004). "The Flower Constellations" (PDF): 4. Archived (PDF) from the original on 2017-08-09. Retrieved 2017-10-02. Cite journal requires |journal= (help)
5. ^ Ilčev, Stojče Dimov (2017). Global Satellite Meteorological Observation (GSMO) Theory. 1. Springer International Publishing. p. 57. Bibcode:2018gsmo.book.....I. ISBN 978-3-319-67119-2. Retrieved 16 April 2019.
6. ^ Soler, Tomás; Eisemann, David W. (August 1994). "Determination of Look Angles To Geostationary Communication Satellites" (PDF). Journal of Surveying Engineering. 120 (3): 123. doi:10.1061/(ASCE)0733-9453(1994)120:3(115). ISSN 0733-9453. Archived (PDF) from the original on 4 March 2016. Retrieved 16 April 2019.
7. Maral, Gerard; Bousquet, Michel (2011-08-24). "2.2.1.2 Tundra Orbits". Satellite Communications Systems: Systems, Techniques and Technology. ISBN 9781119965091.
8. ^ a b Capderou, Michel (2005). Satellites. p. 228. ISBN 9782287213175.
9. ^ Kidder, Stanley Q.; Vonder Haar, Thomas H. (18 August 1989). "On the Use of Satellites in Molniya Orbits of Meteorological Observation of Middle and High Latitudes". Journal of Atmospheric and Oceanic Technology. 7 (3): 517. doi:10.1175/1520-0426(1990)007<0517:OTUOSI>2.0.CO;2.
10. ^ 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 978-1-881883-10-4.
11. ^ Capderou, Michel (2006-01-16). Satellites: Orbits and Missions (PDF). p. 224. ISBN 978-2-287-27469-5. Archived (PDF) from the original on 2018-05-17. Retrieved 2019-04-30.
12. ^ "Sirius Rising: Proton-M Ready to Launch Digital Radio Satellite Into Orbit". AmericaSpace. 2013-10-18. Archived from the original on 28 June 2017. Retrieved 8 July 2017.
13. ^ a b Capderou, Michel (2014-04-23). Handbook of Satellite Orbits: From Kepler to GPS. p. 290. Bibcode:2014hso..book.....C. ISBN 9783319034164.
14. ^ Selding, Peter B. de (October 5, 2012). "Sirius XM Needs To Install 600 New Ground Repeaters". SpaceNews.com.
15. ^ Binkovitz, Leah (24 October 2012). "Sirius Satellite Comes to Udvar-Hazy". Smithsonian. Archived from the original on 8 May 2019. Retrieved 8 May 2019.
16. ^ Clark, Stephen (30 June 2009). "New Sirius XM Radio Satellite Launches to Orbit". Space.com. Archived from the original on 8 May 2019. Retrieved 8 May 2019.
17. ^ Wiley Rein (19 November 2009). Application for Modification (Report). Federal Communications Commission. Archived from the original on 2 October 2017. Retrieved 2 February 2017.
18. ^ Meyer, James E.; Frear, David J., eds. (2 February 2016). Sirius XM Holdings 10-K 2015 Annual Report (PDF) (Report). Sirius XM Holdings. Archived (PDF) from the original on 29 August 2016. Retrieved 2 February 2017.
19. ^ Meyer, James E.; Frear, David J., eds. (2 February 2017). Sirius XM Holdings Inc. 10-K Feb. 2, 2017 11:57 AM. Seeking Alpha (Report). Sirius XM Holdings Inc.
20. ^ Bruno, Michael J.; Pernicka, Henry J. (2005). "Tundra Constellation Design and Stationkeeping". Journal of Spacecraft and Rockets. 42 (5): 902–912. Bibcode:2005JSpRo..42..902B. doi:10.2514/1.7765.
21. ^ "Quasi-Zenith Satellite Orbit (QZO)". Archived from the original on 2018-03-09. Retrieved 2018-03-10.
22. ^ Hoeher, P.; Schweikert, R.; Woerz, T.; Schmidbauer, A.; Frank, J.; Grosskopf, R.; Schramm, R.; Gale, F. C. T.; Harris, R. A. (1996). "Digital Audio Broadcasting (DAB) via Archimedes/Media Star HEO-Satellites". Mobile and Personal Satellite Communications 2. pp. 150–161. doi:10.1007/978-1-4471-1516-8_13. ISBN 978-3-540-76111-2.