# Tundra orbit

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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 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. [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.

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

(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

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
Front view, Earth fixed frame
Side view, Earth fixed frame
Tundra orbit ·   QZSS orbit ·  Molniya orbit ·  Earth

## Related Research Articles

A geosynchronous orbit is an Earth-centered orbit with an orbital period that matches Earth's rotation on its axis, 23 hours, 56 minutes, and 4 seconds. The synchronization of rotation and orbital period means that, for an observer on Earth's surface, an object in geosynchronous orbit returns to exactly the same position in the sky after a period of one sidereal day. Over the course of a day, the object's position in the sky may remain still or trace out a path, typically in a figure-8 form, whose precise characteristics depend on the orbit's inclination and eccentricity. A circular geosynchronous orbit has a constant altitude of 35,786 km (22,236 mi).

A geostationary orbit, also referred to as a geosynchronous equatorial orbit (GEO), is a circular geosynchronous orbit 35,786 km (22,236 mi) in altitude above Earth's Equator and following the direction of Earth's rotation.

A communications satellite is an artificial satellite that relays and amplifies radio telecommunication signals via a transponder; it creates a communication channel between a source transmitter and a receiver at different locations on Earth. Communications satellites are used for television, telephone, radio, internet, and military applications. As of 1 January 2021, there are 2,224 communications satellites in Earth orbit. Most communications satellites are in geostationary orbit 22,300 miles (35,900 km) above the equator, so that the satellite appears stationary at the same point in the sky; therefore the satellite dish antennas of ground stations can be aimed permanently at that spot and do not have to move to track the satellite.

A satellite constellation is a group of artificial satellites working together as a system. Unlike a single satellite, a constellation can provide permanent global or near-global coverage, such that at any time everywhere on Earth at least one satellite is visible. Satellites are typically placed in sets of complementary orbital planes and connect to globally distributed ground stations. They may also use inter-satellite communication.

A geosynchronous transfer orbit or geostationary transfer orbit (GTO) is a type of geocentric orbit. Satellites that are destined for geosynchronous (GSO) or geostationary orbit (GEO) are (almost) always put into a GTO as an intermediate step for reaching their final orbit.

A geocentric orbit or Earth orbit involves any object orbiting Earth, such as the Moon or artificial satellites. In 1997, NASA estimated there were approximately 2,465 artificial satellite payloads orbiting Earth and 6,216 pieces of space debris as tracked by the Goddard Space Flight Center. More than 16,291 objects previously launched have undergone orbital decay and entered Earth's atmosphere.

The Molniya series satellites are military and communications satellites launched by the Soviet Union from 1965 to 2004. These satellites use highly eccentric elliptical orbits known as Molniya orbits, which have a long dwell time over high latitudes. They are suited for communications purposes in polar regions, in the same way that geostationary satellites are used for equatorial regions.

A Molniya orbit is a type of satellite orbit designed to provide communications and remote sensing coverage over high latitudes. It is a highly elliptical orbit with an inclination of 63.4 degrees, an argument of perigee of 270 degrees, and an orbital period of approximately half a sidereal day. The name comes from the Molniya satellites, a series of Soviet/Russian civilian and military communications satellites which have used this type of orbit since the mid-1960s.

A highly elliptical orbit (HEO) is an elliptic orbit with high eccentricity, usually referring to one around Earth. Examples of inclined HEO orbits include Molniya orbits, named after the Molniya Soviet communication satellites which used them, and Tundra orbits.

A Sun-synchronous orbit (SSO), also called a heliosynchronous orbit, is a nearly polar orbit around a planet, in which the satellite passes over any given point of the planet's surface at the same local mean solar time. More technically, it is an orbit arranged so that it precesses through one complete revolution each year, so it always maintains the same relationship with the Sun.

AsiaSat 3, previously known as HGS-1 and then PAS-22, was a geosynchronous communications satellite, which was salvaged from an unusable geosynchronous transfer orbit (GTO) by means of the Moon's gravity.

A supersynchronous orbit is either an orbit with a period greater than that of a synchronous orbit, or just an orbit whose apoapsis is higher than that of a synchronous orbit. A synchronous orbit has a period equal to the rotational period of the body which contains the barycenter of the orbit.

A medium Earth orbit (MEO) is an Earth-centred orbit with an altitude above a low Earth orbit (LEO) and below a high Earth orbit (HEO) – between 2,000 and 35,786 km above sea level.

A ground track or ground trace is the path on the surface of a planet directly below an aircraft's or satellite's trajectory. In the case of satellites, it is also known as a suborbital track, and is the vertical projection of the satellite's orbit onto the surface of the Earth.

A geosynchronous satellite is a satellite in geosynchronous orbit, with an orbital period the same as the Earth's rotation period. Such a satellite returns to the same position in the sky after each sidereal day, and over the course of a day traces out a path in the sky that is typically some form of analemma. A special case of geosynchronous satellite is the geostationary satellite, which has a geostationary orbit – a circular geosynchronous orbit directly above the Earth's equator. Another type of geosynchronous orbit used by satellites is the Tundra elliptical orbit.

An apogee kick motor (AKM) is a rocket motor that is regularly employed on artificial satellites to provide the final impulse to change the trajectory from the transfer orbit into its final orbit. For a satellite launched from the Earth, the rocket firing is done at the highest point of the transfer orbit, known as the apogee.

Sirius FM-5, also known as Radiosat 5, is an American communications satellite which is operated by Sirius XM Radio. It was constructed by Space Systems Loral, based on the LS-1300 bus, and carries a single transponder designed to transmit in the NATO E, F and I bands. It is currently being used to provide satellite radio broadcasting to North America.

Inmarsat-4A F4, also known as Alphasat and Inmarsat-XL, is a large geostationary communications I-4 satellite operated by UK based Inmarsat in partnership with the European Space Agency. Launched in 2013, it is used to provide mobile communications to Africa and parts of Europe and Asia.

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