Geostationary orbit

Uses

Most commercial communications satellites, broadcast satellites and SBAS satellites operate in geostationary orbits.

Communications

Geostationary communication satellites are useful because they are visible from a large area of the earth's surface, extending 81° away in latitude and 77° in longitude. They appear stationary in the sky, which eliminates the need for ground stations to have movable antennas. This means that Earth-based observers can erect small, cheap and stationary antennas that are always directed at the desired satellite. However, latency becomes significant as it takes about 240 ms for a signal to pass from a ground based transmitter on the equator to the satellite and back again. This delay presents problems for latency-sensitive applications such as voice communication, so geostationary communication satellites are primarily used for unidirectional entertainment and applications where low latency alternatives are not available.

Geostationary satellites are directly overhead at the equator and appear lower in the sky to an observer nearer the poles. As the observer's latitude increases, communication becomes more difficult due to factors such as atmospheric refraction, Earth's thermal emission, line-of-sight obstructions, and signal reflections from the ground or nearby structures. At latitudes above about 81°, geostationary satellites are below the horizon and cannot be seen at all. Because of this, some Russian communication satellites have used elliptical Molniya and Tundra orbits, which have excellent visibility at high latitudes.

Meteorology

A worldwide network of operational geostationary meteorological satellites is used to provide visible and infrared images of Earth's surface and atmosphere for weather observation, oceanography, and atmospheric tracking. As of 2019 there are 19 satellites in either operation or stand-by. These satellite systems include:

• the United States' GOES series, operated by NOAA
• the Meteosat series, launched by the European Space Agency and operated by the European Weather Satellite Organization, EUMETSAT
• the Republic of Korea COMS-1 and GK-2A multi mission satellites.
• the Russian Elektro-L satellites
• the Japanese Himawari series
• Chinese Fengyun series
• India's INSAT series

These satellites typically capture images in the visual and infrared spectrum with a spatial resolution between 0.5 and 4 square kilometres. The coverage is typically 70°, and in some cases less.

Geostationary satellite imagery has been used for tracking volcanic ash, measuring cloud top temperatures and water vapour, oceanography, measuring land temperature and vegetation coverage, facilitating cyclone path prediction, and providing real time cloud coverage and other tracking data. Some information has been incorporated into meteorological prediction models, but due to their wide field of view, full-time monitoring and lower resolution, geostationary weather satellite images are primarily used for short-term and real-time forecasting.

Navigation

Geostationary satellites can be used to augment GNSS systems by relaying clock, ephemeris and ionospheric error corrections (calculated from ground stations of a known position) and providing an additional reference signal. This improves position accuracy from approximately 5m to 1m or less.

Past and current navigation systems that use geostationary satellites include:

• The Wide Area Augmentation System (WAAS), operated by the United States Federal Aviation Administration (FAA);
• The European Geostationary Navigation Overlay Service (EGNOS), operated by the ESSP (on behalf of EU's GSA);
• The Multi-functional Satellite Augmentation System (MSAS), operated by Japan's Ministry of Land, Infrastructure and Transport Japan Civil Aviation Bureau (JCAB);
• The GPS Aided Geo Augmented Navigation (GAGAN) system being operated by India.
• The commercial StarFire navigation system, operated by John Deere and C-Nav Positioning Solutions (Oceaneering);
• The commercial Starfix DGPS System and OmniSTAR system, operated by Fugro.

Implementation

Launch

Geostationary satellites are launched to the east into a prograde orbit that matches the rotation rate of the equator. The smallest inclination that a satellite can be launched into is that of the launch site's latitude, so launching the satellite from close to the equator limits the amount of inclination change needed later. Additionally, launching from close to the equator allows the speed of the Earth's rotation to give the satellite a boost. A launch site should have water or deserts to the east, so any failed rockets do not fall on a populated area.

Most launch vehicles place geostationary satellites directly into a geostationary transfer orbit (GTO), an elliptical orbit with an apogee at GEO height and a low perigee. On-board satellite propulsion is then used to raise the perigee, circularise and reach GEO.

Orbit allocation

Satellites in geostationary orbit must all occupy a single ring above the equator. The requirement to space these satellites apart, to avoid harmful radio-frequency interference during operations, means that there are a limited number of orbital slots available, and thus only a limited number of satellites can be operated in geostationary orbit. This has led to conflict between different countries wishing access to the same orbital slots (countries near the same longitude but differing latitudes) and radio frequencies. These disputes are addressed through the International Telecommunication Union's allocation mechanism under the Radio Regulations. In the 1976 Bogota Declaration, eight countries located on the Earth's equator claimed sovereignty over the geostationary orbits above their territory, but the claims gained no international recognition.

Retired satellites

Geostationary satellites require some station keeping to keep their position, and once they run out of thruster fuel they are generally retired. The transponders and other onboard systems often outlive the thruster fuel and by allowing the satellite to move naturally into an inclined geosynchronous orbit some satellites can remain in use, or else be elevated to a graveyard orbit. This process is becoming increasingly regulated and satellites must have a 90% chance of moving over 200 km above the geostationary belt at end of life.

Space debris

Space debris at geostationary orbits typically has a lower collision speed than at low Earth orbit (LEO) since all GEO satellites orbit in the same plane, altitude and speed; however, the presence of satellites in eccentric orbits allows for collisions at up to 4 km/s (14,400 km/h; 8,900 mph). Although a collision is comparatively unlikely, GEO satellites have a limited ability to avoid any debris.

Debris less than 10 cm in size are very challenging to detect from the ground and are not regularly tracked, making it difficult to assess their prevalence.

Despite efforts to reduce risk, spacecraft collisions have occurred. The European Space Agency telecom satellite Olympus-1 was struck by a meteoroid on August 11, 1993, and eventually moved to a graveyard orbit, and in 2006 the Russian Express-AM11 communications satellite was struck by an unknown object and rendered inoperable, although its engineers had enough contact time with the satellite to send it into a graveyard orbit. In 2017, both AMC-9 and Telkom-1 broke apart from an unknown cause.

Properties

A typical geostationary orbit has the following properties:

• Inclination: 0°
• Period: 1436 minutes (one sidereal day)
• Eccentricity: 0
• Argument of perigee: undefined
• Semi-major axis: 42,164 km

Inclination

An inclination of zero ensures that the orbit remains over the equator at all times, making it stationary with respect to latitude from the point of view of a ground observer (and in the Earth-centered Earth-fixed reference frame).

Period

The orbital period is equal to exactly one sidereal day. This means that the satellite will return to the same point above the Earth's surface every (sidereal) day, regardless of other orbital properties. For a geostationary orbit in particular, it ensures that it holds the same longitude over time. This orbital period, T, is directly related to the semi-major axis of the orbit through Kepler's Third Law:

${\displaystyle T=2\pi \sqrt{\frac{a^3}{\mu }}}$

where:

• a is the length of the orbit's semi-major axis
• μ is the standard gravitational parameter of the central body

Eccentricity

The eccentricity is zero, which produces a circular orbit. This ensures that the satellite does not move closer or further away from the Earth, which would cause it to track backwards and forwards across the sky.

Stability

A geostationary orbit can be achieved only at an altitude very close to 35,786 kilometres (22,236 miles) and directly above the equator. This equates to an orbital speed of 3.07 kilometres per second (1.91 miles per second) and an orbital period of 1,436 minutes, one sidereal day. This ensures that the satellite will match the Earth's rotational period and has a stationary footprint on the ground. All geostationary satellites have to be located on this ring.

A combination of lunar gravity, solar gravity, and the flattening of the Earth at its poles causes a precession motion of the orbital plane of any geostationary object, with an orbital period of about 53 years and an initial inclination gradient of about 0.85° per year, achieving a maximal inclination of 15° after 26.5 years. To correct for this perturbation, regular orbital stationkeeping maneuvers are necessary, amounting to a delta-v of approximately 50 m/s per year.

A second effect to be taken into account is the longitudinal drift, caused by the asymmetry of the Earth – the equator is slightly elliptical (equatorial eccentricity). There are two stable equilibrium points sometimes called "gravitational wells" (at 75.3°E and 108°W) and two corresponding unstable points (at 165.3°E and 14.7°W). Any geostationary object placed between the equilibrium points would (without any action) be slowly accelerated towards the stable equilibrium position, causing a periodic longitude variation. The correction of this effect requires station-keeping maneuvers with a maximal delta-v of about 2 m/s per year, depending on the desired longitude.

Solar wind and radiation pressure also exert small forces on satellites: over time, these cause them to slowly drift away from their prescribed orbits.

In the absence of servicing missions from the Earth or a renewable propulsion method, the consumption of thruster propellant for station-keeping places a limitation on the lifetime of the satellite. Hall-effect thrusters, which are currently in use, have the potential to prolong the service life of a satellite by providing high-efficiency electric propulsion.

Derivation

For circular orbits around a body, the centripetal force required to maintain the orbit (F_c) is equal to the gravitational force acting on the satellite (F_g):

${\displaystyle F_{\text{c}}=F_{\text{g}}}$

From Isaac Newton's universal law of gravitation,

${\displaystyle F_{\text{g}}=G\frac{M_{\text{E}}{m}_{\text{s}}}{r^2}}$,

where F_g is the gravitational force acting between two objects, M_E is the mass of the Earth, 5.9736×10²⁴ kg, m_s is the mass of the satellite, r is the distance between the centers of their masses, and G is the gravitational constant, (6.67428±0.00067)×10⁻¹¹ m³ kg⁻¹ s⁻².

The magnitude of the acceleration, a, of a body moving in a circle is given by:

${\displaystyle a=\frac{v^2}{r}}$

where v is the magnitude of the velocity (i.e. the speed) of the satellite. From Newton's second law of motion, the centripetal force F_c is given by:

${\displaystyle F_{\text{c}}=m_{\text{s}}\frac{v^2}{r}}$.

As F_c = F_g,

${\displaystyle m_{\text{s}}\frac{v^2}{r}=G\frac{M_{\text{E}}{m}_{\text{s}}}{r^2}}$,

so that

${\displaystyle v^2=G\frac{M_{\text{E}}}{r}}$

Replacing v with the equation for the speed of an object moving around a circle produces:

${\displaystyle {\left(\frac{2\pi r}{T}\right)}^2=G\frac{M_{\text{E}}}{r}}$

where T is the orbital period (i.e. one sidereal day), and is equal to 86164.09054 s. This gives an equation for r:

${\displaystyle r=\sqrt[3]{\frac{G{M}_{\text{E}}{T}^2}{4{\pi }^2}}}$

The product GM_E is known with much greater precision than either factor alone; it is known as the geocentric gravitational constant μ = 398600.4418±0.0008 km³ s⁻². Hence

${\displaystyle r=\sqrt[3]{\frac{\mu T^2}{4{\pi }^2}}}$

The resulting orbital radius is 42,164 kilometres (26,199 miles). Subtracting the Earth's equatorial radius, 6,378 kilometres (3,963 miles), gives the altitude of 35,786 kilometres (22,236 miles).

The orbital speed is calculated by multiplying the angular speed by the orbital radius:

${\displaystyle v=\omega r\approx 3074.6\text{m/s}}$

In other planets

By the same method, we can determine the orbital altitude for any similar pair of bodies, including the areostationary orbit of an object in relation to Mars, if it is assumed that it is spherical (which it is not entirely). The gravitational constant GM (μ) for Mars has the value of 42830 km³ s⁻², its equatorial radius is 3389.50 km and the known rotational period (T) of the planet is 1.02595676 Earth days (88642.66 s). Using these values, Mars' orbital altitude is equal to 17039 km.