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An areostationary orbit or areosynchronous equatorial orbit (abbreviated AEO) is a circular areo­synchronous orbit in the Martian equatorial plane about 17,032 km (10,583 mi) above the surface, any point on which revolves about Mars in the same direction and with the same period as the Martian surface. Areo­stationary orbit is a concept similar to Earth's geo­stationary orbit. The prefix areo- derives from Ares, the ancient Greek god of war and counterpart to the Roman god Mars, with whom the planet was identified. The modern Greek word for Mars is Άρης (Áris).

To date, no artificial satellites have been placed in this orbit, but it is of interest to some scientists foreseeing a future tele­communications network for the exploration of Mars.[1] An asteroid or station placed in areostationary orbit could also be used to construct a Martian space elevator for use in transfers between the surface of Mars and orbit.

Formula

Orbital speed (how fast a satellite is moving through space) is calculated by multiplying the angular speed of the satellite by the orbital radius:

$${\displaystyle R_{syn}={\sqrt[{3}]{G(m_{2})T^{2} \over 4\pi ^{2}}}}$$ [2]
G = Gravitational constant
m2 = Mass of the celestial body
T = rotational period of the body

By this formula one can find the geostationary-analogous orbit of an object in relation to a given body, in this case, Mars (this type of orbit above is referred to as an areostationary orbit if it is above Mars).

The mass of Mars being 6.4171×1023 kg and the sidereal period 88,642 seconds.[3] The synchronous orbit thus has a radius of 20,428 km (12693 mi) from the centre of mass of Mars,[4] and therefore areostationary orbit can be defined as approximately 17,032 km above the surface of the Mars equator.
Stationkeeping

Any satellites in areostationary orbit will suffer from increased orbital station keeping costs,[5] [6] because the Clarke belt of Mars lies between the orbits of the planet's two natural satellites. Phobos has a semi-major axis of 9,376 km, and Deimos has a semi-major axis of 23,463 km. The close proximity to Phobos' orbit in particular (the larger of the two moons) will cause unwanted orbital resonance effects that will gradually shift the orbit of areostationary satellites.

Geostationary orbit
Areosynchronous orbit
List of orbits

References

Lay, N.; C. Cheetum; H. Mojaradi; J. Neal (15 November 2001). "Developing Low-Power Transceiver Technologies for In Situ Communication Applications" (PDF). IPN Progress Report 42-147. 42 (147): 22. Archived from the original (PDF) on 4 March 2016. Retrieved 2012-02-09.
"Calculating the Radius of a Geostationary Orbit - Ask Will Online". Ask Will Online. 2012-12-27. Retrieved 2017-11-21.
Lodders, Katharina; Fegley, Bruce (1998). The Planetary Scientist's Companion. Oxford University Press. p. 190. ISBN 0-19-511694-1.
"Stationkeeping in Mars orbit". www.planetary.org. Retrieved 2017-11-21.
Romero, P.; Pablos, B.; Barderas, G. (2017-07-01). "Analysis of orbit determination from Earth-based tracking for relay satellites in a perturbed areostationary orbit". Acta Astronautica. 136: 434–442. doi:10.1016/j.actaastro.2017.04.002. ISSN 0094-5765.

Silva and Romero's paper even includes a graph of acceleration, where a reaction force could be calculated using the mass of desired object: Silva, Juan J.; Romero, Pilar (2013-10-01). "Optimal longitudes determination for the station keeping of areostationary satellites". Planetary and Space Science. 87: 16. doi:10.1016/j.pss.2012.11.013. ISSN 0032-0633.