Geostationary Satellites - Mythology, Science Fiction, Physics
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Is it possible to keep an object hanging in the sky above some fixed point on the Earth? The experience is that what goes up must come down. A ball when thrown upward vertically rises to the height determined by its initial speed. The faster it is thrown up the higher it goes. But, it must fall back the same path it travelled when it went vertically up. If it is thrown up with the speed called the escape velocity it will never come back, but it will not remain hanging in space. Therefore, the legend in the Indian mythology that Trisanku is hanging in the sky between the heaven and the Earth, though regarded as incredible, has fascinated one and all. In 1945, Arthur Clarke, who is recognised as one of the outstanding science fiction writers of the twentieth century, wrote in an article published in Wireless World [1] that by placing three geostationay satellites (Trisankus) above the equator would revolutionize global telecommunication. Thus, a mythological idea that objects can be made to appear stationary above the Earth found a place in science fiction. In 1964 the first Trisanku, Syncom, with the generic scientific name geostationary satellite / geosynchronous satellite was placed above a fixed longitude on equator, and thereby a myth became a reality. The purpose of this article is to weave together mythology, science fiction and physics for understanding the features of geosynchronous satellites.
The Mythology
According to the Indian mythology [2], Trisanku, who was first called Satyavrata, decided to perform a great sacrifice which would enable him to ascend bodily to heaven. The sage Visvamitra assisted him in this effort. But in heaven Indra barred his entry, and Trisanku was hurled back earthward from the celestial abode of the gods. Visvamitra in rage started creating new constellations and new forms of life and became a threat to the work of Brahama. A compromise was reached between Brahama and Visvamitra, and Trisanku was made immortal by arresting his downward fall midway between heaven and Earth. Since then he has been hanging up above the Earth.
The Science Fiction
Arthur Clarke in his article [1] entitled " Extra-terrestrial Relays: Can Rocket Stations give World-wide Radio Coverage?" published in October 1945 issue of the Wireless World proposed that three gysynchronous satellites placed suitably in the orbit above the equator with a period of exactly 24 hours can in principle provide telecommunication linkage between all points on the earth. As the earth revolves around its axis once in 24 hours a satellite in the 24-hour orbit outside the earth's atmosphere would appear stationary above the same spot on the planet. It would remain fixed in the sky of a whole hemisphere and unlike all heavenly bodies would neither rise nor set. The need of putting such a satellite was due to the limitation of the ionospheric communication for television broadcast. The ionosphere is transparent to frequencies used for television transmission. Clarke's proposal was far ahead of its time. It was made when the state-of-the-art of the rocket technology was the V2 rocket deployed by the Germany in the Second World War. In 1957, the Soviet Union placed the first manmade object, the Sputnik, in a closed orbit around the Earth. As already mentioned, the first geosynchronous satellite, Syncom, was placed in the geostationary orbit by the Americans on 19th August 1964, just in time to allow the live coverage of the Tokyo Olympics. Clarke's vision is an outstanding example of science fiction anticipating technology.
The Physics
The physics of geosynchronous satellites [3] is simple enough to be understood by secondary school students. It involves use of the concept of the centripetal acceleration and the Newton's law of gravitation. Consider an object of mass m moving with speed v in a circular orbit above the equator at a distance r as measured from the centre of the Earth. Let the mass of the Earth and its radius be denoted by the symbols M and R, respectively. The centripetal force on the object is given by the standard expression mv2/r. The inward pull towards the centre of the Earth is provided by the gravitational attraction of the object by the mass of the Earth. According to the universal law of gravitation the expression for this force is GMm/r2, where G is the Newtonian gravitational constant. These two expressions can be equated. This gives the relationship
m
v2/r = GMm/r2.This fixes the relation between the speed
v and the radius r of the orbit. It isv =
Ö (GM/r) .The relation between orbital period
T, speed v and the radius r isT = 2
Õ r/v .This gives the Keplarian relation
T2 = (4
Õ 2/GM) r3.In this relation substituting the following values
T = 8.64x104 s, M = 5.983x1024 kg
and G = 6.672x 10-11m3 kg-1 s-2, it can be calculated that the radius of the geocsynchronous orbit measured from the centre of the Earth is 42261 km. The height of a geostationary satellite measured along the vertical from the Equator can be found by subtracting the radius of the earth, 6378 km. This is found to be 35883 km. The speed of the geostationary satellite with respect to the fixed stars can be found from the relationV = 2
Õ r/T.By substituting the values of
r and T we find that the geostationary satellite is not stationary as it moves with speed of 3.0 km s-1.Conclusion
The purpose of this article is to point out to students that at times fantastic imagination may anticipate scientific and technological developments. India has been able to put in geosynchronous orbits four commercial second-generation satellites. The INSAT-2D the latest satellite indigenously built by ISRO is collocated with INSAT-2A at a height of 3600 km above the Equator at 74-degree East longitude.
1. A.C.Clarke, Wireless World, 303-308 (1945)
2. B.Walker, Hindu World (vol.2), 522-523 (1968)
3. Physics (vol 1, part1), Class XI, N.C.E.R.T., 176-177 (1988)