Geostationary
Satellites - Mythology, Science Fiction, Physics
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.
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.
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 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
mv2/r = GMm/r2.
This
fixes the relation between the speed v and the radius r of the orbit. It is
v = sqrt
(GM/r).
The
relation between orbital period T, speed v and the radius r is
T = 2 (pi) r/v.
This
gives the Keplarian relation
T2 = (4 (pi) 2/GM)
r3.
In
this relation substituting the following values
(pi) is the ratio of the diameter to the circumference of a
circle. 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 relation
V = 2 (pi) 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)