british media popularized the geostationary orbit as a finding by arthur c clarke as opposed to giving due credit to herman potočnik, who introduced it first in one of his publications in 1929: Das Problem der Befahrung des Weltraums - der Raket1, which translates to The Problem of Space Travel: The Rocket Motor2. the recent demise of arthur c clarke has brought about attention to a paper her wrote: Extra-Terrestrial Relays — Can Rocket Stations Give Worldwide Radio Coverage?3, which was published in 1945. presented below are extracts from herman's book and also from arthur c clarke's paper. furthermore, arthur c clarke in his paper had cited herman's publication.
about the geostationary orbit
the earth rotates one revolution every 24 hours (approximately). that is an observer standing on the equator completes one revolution every 24 hours. for an object orbiting earth to appear stationary, it would have to complete one revolution in 24 hours (or whatever the time duration earth takes to complete one revolution.
the concept is pretty simple - all you have to do is make the object compete one revolution around earth every 24 hours. there are two main forces acting on a orbiting object - gravitational force and centrifugal force. the reason why an object orbits is because these two forces are at equilibrium. if not the object should collapse or move away from earth. its similar to spinning a stone tied to a string. the tension of the string is equal to the centrifugal force acting on the stone. if the string breaks stone would move away from you.
gravity is a force acting between two bodies. that is according to isaac newton. einstein had a different theory but lets not get to that. newton's model is valid and its a part of rocket science. newton said that the gravity (gravitational force) acting due to a large mass on a smaller mass is a mutual force, just like the tensile force acting on a string. he also said that this force is proportional to the masses of each other and inversely proportional to the square of the distance apart.
- the centrifugal force acting on an object is proportional to its speed and inversely proportional to radius of its circular path
- gravitational force is proportional to the masses of each other and inversely proportional to the square of the distance apart
- the object revolves at the same rate earth revolves - one revolution every 24 hours
from the above conditions we can find the distance at which an object would appear to be stationary to someone on earth.
- gravitational force acting on the object - FG
- centrifugal force acting on the object - FC
- time period earth takes to complete one revolution - T = 86,164 seconds
- mass of earth - M = 5.972 × 1024 kg
- mass of object orbiting earth - m in kg
- equatorial radius of earth - R=6,378 km
- radius of orbital path of the object (distance between the center of earth and object) - r in km
- distance between the object and an observer on the equator - h = r-R in km
- gravitational constant - G = 6.674 × 10-11 m3kg-1s-2
- linear speed of the orbiting object - v in ms-1
from newton's law of gravitation: FG = GMm/r2
the object completes one revolution in time T, vT = 2πr
v = 2πr / T
centrifugal force, FC = mv2/r
FC = m (2πr / T)2 / r
FC = mr (2π / T)2
FG = FC
GMm/r2 = mr (2π / T)2
r3 = GM(T/2π)2
r = 42,163 km
distance between the object and an observer on the equator - h = r-R = 35,785 km
linear speed of the orbiting object - v = 3.074 ms-1 = 11,068 kmh-1
citations from herman's book
in 1999 nasa translated herman's book to english. the entire text of the publication is available below (see links).
Furthermore, if we adjust the orbit in such a fashion that it is now exactly in the plane of the equator, then the object would continually remain over one and the same point on the equator, precisely 35,900 km above the Earth's surface, when taking into account the radius of the Earth of around 6,400 km (Figure 54). The object would then so to speak form the pinnacle of a enormously high tower that would not even exist but whose bearing capacity would be replaced by the effect of centrifugal force (Figure 55).
Figure 55. An object orbiting the Earth as in Figure 54 behaves as if it would form the pinnacle of a enormously giant tower (naturally, only imaginary) 35,900,000 meters high.
Key: 1. Earth's axis; 2. Earth's rotation; 3. Free orbit; 4. Equator; 5. Imaginary giant tower 35,900,000 meters high; 6. Freely orbiting object, like a pinnacle of a tower, remaining fixed over the Earth's surface.
Wireless World, Oct 1945: Extra-Terrestrial Relays — Can Rocket Stations Give Worldwide Radio Coverage?
complete text of this article can be found here