The Geosynchronous Orbit
It was only 1945 that the idea of an apparently stationary satellite around the Earth was proposed. The noted science-fiction writer, Arthur C. Clarke put forward the idea to relay radio signals from a satellite around the Earth. In an article entitled ‘Extraterrestrial Relays’, he stated that an orbit with a radius of 42,000 km has a period of 24hours (actually one sidereal day of 86,164.1 seconds) and a body in such an orbit, if its plane coincided with the Earth as stationary above the same area. Today the orbit is also called the Clarke Orbit.
Clarke’s prophetic idea became a reality within two decades. Some British scientists tried the proposal in 1959 using the moon. Radio signals were sent to the moon, which echoed them back. After a period of 2.6 seconds, the signals were detected in a laboratory in America. With the dawn of the Space Age, scientists tried the idea with a satellite sent in an elliptical orbit (180-1,490 km). it was launched in December 1958 and re-entered the Earth in January 1959.
An attempt was then made to send a metalised balloon, 30 meters across, in circular orbit of the Earth and see how well it transmitted a signal from space. It was called Echo and when launched in 1960, it did what its name suggested. It reflected radio waves as it circled the Earth every 100 minutes. However, because of its low orbit, it passed over the ground station very rapidly. As it did not amplify the signals, it was called a passive satellite and it needed powerful ground transmitters to catch its weak signals.
The next step was to develop an active satellite, which amplified the signals sent from the Earth. In 1962, a satellite called Telstar Transmitted television from one continent to another. The transmission between America and France lasted 22 minutes before the satellite went out of sight. As the satellite passed over very rapidly, it was realized that such satellite should be made to orbit at a greater height so that their speed could be decreased. In devising Echo and Telstar, Dr John Pierce of the Bell Laboratory (USA) played a key role.
Once big rockets were available to reach higher altitudes, a new generation of satellites was launched. In February 1963, Syncom-I, the first satellite in synchronous orbit, was launched but it lost contact with the Earth following a malfunction. Syncom-II followed on July 26. Positioned over the Atlantic, it became the first successful geosynchronous satellite. Aircraft Company, USA. The satellite Performed well. In 1964, Syncom-III over the pacific relayed the Tokyo Olympics to America. Soon, international and domestic agencies realized the great potential in the use of geosynchronous satellites.
What exactly is the geosynchronous orbit ? If a satellite is orbited at 11,068.56 km/hours (or 3.0746 km/second) at about 36,000 km (typically 35,786 km to be exact) above the equator, the satellite will synchronize with the speed at which the Earth rotates on its axis at the equator (1,620km/h or 464 meters/s). Further, the satellite should orbit from west to east, as does the Earth. As the satellite’s speed is synchronous with that of the Earth it is called a ‘geosynchronous satellite’. The orbit is called ‘geostationary’, if in addition to it begins geosynchronous; the plane of the satellite’s orbit coincides with any change in its shape. The satellite would then appear as a fixed star to an observer on the Earth.
The satellite’s orbital period is one sidereal day (which is the time taken by the Earth to rotate once relative to the stars. It is a bit shorter (23hours, 56minutes and 04.09053 seconds) than a solar day of 24hours, which is the duration of Earth’s rotation relative to the sun. this is because by the time the Earth has rotated once, it has also moved a little in its orbit around the sun and so the Earth has to rotate for about another four minutes before the sun appears in the same place in the sky as it did a day before. In each orbit, the satellite covers a circumference of 2,65,000 km.
A geosynchronous orbit will be a circle at a uniform distance of 42,164 km from the center of the Earth, with the Earth’s equatorial radius of 6,378 km and the distance of the satellite from the edge of Earth, viz. 35,786 km.
The Transfer Orbit
It is considered economical to reach the synchronous orbit in stages. Moreover, the accuracy demanded in injecting the satellite into the correct orbit is ensured if a series of manoeuvres around the Earth is performed instead of depending on only one step of injecting it into a geosynchronous transfer orbit (GTO) with a perigee (nearest point) of about 250 km and an apogee (farthest point) of 35,800 km. a rocket onboard the satellite, called an ‘apogee motor’, will be fired on radio command when the satellite reaches the apogee. The rocket firing will give it enough push to increase its velocity and circularize the egg-shaped lower orbit.
The point at which the satellite requires minimum velocity changed and therefore minimum consumption of propellant is determined on the basis of a theory elaborated in 1925 by Walter Hohmann (1880-1945). He proved that a satellite at the trajectory that connects two circular orbits in such a manner that it is a fuel-efficient way of transferring from one circular orbit to another that is in the same plane (same inclination) but at a different altitude. This principle is adopted into the transfer of a satellite from the initial elliptical orbit into the geosynchronous circular orbit as shown in the figure below.
A geosynchronous transfer orbit near the Earth is achieved before the higher geosynchronous orbit, because a satellite needs minimum velocity change were the two orbits meet to get into the required orbit.Img-credit:telesat.com
After separation from a rocket or a shuttle, a geosynchronous satellite goes into the transfer orbit. Small corrections are made to the orbit but a lot of calculations would be necessary before the apogee motor is fired. It is generally fired when the satellite reaches the apogee after three or sometimes 10 orbits. Even a slight malfunction in injecting the satellite into this orbit would result in a degraded transfer orbit. The speed of the satellite in the egg-shaped orbit is typically 10.15 km/second at the perigee, while it is 1.46 second km at the apogee. Hence it would need only an addition of about 3.07km second in the circular GSO.
After firing thrice on radio command from ground control, the onboard liquid apogee motor contributes nearly half the velocity of the satellite in the GSO. The process consumes typically more than 70 percent of the onboard fuel, leaving the rest for corrections during the entire lifetime of the satellite.
The Apogee Motor
The apogee motor’s efficiency and strength would depend on the nature of the mission and the weight to be transported. Not all the weight taken at the transfer orbit stage can be put into the synchronous orbit. Only a part of the low-orbit weight can be taken into the final geosynchronous orbit.
For example, in the American rocket, Delta-3914, the payload weight in low-Earth orbit is 2,500 kg, while the satellite weight in geostationary orbit is 440 kg. the Russian A-2 Soyuz rocket takes a payload of 7,500 kg in the lower orbit but puts only 1,100 kg in the geosynchronous orbit. One-fifth of the low-orbit weight can be placed in synchronous orbit if the rocket takes off exactly from the equator so the launch can take full advantage of the Earth’s eastward rotation. When the European Arine rocket launches two satellites, two separate apogee firings are done in view of the elaborate calculations required to position each satellite.
India’s geosynchronous satellite, INSAT-1B, for example, was launched with the help of a spin-stabilized upper stage (PAM). It inserted the satellite into the transfer orbit after its release from the shuttle.
PAM is a bit risky. A similar booster failed in pushing up NASA’s Tracking and Data Relay Satellite (TDRS) system. A major salvage operation had to be undertaken. Almost three months after its tumble in space, TDRS was taken step by step to its slot 35,577 km above the equator over Brazil.
When the apogee motor of a satellite (INTELSAT-603) failed, an unusual technique was successfully tried to place it in the proper geosynchronous orbit. Astronauts on board the shuttle (1992) went up to the standard satellite and replaced the apogee motor. As a result, the satellite was sent in an orbit of 300×82,000 km and a series of burns lowered the apogee and lifted the perigee to a normal orbit of 36,000 km.
It is inserting to know that Russia’s proton rocket can take a payload directly into the final GEO. The fourth stage of Proton has a multiple restart capacity that allows it to perform all the manoeuvres needed to place a satellite into the GEO without requiring the use of the spacecraft’s onboard propellant. The rocket can deliver up to 22 tonnes of payload into low-Earth orbit and or up to 2 tonnes in GSO. Proton has flown over 200 missions and has orbited Salyut station and Mir station.
A geosynchronous satellite experiences an eclipse when the Earth itself hides it from the sun. As the Earth’s north-south axis is tilted by 23.5º, we observe the sun moving from north to south and vice versa, the total swing being ±23.5º. As the satellite approaches the vernal equinox (September 23) around midnight, the satellite moves into a shadow cast by the Earth causing an eclipse to the satellite, which lasts for 45 days in each season. An eclipse period lasts 10-72 minutes a day, when on board batteries supply power to the spacecraft
Sun Interference
Twice a year, in the six-month period between the autumnal and vernal equinoxes in the direction of the Earth station antenna beam, there by degrading the quality of communications. The circuit may be out of service for a total of 23 minutes in a year. The Earth sensor can be blinded by direct sun interference.
Hence on such occasions (which can be predicted), one of the sensors is switched off. In the case of INSAT-1A, a peculiar, unexpected situation developed. Having inhibited one Earth sensor under prolonged sun interference, the computer programme failed to predict the intrusion of the bright full moon on the only remaining Earth sensor that was also switched off. Earth contact was therefore lost and the satellite started drifting. The full moon intruded because of a deviation of the satellite with regards to Earth. The unstable satellite could not receive the corrective commands from the ground.
Stability in Orbit
A satellite in the shape of a drum can take advantage of the laws of Nature and keep steady by spinning at a constant rate. As long as the satellite does not come below the critical height from the Earth, it can stay in orbit. If however, the satellite looks like a drums, its stability is achieved by having a non-spinning part, i.e. a mechanically despun platform. While the spacecraft spins at about 60 revolutions per minute (rpm) to get gyroscopic stability, the top portion with antennas kept pointed at the Earth, does not spin.
METEOSAT, Europe’s meteorological satellite, spin-stabilized in the geosynchronous orbit (unlike INSAT, which is three-axis stabilizes) at 100 revolutions per minute. Europe has also launched polar orbiting satellite.Pic-credit:wikimedia.org
Another method of maintaining the satellite in orbit is called ‘three-axis stabilization’. This method is adopted so that bigger solar arrays can be fixed to a box-like satellite. The three axes are the roll axis to maintain the satellite along the direction of its motion in space, the pitch axis to keep the spacecraft steady in the up-and-down direction, perpendicular to the roll axis; and the yaw axis, which is perpendicular to the other two axes and enables the satellite antenna or sensors to look at the Earth (See Figure below). A geosynchronous satellite’s roll axis is aligned with its direction of travel along the geosynchronous arc.
A three-axis (pitch, yaw and roll) stabilized satellite. Img-credit:wikimedia.org
Rotation about this axis results in a north-south movement of an antenna beam. Rotation about the pitch axis aligned with the Earth’s spin axis produces an east-west movement of the beam. Rotation about the yaw axis, which is aligned to the Earth’s centre, will cause an equivalent rotation of the beam.
Reaction and Momentum Wheels
The references for keeping the axes in position are taken from the position of the sun and the Earth. Any deviations are corrected by a reaction control system. In space many disturbances change the stability of a satellite. The unwanted influences arise from the Earth’s magnetic field, the gravitational field, the residual atmosphere, solar radiation, etc. Most of these disturbing ‘torques’, as they are called, vary cyclically over one orbit of the satellite.
There are two ways of controlling the disturbances. Control rockets can be used but, if they alone were available, they would need a lot of fuel, thereby reducing the payload and even the life of a satellite. Hence control rockets are used sparingly and reaction wheels, spun by electric motors, are used for correcting periodic disturbances.
A reaction wheel is a spinning wheel, which will, according to Newton’s third law, exert an equal and opposite torque on the satellite. If the wheel is rotated faster, the resulting increases in the angular about the wheel axis in the opposite direction. If the wheel is slowed down, the satellite’s rotation is reversed. Three reaction wheels take care of rotations about the pitch, yaw and roll axes, respectively. A fourth wheel is kept as a standby mounted in such a way that it can take over any of the other wheels should a failure occur. Typically, the wheels are rotated at around 2,500 rpm.
Where all the three axes are controlled by reaction wheels, the system is known as zero momentum stabilization, s the unwanted momentum will be reduced to zero. The wheel speed can be varied in response to external torques. When they accumulate too much momentum, control jets or magnetic torques can be used to dump the extra momentum. Reaction wheels are used to provide attitude control.
As an alternative to the standard reaction wheels normally used for pitch control, it is considered possible to impart tiny bits of plasma through a thruster, getting power from a solar-electric device. NASA’s Earth observation satellite (2001) tried this technique, which keeps on giving fine corrections and avoids a build-up of deviation.
In the Indian Remote Sensing Satellite, IRS-1A, for example, a deviation of 0.1º in roll or pitch axis will result in a shift of about 1.5 km in the image location. IRS-1A has a pointing accuracy 0.1º, while the satellite’s position accuracy is better than 1 km. the next generation of satellites in this series, IRS-1C, has a pointing accuracy of 0.01-0.03º.
Wile near-Earth satellites have reaction wheels, those in geosynchronous orbit have, in addition, momentum wheels that give gyroscopic stability, just as the axis of a child’s spinning top remains steady. Compared to reaction wheels, momentum wheels are larger and heavier and consume more power. They can be rotated at 6,000-12,000 rpm. INSAT-2, for instance, has two momentum wheels are operated simultaneously to provide stability or biased momentum to the pitch axis. The pointing accuracy is 0.2-0.4º. While the momentum wheel will always rotate in the same direction, the reaction wheel could turn either way.
More angular momentum may result at times than needed to keep the satellite in orbit. An onboard computer calculates the needed correction and causes a magnetic torque through magnetic coils and the extra momentum is dumped. If the deviations are larger, liquid thrusters are fired to correct the errors or modify the orbit’s height, the speed of the satellite or its orbital inclination.
In a unique configuration, momentum wheels are placed on gimbals to derive more controls than what reaction wheels can provide. Orbital space stations such as Mir and International Space Station use the device called ‘control momentum gyros’.
To Be Continued
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