Everything you need to know about Geostationary Satellite Orbit. The orbits we choose

We rarely think about how movement in near-Earth space is organized. For example, that from Earth to the space station is just a stone's throw away, less than from Moscow to St. Petersburg, and the signal received by a satellite dish has traveled a greater distance than the average car travels in five years. In addition, each launch is preceded by a careful design of the orbit along which the device will move in outer space. The orbits we choose

When in 1961, specialists from the Korolev OKB-1 began creating the first Soviet communications satellite, Molniya-1, for the Orbita television system, they were faced with the problem of choosing a target orbit for their brainchild. At first glance, the geostationary orbit at an altitude of 36 thousand kilometers seemed to be the most effective. The satellite located on it is in direct visibility around the clock for approximately 1/3 of the Earth's surface. However, from such an orbit it is impossible to provide communications at high latitudes and television broadcasting in the Far North. In addition, the Soviet Union did not then have carriers for launching heavy satellites into geostationary orbit.

A solution was found by ballisticians who came up with an orbit into which a communications satellite could be launched by a rocket that was already in development. It was a highly elongated orbit with a minimum altitude (perigee) of 500 kilometers and a maximum altitude (apogee) of 40,000 kilometers. The orbital period was 12 hours, and in accordance with the laws of celestial mechanics, the satellite spent most of the time in the apogee region. The orbital inclination (63.4°) was chosen so that during this period the satellite was visible from most of the territory of the USSR. Favorable conditions for communication lasted eight hours, after which the satellite went to the other side of the Earth, and on the next orbit the apogee passed over North America. Again it became available for television rebroadcast only after 16 hours.

The Molniya-1 communications satellite was successfully launched into this orbit on the third attempt on April 23, 1965, and the very next day the first space communication session in the Soviet Union took place between Moscow and Vladivostok. For round-the-clock television broadcasting, three Molniya satellites had to be kept in space at the same time, and complex antennas had to be built on Earth. Large parabolic “mirrors” tracked the intricate trajectory of the satellite in the sky: it quickly rose in the west, rose to the zenith, crossed over it, then began to move in the opposite direction, turned around again and, accelerating, descended to the eastern horizon. Another complicating factor was the significant changes in speed when moving along an elongated orbit, as a result of which, due to the Doppler effect, the frequency of the signal received on Earth was constantly changing.

The trajectory chosen for the first Soviet communications satellite was later called the Molniya orbit. Its development with the advent of more powerful rockets became the highly elliptical Tundra orbit with a perigee of 500 kilometers, an apogee of 71,000 and an orbital period of 24 hours. Orbits with such a period are called geosynchronous, since, moving along them, the spacecraft always passes its apogee over the same region of the Earth. The efficiency of using satellites in Tundra orbit is significantly increased, since they can serve a selected area for more than 12 hours on each orbit, and two devices are enough to organize round-the-clock communication. However, ground equipment remains complex because geosynchronous satellites constantly change their position in the sky and have to be monitored.

Hovering in the sky

Receiving equipment is radically simplified if the satellite remains stationary relative to the Earth. Of the entire set of geosynchronous orbits, this is achieved only in one circular one, located strictly above the equator (inclination 0°). This orbit is called geostationary because in it the satellite appears to hover above a selected point on the equator at an altitude of 35,786 kilometers.

The Americans were the first to launch a geostationary satellite, but they did not succeed right away. The first two attempts in 1963 ended in failure, and only on September 10, 1964, the Sincom-3 satellite went into geostationary orbit. It is interesting that he launched into space on August 19, and for almost a month, with the help of his own engine, he crept up to the standing point chosen for him. The first domestic geostationary satellite, Raduga-1, was launched only on December 22, 1975. Since then, the GEO has been constantly replenished, and today there are more than 400 satellites located on it and another 600 vehicles moving near it.

Strictly speaking, due to various disturbances and errors in placement, the geostationary satellite does not “hang” completely motionless above the equator, but makes an oscillatory movement relative to its stationary point. When projected onto the earth's surface, its trajectory resembles a small figure eight. In addition, due to gravitational disturbances, the device can “drift” along its orbit. In order to stay at the selected stationary point and not leave the target of ground-based antennas, the device must regularly adjust its orbit. For this purpose, there is a fuel reserve on board. The service life of a geostationary satellite sometimes depends on it.

Simple geometric constructions show that at latitudes above 81°, geostationary satellites are below the horizon, which means that communication with their help in the polar regions is impossible. In practice, mobile communications via a geostationary satellite are limited to a latitude of 65-70°, and fixed communications - 70-75°. Communication via GSO has another serious drawback. On the way to the satellite and back, the radio signal travels more than 70 thousand kilometers, spending a quarter of a second on it. Taking into account the time it takes to process the signal and transmit it over land lines, the delay can significantly exceed half a second. As a result, Internet services via satellite respond slowly, and telephone communication becomes uncomfortable, since even modern “echo cancellation” tools cannot always cope with large delays. To get rid of these shortcomings, it is necessary to reduce the height of the satellites.

Orbital elements

The word "orbit" in Latin means "track" or "path". The near-Earth orbit is characterized by a number of parameters: the lowest and highest altitude (perigee and apogee, which also determine the orbital period), inclination (the angle between the orbital plane and the plane of the earth’s equator), the longitude of the ascending node, which specifies “in which direction” (around which line in plane of the equator) the orbit is tilted, and the perigee argument, which indicates how the elliptical orbit is rotated in its own plane. Gravitational disturbances from other planets, the pressure of solar radiation, the non-spherical shape of the Earth, its magnetic field and atmosphere lead to the fact that the orbits of satellites can change noticeably over time. Therefore, during the operation of the satellite, trajectory measurements are regularly carried out, and, if necessary, its orbit is adjusted.

Constellation Iridium

Commercial and government communications satellite systems are being formed in relatively low orbits. Technically, these trajectories cannot be called convenient for communication, since the satellites on them are visible most of the time low above the horizon, which negatively affects the quality of reception, and in mountainous terrain can make it impossible. Therefore, the lower the orbit, the more satellites there should be in the system. If three satellites are sufficient for a global communications system in GSO, then in medium-altitude orbits (5000-15,000 kilometers) from 8 to 12 spacecraft are required. And for altitudes of 500-2000 kilometers, more than fifty satellites are needed.

And yet, by the end of the 1980s, the prerequisites had developed for the implementation of low-orbit communication systems. Firstly, it was becoming increasingly crowded for satellites in GEO. “Parking spaces” in this orbit are subject to international registration, and neighboring satellites should not operate on the same radio frequencies so as not to interfere with each other. Secondly, progress in the field of radio electronics has made it possible to create inexpensive (and most importantly, lightweight) satellites with fairly broad capabilities. A rocket capable of launching just one large communications satellite into geostationary orbit could throw a whole “pack” of such devices into low orbit. Third, the end of the Cold War and the disarmament process released hundreds of intercontinental ballistic missiles that could be used to launch small satellites at bargain prices. And finally, it was during these years that the demand for mobile communications, which is characterized by the use of low-power omnidirectional antennas that “do not reach” the GSO, began to grow rapidly. All these factors made launching even a very large number of inexpensive low-orbit satellites more profitable than creating a constellation of several heavy geostationary satellites.

Among the first low-orbit communication systems were Orbcomm (USA) and Gonets (Russia). They did not provide voice transmission, but were intended for sending text messages and collecting information from various sensors, such as meteorological ones. Today, Orbcomm includes 29 satellites weighing 42 kilograms in orbits at an altitude of 775 kilometers. The Messenger system initially contained only 6 satellites, which is why message delivery times could take several hours. Now it is undergoing the third generation of satellites, the number of operating devices has reached nine, but in the future it should be increased to 45 - nine each in five almost polar orbits (inclination 82.5°) at an altitude of 1500 kilometers.

Polar orbits are those that pass over the North and South poles of the Earth, that is, they are located perpendicular to the equator. Any part of the earth's surface periodically falls into the field of view of a satellite in polar orbit. If you use several such orbits, turned at an angle to each other, and launch several satellites in each at equal intervals, you can continuously survey the entire surface of the Earth. This is exactly how the Iridium satellite telephony network works. It uses polar orbits with an inclination of 86.4° and an altitude of 780 kilometers. Initially, they housed 77 satellites, which is where the name of the system came from: iridium - the 77th element of the Mendeleev Periodic Table. However, nine months after launch, in November 1998, Iridium went bankrupt. The call price, reaching up to seven dollars per minute, proved too high for consumers, in part because the Iridium system provided truly global communications - from pole to pole. The GlobalStar system, launched a little later, for the sake of economy, uses instead of polar orbits with an inclination of 52°, which limits communications to the 70th parallel (approximately at the latitude of Yamal). But 48 satellites are enough for operation (plus four spare ones), and the cost of communication in the same 1999 was no more than two dollars per minute.

The Iridium satellites were already preparing to be deorbited and burned in the dense layers of the atmosphere when the entire system was purchased by the US Department of Defense. To this day, Iridium remains the only satellite communications system that provides continuous telephone service around the globe. For example, since 2006, it has provided a permanent Internet connection to the Amundsen-Scott polar station at the South Pole. The connection speed is 28.8 kilobits per second, similar to an old telephone modem.

Use of near-Earth space

To a first approximation, satellite orbits are divided into low (up to 2000 kilometers from the Earth), medium (below geostationary orbit) and high. Manned flights are carried out no higher than 600 kilometers, since spacecraft should not enter the radiation belts surrounding our planet. Energetic protons from the inner radiation belt pose a danger to the lives of astronauts. The maximum intensity of radiation is achieved at an altitude of about 3000 kilometers, which is avoided by all spacecraft. An external electronic belt is not as dangerous. Its maximum lies somewhere between the zones of navigation and geostationary satellites. Satellites operating in highly elongated elliptical orbits usually rise even higher. These are, for example, the Chandra X-ray observatory (USA), which observes far from radiation belts to avoid interference, and the future Russian Radioastron observatory, the data of which is more accurate the greater the distance from a pair of terrestrial radio telescopes working with it. The highest Earth orbits, which can equally be considered near-solar orbits, lie at an altitude of 1.5 million kilometers near the so-called Lagrange points.

Together with the sun

Close to polar are another important class of orbits called sun-synchronous (SSO), which always have a constant orientation relative to the Sun. At first glance, it seems that this contradicts the laws of celestial mechanics, according to which the plane of the orbit remains constant, which means that as the Earth moves around the Sun, it must turn to it first on one side or the other. But if we take into account that the Earth has a flattened shape, it turns out that the orbital plane experiences precession, that is, it rotates slightly from turn to turn. By choosing the right height and inclination, you can ensure that the rotation of the orbital plane exactly corresponds to the arc traversed by the Earth around the Sun. For example, for an orbital altitude of 200 kilometers the inclination should be slightly more than 96° degrees, and for 1000 kilometers it should be more than 99° (figures more than 90° correspond to orbital movement against the daily rotation of the Earth).

The value of the SSO lies in the fact that, moving along it, the satellite flies over terrestrial objects always at the same time of day, which is important for space photography. In addition, due to the proximity of SOF to polar orbits, they can monitor the entire earth's surface, which is important for meteorological, mapping and reconnaissance satellites, which are collectively called Earth remote sensing (ERS) satellites. A certain choice of SSO parameters allows the satellite to never go into the Earth's shadow, always remaining in the sun near the boundary of day and night. The satellite does not experience temperature changes, and solar panels continuously provide it with energy. Such orbits are convenient for radar mapping of the earth's surface.

Civilian remote sensing satellites, which are required to distinguish objects about a meter in size, usually operate at altitudes of 500-600 kilometers. For military reconnaissance satellites with a shooting resolution of 10-30 centimeters, such heights are too high. Therefore, their orbits are often chosen so that the perigee lies above the survey point. If there is more than one “object of attention,” the reconnaissance officer has to change the shape of the orbit using the engine, sometimes making “dives” to the upper layers of the atmosphere, descending to altitudes of about 150 kilometers. The need to “get” as close to the Earth as possible has a significant drawback - atmospheric resistance sharply reduces the satellite’s stay in space. If you gape a little, the atmosphere will drag the satellite into its abyss, where it will inevitably burn up. Because of this, large reserves of fuel have to be kept on board low-orbit “spies” to correct the orbit and periodically raise the altitude. For example, of the 18 tons of launch mass of the American KH-11 photo reconnaissance aircraft, fuel accounts for approximately 40%. Thus, the chosen orbit can directly influence the design and sometimes the appearance of the vehicle.

This dependence was especially clearly manifested in the design of the European scientific apparatus GOCE, recently launched from the Russian Plesetsk cosmodrome. It has an unusual arrow-shaped shape, unlike the angular contours of most modern satellites, and even evokes associations with a high-speed aircraft. The fact is that for the satellite studying the Earth’s gravitational field, a low SSO with an altitude of 240-250 kilometers was chosen. It is optimal from the point of view of measurement accuracy, but in order to withstand the braking effect of the atmosphere, the satellite was shaped with a minimal cross-section. In addition, ion electric rocket engines are installed in the aft part of the device to correct the trajectory.

"Clark's Orbit"

Probably, the first to talk about the possibility of geostationary satellites were Konstantin Eduardovich Tsiolkovsky and Herman Potochnik, an astronautics theorist from Slovenia, better known as Herman Noordung. However, the idea of ​​using them for communication became widespread at the suggestion of the famous British scientist and science fiction writer Arthur C. Clarke. In 1945, he published a popular science article in Wireless World describing communications satellites in geostationary orbit (GSO), now often called the “Clark Orbit.”

Global view

But not all remote sensing satellites require high resolution. What good is the ability to detect an object 30 centimeters in size if the task of the device is to monitor regional or global movements of air masses and thermal regimes of large regions. For its implementation, breadth of coverage is much more important. In global meteorological monitoring, satellites are usually placed in GSO or high MSO, and in regional meteorological monitoring, satellites are usually placed in an orbit of relatively low altitude (500-1000 kilometers) with an inclination that allows regular surveying of the selected area. For example, a promising Russian satellite

"Meteor-M" should monitor the hydrometeorological situation on a global scale with the SSO at an altitude of 830 kilometers. And for the Elektro-L apparatus, GSO was chosen, since its main purpose will be to photograph the entire disk of the Earth in the visible and infrared ranges. In addition, GSO in this case is optimal for obtaining information about global atmospheric processes occurring in the equatorial zone.

Precisely because it is possible to survey a significant part of the earth’s surface from the GEO, it is “populated” not only by communication devices and weather satellites, but also by missile attack warning systems. Their main task is to detect ballistic missile launches, for which the equipment includes an infrared telescope capable of detecting the torch of a running engine. The disadvantages of GSO do not play a role in this case - after all, the satellite does not need to transmit information to the North or South Pole, but a third of the earth's surface is clearly visible.

The choice of orbital parameters for satellites of the global navigation systems GPS and GLONASS turned out to be very difficult. Although the idea itself (to measure the distance to satellites with well-known coordinates by signal delay) was obvious, its implementation dragged on for decades. In the USSR, research in this direction began back in 1958. Five years later, work began on the first satellite navigation system, “Cicada,” which was put into operation only 16 years later. Its four navigation satellites operated in low circular orbits at an altitude of 1000 kilometers with an inclination of 83°. The planes of their orbits were evenly distributed along the equator. Approximately once every one and a half to two hours, a consumer could enter into radio contact with one of the Cicada satellites and, after 5-6 minutes of communication, determine their latitude and longitude. Of course, military customers of satellite navigation were not satisfied with this mode of operation. They needed to determine three spatial coordinates, a velocity vector and exact time at any moment and at any point on the Earth. To do this, it is necessary to simultaneously receive signals from at least four satellites. This would require placing hundreds of spacecraft in low orbits, which would not only be insanely expensive, but also simply unfeasible. The fact is that the service life of Soviet satellites did not exceed one or two years (and more often - several months), and it would turn out that the entire rocket and space industry would work exclusively on the manufacture and launch of navigation satellites. In addition, low-orbit satellites experience significant disturbances due to the influence of the earth's atmosphere, which affects the accuracy of the coordinates determined from them.

Research has shown that the necessary parameters of the navigation system are provided by placing satellites on circular trajectories at an altitude of 19,000-20,000 kilometers (an altitude of 19,100 kilometers was chosen for GLONASS) with an inclination of about 64°. The influence of the atmosphere here is already insignificant, and gravitational disturbances from the Moon and the Sun do not yet lead to rapid changes in the orbit.

Satellite Graveyard

Over the past 20 years, more and more countries have acquired their own telecommunications, meteorological and military satellites in geostationary orbit. As a result, the GSO became crowded. The average distance between satellites is about 500 kilometers, and in some areas heavy vehicles “hang” just a few tens of kilometers from each other. This may cause communication interference and even lead to collisions. Returning satellites from high orbit to Earth is too expensive. Therefore, in order to clear the geostationary orbit, it was decided that after completion of active operation they should be transferred with the remaining fuel to a “disposal orbit” located 200-300 kilometers higher. This “satellite graveyard” is still much freer than the working orbit.

Theoretically, at this altitude, 18 satellites in three orbital planes are enough for at least four satellites to be visible from any point on Earth at the same time. But in fact, to increase the accuracy of determining the location of the spacecraft themselves, the GLONASS constellation will have to be expanded to 24 operating satellites, and taking into account the reserve, the system must have 27-30 satellites. Other navigation systems are built on approximately the same principles - GPS (USA), Galileo (Europe) and Beidou (China). Their satellite constellations are located in circular orbits at an altitude of 20,000-23,500 kilometers with an inclination of 55-56°.

Pilot tracks

The orbits of manned vehicles are specially selected. Thus, during the construction of the International Space Station (ISS), the convenience of launching new modules and spacecraft to it, the safety of the crew, and fuel consumption to maintain altitude were taken into account. As a result, the station was launched into an orbit at an altitude of about 400 kilometers. This is slightly below the boundary of the Earth's radiation belt, in which charged particles from the solar wind accumulate under the influence of our planet's magnetic field. A prolonged stay inside the radiation belt would expose the crew to dangerous radiation or would require powerful radiation protection measures for the orbital station. It is also impossible to lower the orbit significantly lower, otherwise, due to significant aerodynamic drag, the station will decelerate and a lot of fuel will be required to maintain its altitude. The inclination of the orbital plane (51.6°) is determined by the launch conditions from Baikonur, the northernmost cosmodrome from which manned flights take place.

Similar considerations dictated the choice of orbit for the Hubble Space Telescope, since from the very beginning it was assumed that astronauts would periodically visit it. Therefore, the orbital inclination of 28.5° was chosen based on the latitude of the American Canaveral Spaceport. As a result, the orbits of the ISS and the telescope are located at a significant angle to each other, and the space shuttle cannot visit them in one flight, because changing the orbital plane is one of the most “expensive” maneuvers; the shuttle simply does not have enough fuel for it. Because of this, the work of the space telescope almost ended prematurely. After the Columbia disaster in 2003, it was decided that astronauts should be able to take refuge on the ISS if serious damage was discovered during the flight. The flight to the Hubble telescope ruled out this possibility and was almost cancelled. In the end, it was approved, and after a major modernization in 2009, Hubble, which was on the verge of failure, will be able to work for another five years until it is replaced by the new James Webb telescope. True, it will no longer be launched into low-Earth orbit, but much further - to the Lagrange point at an altitude of 1.5 million kilometers, where the orbital period is exactly equal to a year, and the telescope will constantly hide from the Sun behind the Earth. There are no manned flights there yet.

We have described a number of different orbits, but this is by no means the end of their diversity. For any type of orbit, there are variations designed to enhance their positive properties and weaken their negative properties. For example, some satellites move near geostationary orbit with an inclination of up to 10°. This allows them to periodically peer into high latitudes, but ground-based antennas require the ability to tilt up and down to track the satellite's vibrations. Various transition trajectories connecting the two orbits play an important role. With the spread of ion thrusters in near-Earth space, complex spiral paths began to be used. Ballistics specialists are involved in choosing the trajectory of a spacecraft. There is even the term “ballistic design”, which means the joint development of the optimal flight path of the device, its appearance and basic design parameters. In other words, the orbit is developed together with the satellite and the rocket that launches it.

With an angular velocity equal to the angular velocity of the Earth's rotation around its axis. In a horizontal coordinate system, the direction to the satellite does not change either in azimuth or height above the horizon; the satellite “hangs” motionless in the sky. Therefore, a satellite dish, once pointed at such a satellite, remains pointed at it all the time. Geostationary orbit is a type of geosynchronous orbit and is used to place artificial satellites (communications, television broadcasting, etc.).

The satellite should orbit in the direction of Earth's rotation, at an altitude of 35,786 km above sea level. It is this altitude that provides the satellite with an orbital period equal to the relative rotation period of the Earth (sidereal day: 23 hours 56 minutes 4.091 seconds).

The idea of ​​using geostationary satellites for communication purposes was expressed by the Slovenian astronautics theorist Herman Potocnik in 1928.

The advantages of the geostationary orbit became widely known after the publication of Arthur C. Clarke's popular science article in Wireless World magazine in 1945, so in the West geostationary and geosynchronous orbits are sometimes called " Clarke orbits", A " Clark's belt" refers to the region of outer space at a distance of 36,000 km above sea level in the plane of the earth's equator, where the orbital parameters are close to geostationary. The first satellite successfully launched into GEO was Syncom-3, launched by NASA in August 1964.

Standing point

A satellite located in geostationary orbit is stationary relative to the surface of the Earth, therefore its location in orbit is called the stationary point. As a result, a satellite-oriented and fixed directional antenna can maintain constant communication with this satellite for a long time.

Placing satellites in orbit

Geostationary orbit can only be accurately achieved on a circle located directly above the equator, with an altitude very close to 35,786 km.

If geostationary satellites were visible in the sky with the naked eye, then the line on which they would be visible would coincide with the “Clark Belt” for a given area. Geostationary satellites, thanks to the available mounting points, are convenient to use for satellite communications: once oriented, the antenna will always be directed at the selected satellite (if it does not change its position).

To transfer satellites from low-altitude orbit to geostationary orbit, geostationary transfer orbits (GTO) are used - elliptical orbits with a perigee at a low altitude and an apogee at an altitude close to the geostationary orbit.

After completing active operation on the remaining fuel, the satellite must be transferred to a location located 200-300 km above the GSO.

Calculation of geostationary orbit parameters

Orbital radius and orbital altitude

In a geostationary orbit, a satellite does not approach or move away from the Earth, and in addition, rotating with the Earth, it is constantly located above any point on the equator. Consequently, the forces acting on the satellite and the centrifugal force must balance each other. To calculate the altitude of the geostationary orbit, you can use the methods of classical mechanics and, moving to the satellite’s reference frame, proceed from the following equation:

Where is the force of inertia, and in this case, the centrifugal force; - gravitational force. The magnitude of the gravitational force acting on the satellite can be determined by Newton’s law of universal gravitation:

Where is the mass of the satellite, is the mass of the Earth in kilograms, is the gravitational constant, and is the distance in meters from the satellite to the center of the Earth or, in this case, the radius of the orbit.

The magnitude of the centrifugal force is equal to:

Where is the centripetal acceleration that occurs during circular motion in orbit.

As you can see, the mass of the satellite is present as a factor in the expressions for the centrifugal force and for the gravitational force, that is, the altitude of the orbit does not depend on the mass of the satellite, which is true for any orbits and is a consequence of the equality of gravitational and inertial mass. Consequently, the geostationary orbit is determined only by the altitude at which the centrifugal force will be equal in magnitude and opposite in direction to the gravitational force created by the Earth's gravity at a given altitude.

Centripetal acceleration is equal to:

Where is the angular speed of rotation of the satellite, in radians per second.

Let's make one important clarification. In fact, centripetal acceleration has a physical meaning only in an inertial frame of reference, while centrifugal force is a so-called imaginary force and occurs exclusively in frames of reference (coordinates) that are associated with rotating bodies. Centripetal force (in this case, the force of gravity) causes centripetal acceleration. In absolute value, the centripetal acceleration in the inertial reference frame is equal to the centrifugal acceleration in the reference frame associated in our case with the satellite. Therefore, further, taking into account the remark made, we can use the term “centripetal acceleration” together with the term “centrifugal force”.

Equating the expressions for gravitational and centrifugal forces with the substitution of centripetal acceleration, we obtain:

Reducing , translating to the left and to the right, we get:

Or

This expression can be written differently, replacing it with the geocentric gravitational constant:

Angular velocity is calculated by dividing the angle traveled per revolution (radians) by the orbital period (the time it takes to complete one revolution in the orbit: one sidereal day, or 86,164 seconds). We get:

rad/s The resulting orbital radius is 42,164 km. Subtracting the equatorial radius of the Earth, 6,378 km, we get an altitude of 35,786 km.

You can do the calculations in another way. The altitude of the geostationary orbit is the distance from the center of the Earth where the angular velocity of the satellite, coinciding with the angular velocity of the Earth's rotation, generates an orbital (linear) velocity equal to the first escape velocity (to ensure a circular orbit) at a given altitude.

The linear speed of a satellite moving with angular velocity at a distance from the center of rotation is equal to

The first escape velocity at a distance from an object of mass is equal to

Equating the right-hand sides of the equations to each other, we arrive at the previously obtained expression radius GSO:

Orbital speed

The speed of movement in geostationary orbit is calculated by multiplying the angular speed by the radius of the orbit:

km/s This is approximately 2.5 times less than the first escape velocity of 8 km/s in low-Earth orbit (with a radius of 6400 km). Since the square of the speed for a circular orbit is inversely proportional to its radius,

That decrease in speed relative to the first cosmic speed is achieved by increasing the orbital radius by more than 6 times.

Orbit length

Geostationary orbit length: . With an orbital radius of 42,164 km, we obtain an orbital length of 264,924 km.

The length of the orbit is extremely important for calculating the “standing points” of the satellites.

Keeping a satellite in orbital position in geostationary orbit

A satellite orbiting in geostationary orbit is under the influence of a number of forces (disturbances) that change the parameters of this orbit. In particular, such disturbances include gravitational lunar-solar disturbances, the influence of the inhomogeneity of the Earth’s gravitational field, the ellipticity of the equator, etc. Orbital degradation is expressed in two main phenomena:

1) The satellite moves along the orbit from its original orbital position towards one of the four points of stable equilibrium, the so-called. “potential geostationary orbit holes” (their longitudes are 75.3°E, 104.7°W, 165.3°E, and 14.7°W) above the Earth’s equator;

2) The inclination of the orbit to the equator increases (from the initial 0) at a rate of about 0.85 degrees per year, and reaches a maximum value of 15 degrees in 26.5 years.

To compensate for these disturbances and keep the satellite at the designated stationary point, the satellite is equipped with a propulsion system (chemical or electric rocket). By periodically turning on the low-thrust engines (correction “north-south” to compensate for the increase in orbital inclination and “west-east” to compensate for drift along the orbit), the satellite is kept at the designated stationary point. Such inclusions are made several times every 10-15 days. It is significant that the north-south correction requires a significantly larger increase in the characteristic velocity (about 45-50 m/s per year) than for the longitudinal correction (about 2 m/s per year). To ensure correction of the satellite's orbit throughout its entire service life (12-15 years for modern television satellites), a significant supply of fuel on board is required (hundreds of kilograms in the case of a chemical engine). The satellite's chemical rocket engine has a displacement fuel supply (boost gas - helium) and runs on long-lasting high-boiling components (usually unsymmetrical dimethylhydrazine and dinitrogen tetroxide). A number of satellites are equipped with plasma engines. Their thrust is significantly less than chemical ones, but their greater efficiency allows (due to long-term operation, measured in tens of minutes for a single maneuver) to radically reduce the required mass of fuel on board. The choice of the type of propulsion system is determined by the specific technical features of the device.

The same propulsion system is used, if necessary, to maneuver the satellite into another orbital position. In some cases, usually at the end of the satellite's life, to reduce fuel consumption, the north-south orbit correction is stopped, and the remaining fuel is used only for the west-east correction.

Fuel reserve is the main limiting factor in the service life of a satellite in geostationary orbit.

Disadvantages of geostationary orbit

Signal delay

Communications via geostationary satellites are characterized by large delays in signal propagation. With an orbital altitude of 35,786 km and a speed of light of about 300,000 km/s, the Earth-to-satellite beam travel requires about 0.12 s. Beam path “Earth (transmitter) → satellite → Earth (receiver)” ≈0.24 s. The total latency (measured by the Ping utility) when using satellite communications to receive and transmit data will be almost half a second. Taking into account the signal delay in satellite equipment, in equipment and in cable transmission systems of terrestrial services, the total signal delay on the route “signal source → satellite → receiver” can reach 2-4 seconds. This delay makes it difficult to use GSO satellites in telephony and makes it impossible to use satellite communications using GSO in various real-time services (for example, in online games).

Invisibility of GSO from high latitudes

Since the geostationary orbit is not visible from high latitudes (from approximately 81° to the poles), and at latitudes above 75° it is observed very low above the horizon (in real conditions, satellites are simply hidden by protruding objects and terrain) and only a small part of the orbit is visible ( see table), then communication and television broadcasting using GSO is impossible in the high-latitude regions of the Far North (Arctic) and Antarctica. For example, American polar explorers at the Amundsen-Scott station use a fiber-optic cable 1,670 kilometers long to communicate with the outside world (telephony, Internet) to a location located at 75° S. French station Concordia, from which several American geostationary satellites are already visible.

Table of the observed sector of the geostationary orbit depending on the latitude of the place
All data is given in degrees and their fractions.

From the table above it can be seen, for example, that if at the latitude of St. Petersburg (~60°) the visible sector of the orbit (and accordingly the number of received satellites) is equal to 84% of the maximum possible (at the equator), then at the latitude of the Taimyr Peninsula (~75° ) the visible sector is 49%, and at the latitude of Spitsbergen and Cape Chelyuskin (~78°) it is only 16% of that observed at the equator. This sector of the orbit in the Siberian region contains 1-2 satellites (not always of the required country).

Solar interference

One of the most unpleasant disadvantages of the geostationary orbit is the reduction and complete absence of the signal in a situation where the transmitter satellite is in line with the receiving antenna (the “Sun behind the satellite” position). This phenomenon is also inherent in other orbits, but it is in geostationary orbits, when the satellite is “stationary” in the sky, that it manifests itself especially clearly. In the mid-latitudes of the northern hemisphere, solar interference occurs during the periods from February 22 to March 11 and from October 3 to 21, with a maximum duration of up to ten minutes. At such moments in clear weather, the sun's rays focused by the light coating of the antenna can damage (melt or overheat) the receiving and transmitting equipment of the satellite antenna.

International legal status of GSO

The use of the geostationary orbit poses a number of not only technical, but also international legal problems. The UN, as well as its committees and other specialized agencies, make a significant contribution to their resolution.

Some equatorial countries have at various times made claims (for example, the Declaration on the Establishment of Sovereignty in the GSO Area, signed in Bogotá by Brazil, Colombia, Congo, Ecuador, Indonesia, Kenya, Uganda and Zaire on December 3, 1976) to extend their sovereignty to those located above their territories are the part of outer space in which the orbits of geostationary satellites pass. In particular, it was stated that the geostationary orbit is a physical factor associated with the existence of our planet and completely dependent on the gravitational field of the Earth, and therefore the corresponding parts of space (segments of the geostationary orbit) are, as it were, a continuation of the territories over which they are located. The corresponding provision is enshrined in the Constitution of Colombia.

These claims of the equatorial states were rejected as contrary to the principle of non-appropriation of outer space. Such statements were justifiably criticized by the UN Committee on Outer Space. Firstly, one cannot claim to appropriate any territory or space located at such a significant distance from the territory of the relevant state. Secondly, outer space is not subject to national appropriation. Thirdly, it is technically incompetent to talk about any physical relationship between state territory and such a distant region of space. Finally, in each individual case the phenomenon of a geostationary satellite is associated with a specific space object. If there is no satellite, then there is no geostationary orbit.

In a geostationary orbit, a satellite does not approach or move away from the Earth, and in addition, rotating with the Earth, it is constantly located above any point on the equator. Consequently, the gravitational and centrifugal forces acting on the satellite must balance each other. To calculate the altitude of the geostationary orbit, you can use the methods of classical mechanics and, moving to the satellite’s reference frame, proceed from the following equation:

where is the inertial force, and in this case, the centrifugal force; is the gravitational force. The magnitude of the gravitational force acting on the satellite can be determined by Newton’s law of universal gravitation:

where is the mass of the satellite, is the mass of the Earth in kilograms, is the gravitational constant, and is the radius of the orbit (the distance in meters from the satellite to the center of the Earth).

The magnitude of the centrifugal force is equal to:

where is the centripetal acceleration that occurs during circular motion in orbit.

As can be seen, the mass of the satellite is present in the expressions for both the centrifugal force and the gravitational force. That is, the altitude of the orbit does not depend on the mass of the satellite, which is true for any orbits and is a consequence of the equality of gravitational and inertial mass. Consequently, the geostationary orbit is determined only by the altitude at which the centrifugal force will be equal in magnitude and opposite in direction to the gravitational force created by the Earth's gravity at a given altitude.

Centripetal acceleration is equal to:

where is the angular speed of rotation of the satellite, in radians per second.

Based on the equality of gravitational and centrifugal forces, we obtain:

Angular velocity ω is calculated by dividing the angle traversed in one revolution by the orbital period (the time it takes to complete one complete revolution in the orbit: one sidereal day, or 86,164 seconds). We get: rad/s

The estimated orbital radius is 42,164 km. Subtracting the equatorial radius of the Earth, 6,378 km, we obtain the GEO altitude of 35,786 km.

Orbital speed

The speed of movement in geostationary orbit is calculated by multiplying the angular speed by the radius of the orbit: km/s

This is approximately 2.5 times less than the first escape velocity of 8 km/s for near-Earth orbit (with a radius of 6400 km). Since the square of the speed for a circular orbit is inversely proportional to its radius, a decrease in speed relative to the first cosmic speed is achieved by increasing the orbital radius by more than 6 times.

Orbit length

Geostationary orbit length: . With an orbital radius of 42,164 km, we obtain an orbital length of 264,924 km. The length of the orbit is extremely important for calculating the “standing points” of the satellites.

Maintaining a satellite in an orbital position in a geostationary orbit. A satellite orbiting in a geostationary orbit is under the influence of a number of forces (disturbances) that change the parameters of this orbit. In particular, such disturbances include gravitational lunar-solar disturbances, the influence of the inhomogeneity of the Earth’s gravitational field, the ellipticity of the equator, etc. Orbital degradation is expressed in two main phenomena:

1) The satellite moves along the orbit from its original orbital position towards one of four points of stable equilibrium, the so-called “potential holes of geostationary orbit” (their longitudes are 75.3°E, 104.7°W, 165.3°E, and 14.7°W) above the Earth's equator;

2) The inclination of the orbit to the equator increases (from the initial = 0) at a rate of about 0.85 degrees per year and reaches a maximum value of 15 degrees in 26.5 years.

To compensate for these disturbances and keep the satellite at the designated stationary point, the satellite is equipped with a propulsion system (chemical or electric rocket). By periodically turning on the low-thrust engines (correction “north-south” to compensate for the increase in orbital inclination and “west-east” to compensate for drift along the orbit), the satellite is kept at the designated stationary point. Such inclusions are made several times every few (10-15) days. It is significant that the north-south correction requires a significantly larger increase in the characteristic velocity (about 45-50 m/s per year) than for the longitudinal correction (about 2 m/s per year). To ensure correction of the satellite's orbit throughout its entire service life (12-15 years for modern television satellites), a significant supply of fuel on board is required (hundreds of kilograms, in the case of using a chemical engine). The satellite's chemical rocket engine has a displacement fuel supply system (boost gas - helium) and runs on long-lasting, high-boiling components (usually unsymmetrical dimethylhydrazine and nitrogen tetroxide). A number of satellites are equipped with plasma engines. Their thrust is significantly less than that of chemical ones, but their greater efficiency allows (due to prolonged operation, measured in tens of minutes for a single maneuver) to radically reduce the required mass of fuel on board. The choice of the type of propulsion system is determined by the specific technical features of the device.

The same propulsion system is used, if necessary, to maneuver the satellite into another orbital position. In some cases, usually at the end of the satellite's life, to reduce fuel consumption, the north-south orbit correction is stopped, and the remaining fuel is used only for the west-east correction. Fuel reserve is the main limiting factor in the service life of a satellite in geostationary orbit.

Geostationary orbit (Figure 13.7) is characterized by the fact that if the satellites located on it move with angular velocities equal to the angular velocity of the Earth’s rotation around its axis, then from the Earth’s surface they appear motionless, “hanging” in one place, at one point. Since the distance from a satellite moving in geostationary orbit to the Earth is three times the diameter of the Earth, the satellite “sees” about 40% of the Earth’s surface at once.

Putting artificial satellites into geostationary orbit is not an easy task. Previously, there were not sufficiently powerful launch vehicles to launch it, so the first communications satellites were in elliptical, low-Earth orbit (for example, the first American relay satellite Telstar).

Figure 13.7 - Geostationary orbit

Maintaining communications with satellites in elliptical orbit is very complex and expensive, both in terms of transmission and reception.

Due to the rapid change in the location of satellites, it is necessary to have a mobile tracking antenna system. Satellites in such orbits can be used to create permanent communications only when they are above the horizon in relation to both the transmitting and receiving devices, i.e. for them, both the “rising” of one satellite and the “setting” of another should be visible.

The development of rocket technology and the creation of powerful rocket launchers have made it possible to widely use the geostationary orbit to “install” relay satellites on it. Figure 13.8 shows a commonly used method for launching satellites into geostationary orbit. An artificial satellite is first launched into a circular orbit close to the Earth's surface (250...300 km from the surface), then, increasing its speed, it is transferred to an elliptical intermediate orbit, the closest point of which - perigee - is approximately 270 km from the Earth, and the distant point is the apogee at a distance of about 36,000 km, which already corresponds to the altitude of the geostationary orbit*.

Figure 13.8 - Sequence of launching a satellite into geostationary orbit:

1 - fairing release; 2 - completion of the initial flight; 3 - complete separation of the last stage; 4 - determination of the position for the first activation of the own (apogee) engine; 5 - first activation of its own engine to enter an intermediate (transfer) orbit; 6 - determination of position in an intermediate orbit; 7 - second activation of its own engine to enter geostationary orbit; 8 - reorientation of the satellite orbital plane and error correction; 9 - satellite orientation perpendicular to the orbital plane and error correction; 10-stop, deployment of solar panels, complete undocking; 11 - deployment of antennas, activation of stabilizers; 12 - position stabilization and start of work

When an artificial satellite “stands” in an elliptical intermediate (transfer) orbit, and if everything is functioning flawlessly, then at the apogee point its own jet, so-called apogee engines are turned on, which quickly increase the linear speed of the satellite to 3.074 km / s. This speed is necessary to move to geostationary orbit and “stop” (more precisely, to move along it), after which the satellite, following commands from the Earth, is moved along geostationary orbit to a planned position at the standing point. Then the solar panels are deployed, the antennas are deployed, they are oriented to a given territory of the Earth, the solar panels are oriented to the Sun, and the on-board transmitter-relay is turned on. The precise installation of a satellite in geostationary orbit is carried out by its own jet engines running on solid or liquid fuel. After the satellite is launched into its orbital position, the engines are turned off and it moves in geostationary orbit as a celestial body under the influence of inertia at a speed of 3.074 km/s and the forces of gravity of the Earth. It is very important for a relay satellite that its own orbit corresponds perfectly to the geostationary one. So, if a satellite moves in an orbit that is slightly smaller than the geostationary one, then it gradually shifts from its position in the western direction, and if its orbit exceeds the geostationary one, then the displacement occurs in the eastern direction, i.e. in the direction of the Earth’s movement. A shift of 1° in geostationary orbit corresponds to a distance of approximately 750 km. If the ground receiver has a rotating tracking antenna, it is easy to point it again accurately at the satellite. However, most individual ground-based devices for receiving from satellites have fixed antennas with very narrow, “needle-shaped” radiation patterns, and it is quite cumbersome to constantly adjust the direction of the antenna to the satellite manually, and due to the inaccuracy of its pointing, the received television image noticeably deteriorates or disappears altogether. In this regard, in order to ensure reliable and reliable reception, it is necessary to ensure that the “footprint” of the satellite is constant over time and that the radiation of its on-board antennas is stable only in a designated area. Therefore, the satellite needs to frequently correct its position and orbit, which it does using its own engines and leads to fuel consumption. This affects its service life. In the absence of fuel for the engines, the satellite begins to move from its position, which leads to periodic convergence of neighboring satellites and, accordingly, to an increase in mutual interference, and to an increase in interference to receiving devices on Earth.

From the point of view of the life of the satellite, the amount of fuel consumed by its own jet (apogee) engines is extremely important. And, obviously, the more fuel left after the initial installation of the satellite in orbit, the more position adjustments can be made and, therefore, the longer the satellite will operate. The “life” of a satellite in orbit is usually 5...7 years, and some - 10 years or more, after which it is replaced by a new one installed in the same position.

Advantages of geostationary orbit. The geostationary orbit (called the Clark Belt in England and some European countries) is unique and has significant operational value. A number of equatorial states previously wanted the portion of the orbit located above their territory to be used only by agreement with them. Non-equatorial countries, naturally, could not agree with this, considering the geostationary orbit as the common heritage of mankind. Only in 1988 was it possible to agree on a plan for the distribution of satellite positions for broadcasting in the 6/4 GHz and 14/11 GHz frequency bands.

The advantages of the geostationary orbit encourage an increasing number of users to place satellites for various purposes on it. From the European continent you can “observe” several dozen artificial satellites moving in geostationary orbit. Through them, telephone communications are primarily carried out with the countries of the American continent and the countries of the Middle East. In addition, many satellites are used to relay television and sound broadcasts. Using geostationary orbit for these purposes provides the following advantages:

§ the satellite moves in a geostationary orbit from West to East for a long time without spending energy on this movement (like a celestial body) due to the gravitational attraction of the Earth and its own inertia, with a linear speed of 3.074 km/s;

§ moving in a geostationary orbit with an angular velocity equal to the angular velocity of the Earth’s rotation, the satellite makes a revolution exactly in one day, as a result of which it finds itself motionless “hanging” above the earth’s surface;

§ the energy supply of its systems is carried out from solar panels illuminated by the Sun;

§ since the satellite does not cross the Earth’s radiation belt, but is located above it, the reliability and service life of its electronic devices and power sources – solar panels – increases;

§ communication with the transmitting station is carried out continuously, without switching from one “incoming” satellite to another – “upstream”, i.e. only one satellite is needed to ensure continuous constant communication;

§ in transmitting antennas in the Earth-Satellite system, automatic satellite tracking devices can be simplified or eliminated altogether, and in ground-based receiving antennas there is virtually no need for them, which ensures the simplicity of receiving devices, their low cost, availability and mass distribution;

§ since the distance to a satellite in geostationary orbit is always constant, the attenuation of the signal when passing along the Earth-Satellite-Earth path is always certain and does not change as the satellite moves in orbit, which makes it possible to accurately calculate the power of its onboard transmitter;

§ The geostationary orbit is unique - satellites located in orbits above it “go” into outer space, and those located in orbits below it gradually approach the Earth. And only satellites located in geostationary orbit rotate synchronously at a constant distance from the Earth and are motionless relative to it;

§ after the end of its operational life, the satellite is transferred to the so-called “cemetery” orbit, which is 200 km above the geostationary one, and it gradually moves away from the Earth into outer space.

However, orbital constellations consisting of geostationary satellites have one major drawback: the long propagation time of radio signals, which leads to delays in signal transmission during radiotelephone communications. Waiting for a response signal to arrive can cause dissatisfaction among impatient subscribers.

Due to its unique properties and advantages, the geostationary orbit in the most convenient areas (especially over the Pacific and Indian oceans, as well as over the African continent) is “populated” with satellites to the limit. There are 425 “standing” points identified in geostationary orbit—satellite positions. The word “position” unambiguously determines the position of the satellite in geostationary orbit and its longitude.

The Earth, like any cosmic body, has its own gravitational field and nearby orbits in which bodies and objects of different sizes can be located. Most often they refer to the Moon and the International Space Station. The first one walks in its own orbit, and the ISS - in a low near-Earth orbit. There are several orbits that differ in their distance from the Earth, their relative location relative to the planet, and the direction of rotation.

Orbits of artificial earth satellites

Today, in the nearest near-Earth space there are many objects that are the results of human activity. Basically, these are artificial satellites used to provide communications, but there is also a lot of space debris. One of the most famous artificial satellites of the Earth is the International Space Station.

Satellites move in three main orbits: equatorial (geostationary), polar and inclined. The first lies entirely in the plane of the equatorial circle, the second is strictly perpendicular to it, and the third is located between them.

Geosynchronous orbit

The name of this trajectory is due to the fact that the body moving along it has a speed equal to the sidereal period of the Earth’s rotation. Geostationary orbit is a special case of geosynchronous orbit, which lies in the same plane as the Earth's equator.

With an inclination not equal to zero and zero eccentricity, the satellite, when observed from the Earth, describes a figure eight in the sky during the day.

The first satellite in geosynchronous orbit is the American Syncom-2, launched into it in 1963. Today, in some cases, satellites are placed in geosynchronous orbit because the launch vehicle cannot place them in geosynchronous orbit.

Geostationary orbit

This trajectory has this name for the reason that, despite the constant movement, the object located on it remains static relative to the earth's surface. The place where the object is located is called the standing point.

Satellites placed in such an orbit are often used to transmit satellite television, because the static nature allows you to point the antenna at it once and remain connected for a long time.

The altitude of the satellites in geostationary orbit is 35,786 kilometers. Since they are all directly above the equator, only the meridian is named to indicate the position, for example, 180.0˚E Intelsat 18 or 172.0˚E Eutelsat 172A.

The approximate orbital radius is ~42,164 km, the length is about 265,000 km, and the orbital speed is approximately 3.07 km/s.

High elliptical orbit

A high elliptical orbit is a trajectory whose height at perigee is several times less than at apogee. Putting satellites into such orbits has a number of important advantages. For example, one such system may be sufficient to serve the whole of Russia or, accordingly, a group of states with an equal total area. In addition, VEO systems at high latitudes are more capable than geostationary satellites. And putting a satellite into a high elliptical orbit costs approximately 1.8 times less.

Large examples of systems running on VEO:

• Space observatories launched by NASA and ESA.
• Sirius XM Radio Satellite Radio.
• Satellite communications Meridian, -Z and -ZK, Molniya-1T.
• GPS satellite correction system.

Low Earth orbit

This is one of the lowest orbits, which, depending on various circumstances, can have an altitude of 160-2000 km and an orbital period of 88-127 minutes, respectively. The only time LEO was overcome by manned spacecraft was the Apollo program with the landing of American astronauts on the moon.

Most of the artificial earth satellites currently in use or ever used operated in low Earth orbit. For the same reason, the bulk of space debris is now located in this zone. The optimal orbital speed for satellites located in LEO is, on average, 7.8 km/s.

Examples of artificial satellites in LEO:

• International Space Station (400 km).
• Telecommunication satellites of a wide variety of systems and networks.
• Reconnaissance vehicles and probe satellites.

The abundance of space debris in orbit is the main modern problem of the entire space industry. Today the situation is such that the likelihood of collisions between various objects in LEO is growing. And this, in turn, leads to destruction and the formation of even more fragments and parts in orbit. Pessimistic forecasts suggest that the launched Domino Principle can completely deprive humanity of the opportunity to explore space.

Low reference orbit

Low reference is usually called the orbit of the device, which provides for a change in inclination, altitude or other significant changes. If the device does not have an engine and does not perform maneuvers, its orbit is called low Earth orbit.

It is interesting that Russian and American ballisticians calculate its height differently, because the former are based on an elliptical model of the Earth, and the latter on a spherical one. Because of this, there is a difference not only in height, but also in the position of perigee and apogee.