As you know, geostationary satellites hang motionless above the earth over the same point. Why don't they fall? Is there no gravity at that height?
Answer
A geostationary artificial Earth satellite is a device that moves around the planet in an easterly direction (in the same direction as the Earth itself rotates), along a circular equatorial orbit with a period of revolution equal to the period of the Earth's own rotation.
Thus, if we look from the Earth at a geostationary satellite, we will see it hanging motionless in the same place. Because of this immobility and high altitude about 36,000 km, from which almost half of the Earth's surface is visible, relay satellites for television, radio and communications are placed into geostationary orbit.
From the fact that a geostationary satellite constantly hangs over the same point on the Earth's surface, some people make the wrong conclusion that the force of attraction to the Earth does not act on the geostationary satellite, that the force of gravity disappears at a certain distance from the Earth, i.e. they refute the very Newton. Of course it is not. The very launch of satellites into geostationary orbit is calculated precisely according to the law gravity Newton.
Geostationary satellites, like all other satellites, actually fall to the Earth, but do not reach its surface. They are affected by the force of attraction to the Earth (gravitational force), directed towards its center, and in the opposite direction, the satellite is affected by the centrifugal force repelling from the Earth (inertia force), which balance each other - the satellite does not fly away from the Earth and does not fall on it exactly just like a bucket spinning on a rope remains in its orbit.
If the satellite did not move at all, then it would fall to the Earth under the influence of attraction to it, but satellites move, including geostationary ones (geostationary ones - with an angular velocity equal to angular velocity rotation of the Earth, i.e., one revolution per day, and the satellites of lower orbits have a higher angular velocity, i.e., they manage to make several revolutions around the Earth per day). The linear velocity reported to the satellite parallel to the Earth's surface during direct launch into orbit is relatively large (in low Earth orbit - 8 kilometers per second, in geostationary orbit - 3 kilometers per second). If there were no Earth, then the satellite would fly in a straight line at such a speed, but the presence of the Earth makes the satellite fall on it under the influence of gravity, bending the trajectory towards the Earth, but the surface of the Earth is not flat, it is curved. As far as the satellite approaches the surface of the Earth, so much the surface of the Earth goes from under the satellite and, thus, the satellite is constantly at the same height, moving along a closed trajectory. The satellite is falling all the time, but it can never fall.
So, all artificial satellites of the Earth fall to the Earth, but - along a closed trajectory. Satellites are in a state of weightlessness, like all falling bodies (if the elevator in a skyscraper breaks down and starts to fall freely, then the people inside will also be in a state of weightlessness). The astronauts inside the ISS are in weightlessness not because the force of attraction to the Earth does not act in orbit (it is almost the same there as on the surface of the Earth), but because the ISS falls freely to the Earth - along a closed circular trajectory.
Just as the seats in a theater provide different perspectives on a performance, the different orbits of the satellites provide a perspective, each with a different purpose. Some appear to be hovering over a point on the surface, providing a constant view of one side of the Earth, while others circle our planet, sweeping over many places in a day.
Orbit types
At what altitude do satellites fly? There are 3 types of Earth orbits: high, medium and low. As a rule, many weather and some communication satellites are located on the high, most distant from the surface. Satellites rotating in medium near-Earth orbit include navigation and special satellites designed to monitor a particular region. Most scientific spacecraft, including the NASA Earth Observation System fleet, are in low orbit.
The speed at which satellites fly depends on the speed of their movement. As we get closer to the Earth, gravity becomes stronger and the movement speeds up. For example, NASA's Aqua satellite takes about 99 minutes to fly around our planet at an altitude of about 705 km, while a meteorological apparatus 35,786 km from the surface takes 23 hours, 56 minutes and 4 seconds. At a distance of 384,403 km from the center of the Earth, the Moon completes one rotation in 28 days.
Aerodynamic paradox
Changing the height of a satellite also changes its orbital speed. There is a paradox here. If the operator of a satellite wants to increase its speed, he cannot simply start the engines to speed it up. This will increase the orbit (and height), resulting in a decrease in speed. Instead, you should start the engines in the direction opposite to the direction of the satellite, i.e., perform an action that on Earth would slow down the moving vehicle. This action will move it lower, which will increase the speed.
Orbit characteristics
In addition to altitude, the path of a satellite is characterized by eccentricity and inclination. The first relates to the shape of the orbit. A satellite with a low eccentricity moves along a trajectory close to circular. The eccentric orbit has the shape of an ellipse. The distance from the spacecraft to the Earth depends on its position.
The inclination is the angle of the orbit with respect to the equator. A satellite that orbits directly above the equator has zero inclination. If the spacecraft passes over the northern and south poles(geographic, not magnetic), its slope is 90°.
All together - height, eccentricity and inclination - determine the movement of the satellite and how the Earth will look from its point of view.
high near earth
When a satellite reaches exactly 42,164 km from the center of the Earth (about 36,000 km from the surface), it enters a zone where its orbit corresponds to the rotation of our planet. Since the vehicle is moving at the same speed as the Earth, i.e., its period of revolution is 24 hours, it seems to remain in place over a single longitude, although it may drift from north to south. This special high orbit is called geosynchronous.
The satellite moves in a circular orbit directly above the equator (eccentricity and inclination are zero) and stands still relative to the Earth. It is always located above the same point on its surface.
The Molniya orbit (inclination 63.4°) is used for observation at high latitudes. Geostationary satellites are tied to the equator, so they are not suitable for far northern or southern regions. This orbit is quite eccentric: the spacecraft moves in an elongated ellipse with the Earth close to one edge. Since the satellite accelerates under the influence of gravity, it moves very quickly when it is close to our planet. When moving away, its speed slows down, so it spends more time at the top of the orbit in the farthest edge from the Earth, the distance to which can reach 40 thousand km. The orbital period is 12 hours, but the satellite spends about two-thirds of this time over one hemisphere. Like a semi-synchronous orbit, the satellite follows the same path every 24 hours. Used for communication in the far north or south.
Low Earth
Most scientific satellites, many meteorological and space stations are in a nearly circular low Earth orbit. Their slope depends on what they are monitoring. TRMM was launched to monitor rainfall in the tropics, so it has a relatively low inclination (35°) while staying close to the equator.
Many of NASA's surveillance satellites have a near-polar, highly inclined orbit. The spacecraft moves around the Earth from pole to pole with a period of 99 minutes. Half the time it passes over the day side of our planet, and at the pole it passes to the night side.
As the satellite moves, the Earth rotates underneath it. By the time the spacecraft moves to the illuminated area, it is above the area adjacent to the zone of passage of its last orbit. In a 24-hour period, polar satellites cover most of the Earth twice: once during the day and once at night.
Sun-synchronous orbit
Just as geosynchronous satellites must be above the equator, which allows them to stay above the same point, polar orbiting satellites have the ability to stay in the same time. Their orbit is sun-synchronous - when the spacecraft crosses the equator, the local solar time always the same. For example, the Terra satellite crosses it over Brazil always at 10:30 am. The next crossing in 99 minutes over Ecuador or Colombia also occurs at 10:30 local time.
A sun-synchronous orbit is necessary for science, as it allows sunlight to be kept on the Earth's surface, although it will change with the season. This consistency means that scientists can compare images of our planet at the same time of the year over several years without worrying about too many jumps in lighting that can give the illusion of change. Without a sun-synchronous orbit, it would be difficult to track them over time and collect the information needed to study climate change.
The path of the satellite is very limited here. If it is at an altitude of 100 km, the orbit should have an inclination of 96°. Any deviation will be invalid. Because atmospheric drag and the gravitational pull of the Sun and Moon change the orbit of the spacecraft, it must be corrected regularly.
Orbital insertion: launch
The launch of a satellite requires energy, the amount of which depends on the location of the launch site, the height and inclination of the future trajectory of its movement. To get to a distant orbit, more energy is required. Satellites with a significant inclination (for example, polar ones) are more energy-consuming than those that circle the equator. The low-inclination orbit is assisted by the Earth's rotation. moves at an angle of 51.6397°. This is necessary to make it easier for space shuttles and Russian rockets to reach it. The height of the ISS is 337-430 km. Polar satellites, on the other hand, are not assisted by Earth's momentum, so they require more energy to travel the same distance.
Adjustment
After launching a satellite, efforts must be made to keep it in a certain orbit. Since the Earth is not a perfect sphere, its gravity is stronger in some places. This unevenness, along with the attraction of the Sun, Moon and Jupiter (the most massive planet solar system), changes the inclination of the orbit. Over the course of its lifetime, GOES satellites have been corrected three or four times. NASA's LEOs must adjust their inclination annually.
In addition, near-Earth satellites are affected by the atmosphere. The uppermost layers, although quite rarefied, offer strong enough resistance to pull them closer to the Earth. The action of gravity leads to the acceleration of the satellites. Over time, they burn up, spiraling lower and faster into the atmosphere, or fall to Earth.
Atmospheric drag is stronger when the Sun is active. Just like the air in hot-air balloon expands and rises when heated, the atmosphere rises and expands when the Sun gives it extra energy. The rarefied layers of the atmosphere rise, and denser ones take their place. Therefore, satellites in Earth orbit must change their position about four times a year to compensate for atmospheric drag. When solar activity is maximum, the position of the device has to be adjusted every 2-3 weeks.
space junk
The third reason forcing to change the orbit is space debris. One of the Iridium communications satellites collided with a non-functioning Russian spacecraft. They crashed, forming a cloud of debris, consisting of more than 2500 parts. Each element has been added to the database, which today has over 18,000 man-made objects.
NASA carefully monitors everything that may be in the path of satellites, because space debris has already had to change orbits several times.
Engineers monitor the position of space debris and satellites that can interfere with movement and carefully plan evasive maneuvers as necessary. The same team plans and executes maneuvers to adjust the tilt and height of the satellite.
Or why satellites don't fall? A satellite's orbit is a delicate balance between inertia and gravity. The force of gravity continuously pulls the satellite towards the Earth, while the inertia of the satellite tends to keep its motion in a straight line. If there were no gravity, the inertia of the satellite would send it straight out of Earth orbit into outer space. However, at every point in the orbit, gravity keeps the satellite tethered.
To achieve a balance between inertia and gravity, the satellite must have a strictly defined speed. If it flies too fast, the inertia overcomes gravity and the satellite leaves orbit. (The calculation of the so-called second space velocity, which allows the satellite to leave Earth orbit, plays an important role in launching interplanetary space stations.) If the satellite is moving too slowly, gravity will win the fight against inertia and the satellite will fall to Earth. This is exactly what happened in 1979, when the American space station Skylab began to decline as a result of the growing resistance. upper layers earth's atmosphere. Having fallen into the iron tongs of gravity, the station soon fell to Earth.
Speed and distance
Insofar as Earth gravity weakens with distance, the speed required to keep a satellite in orbit varies with altitude. Engineers can calculate how fast and how high a satellite needs to orbit. For example, a geostationary satellite, located always above the same point on the earth's surface, must complete one revolution in 24 hours (which corresponds to the time of one revolution of the Earth around its axis) at an altitude of 357 kilometers.
Gravity and inertia
Balancing a satellite between gravity and inertia can be simulated by rotating a load on a rope tied to it. The inertia of the load tends to move it away from the center of rotation, while the tension of the rope, acting as gravity, keeps the load in a circular orbit. If the rope is cut, the load will fly away along a straight trajectory perpendicular to the radius of its orbit.
To launch a satellite into near-Earth orbit, it is necessary to give it an initial velocity equal to the first space velocity or slightly higher than the latter. This does not happen immediately, but gradually. A multi-stage satellite-carrying rocket slowly picks up speed. When the speed of its flight reaches the calculated value, the satellite is separated from the rocket and begins its free movement in orbit. The shape of the orbit depends on the initial velocity given to it and its direction: its dimensions and eccentricity.
If there were no resistance of the environment and the perturbing attraction of the Moon and the Sun, and the Earth would have a spherical shape, then the satellite's orbit would not undergo any changes, and the satellite itself would move along it forever. However, in reality, the orbit of each satellite changes under the influence of various reasons.
The main force that changes the satellite's orbit is the deceleration that occurs due to the resistance of the rarefied medium through which the satellite flies. Let's see how it affects his movement. Since the orbit of a satellite is usually elliptical, its distance from the Earth changes periodically. It decreases towards the perigee and reaches its maximum distance at the apogee. The density of the earth's atmosphere rapidly decreases with increasing altitude, and therefore the satellite encounters the greatest resistance near the perigee. Having spent part of the kinetic energy to overcome this, albeit small, resistance, the satellite can no longer rise to its previous height, and its apogee gradually decreases. The decrease in perigee also occurs, but much more slowly than the decrease in apogee. Thus, the dimensions of the orbit and its eccentricity gradually decrease: the elliptical orbit approaches a circular one. The satellite moves around the Earth in a slowly coiling spiral and eventually ends its existence in the dense layers of the earth's atmosphere, warming up and evaporating like a meteoroid. With large sizes, it can reach the surface of the Earth.
It is interesting to note that the deceleration of the satellite does not decrease its speed, but, on the contrary, increases it. Let's do some simple calculations.
From Kepler's third law it follows that
where C is a constant, M is the mass of the Earth, m is the mass of the satellite, P is the period of its revolution, and a is the semi-major axis of the orbit. Neglect
by the mass of the satellite in comparison with the mass of the Earth, we obtain
For simplicity of calculations, let us take the satellite orbit as circular. Moving at a constant speed υ, the satellite passes the distance υ Р = 2 πа along the orbit during a complete revolution, whence Р = 2πa/υ. Substituting this value of P into formula (9.1) and performing transformations, we find
So, with a decrease in the size of the orbit and the speed of the satellite v increases: the kinetic energy of the satellite increases due to the rapid decrease in potential energy.
The second force that changes the shape of the satellite's orbit is the pressure of solar radiation, i.e. light and corpuscular streams (solar wind). For small satellites, this force practically does not affect, but for such satellites as Pageos, it is very significant. At launch, Pageos had a circular orbit, and two years later it became a very elongated elliptical.
The movement of the satellite is also affected by the Earth's magnetic field, since the satellite can acquire some electric charge and when it moves in a magnetic field, changes in the trajectory should occur.
However, all these forces are perturbing. The main force holding the satellite in its orbit is the force of gravity. And here we meet with some features. We know that as a result axial rotation the figure of the Earth differs from a spherical one and that the earth's gravity is not directed exactly to the center of the Earth. This does not affect very distant objects, but a satellite located near the Earth reacts to the presence of “equatorial bulges” near the Earth. The plane of its orbit slowly but quite regularly rotates around the Earth's axis of rotation. This phenomenon is clearly visible from observations made over a period of one week. All these changes in orbits are of great scientific interest, and therefore systematic observations are being made of the movement of artificial satellites.
What is the geostationary orbit? This is a circular field, which is located above the Earth's equator, along which an artificial satellite circulates with the angular velocity of the planet's rotation around its axis. It does not change its direction in the horizontal coordinate system, but hangs motionless in the sky. The geostationary orbit of the Earth (GSO) is a kind of geosynchronous field and is used to accommodate communication, television broadcasting and other satellites.
The idea of using artificial devices
The very concept of the geostationary orbit was initiated by the Russian inventor K. E. Tsiolkovsky. In his works, he proposed to populate space with the help of orbital stations. Foreign scientists also described the work of space fields, for example, G. Oberth. The person who developed the concept of using the orbit for communication is Arthur Clarke. In 1945, he published an article in the Wireless World magazine, where he described the advantages of the geostationary field. For active work in this area in honor of the scientist, the orbit received its second name - "Clark's belt". Many theorists have thought about the problem of implementing a qualitative connection. So, Herman Potochnik in 1928 expressed the idea of how geostationary satellites can be used.
Characteristics of the "Clark belt"
For an orbit to be called geostationary, it must meet a number of parameters:
1. Geosynchrony. This characteristic includes a field that has a period corresponding to the period of the Earth's revolution. A geosynchronous satellite completes its orbit around the planet in a sidereal day, which is 23 hours 56 minutes and 4 seconds. The same time is necessary for the Earth to complete one revolution in a fixed space.
2. To maintain a satellite at a certain point, the geostationary orbit must be circular, with zero inclination. An elliptical field will result in either an east or west shift, as the spacecraft moves differently at certain points in its orbit.
3. The "hovering point" of the space mechanism must be on the equator.
4. The location of satellites in geostationary orbit should be such that a small number of frequencies intended for communication does not lead to overlapping frequencies of different devices during reception and transmission, as well as to exclude their collision.
5. Enough propellant to keep the spacecraft stationary.
The geostationary orbit of a satellite is unique in that it is only by combining its parameters that it is possible to achieve the immobility of the apparatus. Another feature is the ability to see the Earth at an angle of seventeen degrees from those located on space field satellites. Each device covers approximately one-third of the orbital surface, so three mechanisms are capable of covering almost the entire planet.
artificial satellites
Satellites have been launched by many countries and companies. The world's first artificial apparatus was created in the USSR and flew into space on October 4, 1957. He bore the name "Sputnik-1". In 1958, the United States launched a second device, the Explorer 1. The first satellite launched by NASA in 1964 was named Syncom-3. Artificial devices are mostly non-returnable, but there are those that return partially or completely. They are used to carry out scientific research and solving various problems. So, there are military, research, navigation satellites and others. Devices created by university employees or radio amateurs are also launched.
"Stop point"
Geostationary satellites are located at an altitude of 35,786 kilometers above sea level. This height provides a period of revolution that corresponds to the period of the Earth's circulation in relation to the stars. The artificial vehicle is stationary, so its location in geostationary orbit is called the “station point”. Hovering provides a constant long-term connection, once the antenna is oriented, it will always be directed to the correct satellite.
Movement
Satellites can be transferred from a low-altitude orbit to a geostationary one using geo-transfer fields. The latter are an elliptical path with a point at low altitude and a peak at an altitude that is close to the geostationary circle. A satellite that has become unusable for further work is sent to a disposal orbit located 200-300 kilometers above the GSO.
Geostationary orbit altitude
A satellite in a given field keeps at a certain distance from the Earth, neither approaching nor moving away. It is always located above some point on the equator. Based on these features, it follows that the forces of gravity and centrifugal force balance each other. The height of the geostationary orbit is calculated by methods based on classical mechanics. This takes into account the correspondence of gravitational and centrifugal forces. The value of the first quantity is determined using Newton's law of universal gravitation. The centrifugal force index is calculated by multiplying the mass of the satellite by the centripetal acceleration. The result of the equality of the gravitational and inertial masses is the conclusion that the height of the orbit does not depend on the mass of the satellite. Therefore, the geostationary orbit is determined only by the height at which the centrifugal force is equal in absolute value and opposite in direction gravitational force, created by the attraction of the Earth at a given height.
From the formula for calculating centripetal acceleration, you can find the angular velocity. The radius of the geostationary orbit is also determined by this formula, or by dividing the geocentric gravitational constant by the angular velocity squared. It is 42164 kilometers. Given the equatorial radius of the Earth, we get a height equal to 35786 kilometers.
Calculations can be done in another way, based on the statement that the height of the orbit, which is the distance from the center of the Earth, with the angular velocity of the satellite, coinciding with the motion of the planet's rotation, gives rise to a linear velocity, which is equal to the first cosmic velocity at a given altitude.
speed in geostationary orbit. Length
This indicator is calculated by multiplying the angular velocity by the radius of the field. The value of the speed in orbit is 3.07 kilometers per second, which is much less than the first space velocity on the near-Earth path. To reduce the exponent, it is necessary to increase the radius of the orbit by more than six times. The length is calculated by multiplying pi times the radius by two. It is 264924 kilometers. The indicator is taken into account when calculating the "standing points" of the satellites.
Influence of forces
The parameters of the orbit along which the artificial mechanism circulates can change under the influence of gravitational lunar-solar perturbations, the inhomogeneity of the Earth's field, and the ellipticity of the equator. The transformation of the field is expressed in such phenomena as:
- The displacement of a satellite from its position along its orbit towards points of stable equilibrium, which are called potential holes in the geostationary orbit.
- The angle of inclination of the field to the equator grows at a certain rate and reaches 15 degrees once in 26 years and 5 months.
To keep the satellite at the desired “standing point”, it is equipped with a propulsion system, which is turned on several times every 10-15 days. So, to compensate for the growth of the orbit inclination, the "north-south" correction is used, and to compensate for the drift along the field, the "west-east" correction is used. To regulate the path of the satellite during the entire period of its operation, a large supply of fuel on board is required.
Propulsion systems
The choice of device is determined by the individual technical features of the satellite. For example, chemical rocket engine has a displacement fuel supply and operates on long-term stored high-boiling components (diazote tetroxide, asymmetric dimethylhydrazine). Plasma devices have a significantly lower thrust, but due to the long operation, which is measured in tens of minutes for a single movement, they can significantly reduce the amount of fuel consumed on board. This type of propulsion system is used to maneuver the satellite to another orbital position. The main limiting factor in the service life of the device is the fuel supply in geostationary orbit.
Disadvantages of an artificial field
A significant defect in interaction with geostationary satellites are large delays in signal propagation. So, at a speed of light of 300 thousand kilometers per second and an orbital altitude of 35,786 kilometers, the movement of the Earth-satellite beam takes about 0.12 seconds, and the Earth-satellite-Earth beam takes 0.24 seconds. Taking into account the signal delay in the equipment and cable transmission systems of terrestrial services, the total delay of the signal "source - satellite - receiver" reaches approximately 2-4 seconds. Such an indicator significantly complicates the use of devices in orbit in telephony and makes it impossible to use satellite communications in real-time systems.
Another disadvantage is the invisibility of the geostationary orbit from high latitudes, which interferes with the conduction of communications and television broadcasts in the regions of the Arctic and Antarctica. In situations where the sun and the transmitter satellite are in line with the receiving antenna, there is a decrease, and sometimes even a complete absence of the signal. In geostationary orbits, due to the immobility of the satellite, this phenomenon is especially pronounced.
Doppler effect
This phenomenon consists in changing the frequencies of electromagnetic vibrations with the mutual advancement of the transmitter and receiver. The phenomenon is expressed by a change in distance over time, as well as by the movement of artificial vehicles in orbit. The effect manifests itself as the instability of the carrier frequency of the satellite oscillations, which is added to the instrumental frequency instability of the onboard repeater and the earth station, which complicates the reception of signals. The Doppler effect contributes to a change in the frequency of the modulating vibrations, which cannot be controlled. In the case when communication and direct television broadcasting satellites are used in orbit, this phenomenon is practically eliminated, that is, there are no changes in the signal level at the receiving point.
Attitude in the world to geostationary fields
The birth of the space orbit created many questions and international legal problems. A number of committees, in particular the United Nations, deal with them. Some countries located on the equator made claims to the extension of their sovereignty to the part of the space field located above their territory. States have stated that the geostationary orbit is a physical factor that is associated with the existence of a planet and depends on gravitational field Land, so the segments of the field are an extension of the territory of their countries. But such claims were rejected, since in the world there is a principle of non-appropriation outer space. All problems associated with the operation of orbits and satellites are resolved at the world level.
