Cosmonautics regularly achieves staggering success. Artificial Earth satellites are constantly finding more and more diverse applications. The astronaut's stay in Earth orbit has become commonplace. This would not have been possible without the main formula for cosmonautics - the Tsiolkovsky equation.
Nowadays, the study of both planets and other bodies of our solar system (Venus, Mars, Jupiter, Uranus, Earth, etc.) and distant objects (asteroids, other systems and galaxies) continues. The conclusions about the characterization of the cosmic motion of Tsiolkovsky’s bodies laid the foundation for the theoretical foundations of astronautics, which led to the invention of dozens of models of electro-jet engines and extremely interesting mechanisms, for example, the solar sail.
The main problems of space exploration
As the problems of space exploration, three areas of research and development in science and technology are clearly distinguished:
- Flights near the Earth or the construction of artificial satellites.
- Lunar flights.
- Planetary flights and flights to the objects of the solar system.
The Tsiolkovsky equation for jet propulsion contributed to the fact that mankind in each of these areas has achieved amazing results. And also a lot of new applied types of sciences appeared: space medicine and biology, life support systems on a spacecraft, space communications, etc.
Achievements in astronautics
Most people today heard about the main achievements: the first moon landing (USA), the first satellite (USSR) and the like. In addition to the most famous achievements that everyone has heard, there are many others. In particular, the USSR owns:
- first orbital station;
- first moonlight and photographs of the reverse side;
- first moon landing of an automated station;
- the first flights of vehicles to other planets;
- first landing on Venus and Mars, etc.
Many do not even realize how huge the achievements of the USSR in the field of astronautics were. In any case, they were much more than just the first satellite.
But the United States also made an equal contribution to the development of astronautics. In the USA:
- All major achievements in the use of near-Earth orbit (satellites and satellite communications) for scientific purposes and solving applied problems.
- Many expeditions to the moon, exploration of Mars, Jupiter, Venus and Mercury from the distance of flying trajectories.
- Many scientific and medical experiments conducted in zero gravity.
And although at the moment the achievements of other countries are fading against the background of the USSR and the USA, but China, India and Japan have actively joined the study of space in the period after 2000.
However, the achievements of astronautics are not limited only to the upper layers of the planet and high scientific theories. She also had a great influence on simple life. As a result of space exploration, such things came into our lives: lightning, Velcro, Teflon, satellite communications, mechanical manipulators, cordless tools, solar panels, artificial hearts and much more. And it was Tsiolkovsky’s speed formula, which helped to overcome gravitational attraction and contributed to the emergence of space practice in science, that helped to achieve all this.
The term "cosodynamics"
The Tsiolkovsky equation formed the basis of cosodynamics. However, you should understand this term in more detail. Especially in the issue of concepts that are close to it in meaning: astronautics, celestial mechanics, astronomy, and others. Cosmonautics is translated from Greek as "swimming in the Universe." In the usual case, this term refers to the mass of all technical capabilities and scientific achievements that allow us to study comic space and celestial bodies.
Space travel is what mankind has been dreaming of for centuries. And these dreams turned into reality, from theory into science, and all thanks to Tsiolkovsky’s formula for rocket speed. From the works of this great scientist, we know that the theory of astronautics is on three pillars:
- The theory that describes the movement of spacecraft.
- Electro-rocket engines and their production.
- Astronomical knowledge and research of the Universe.
As previously noted, many other scientific and technical disciplines appeared in the space age, such as: spacecraft control systems, communication and data transmission systems in space, navigation in outer space, space medicine, and much more. It is worth noting that at the time of the founding of the basics of astronautics there was not even a radio as such. The study of electromagnetic waves and long-distance transmission of information with their help has only just begun. Therefore, the founders of the theory seriously considered light signals - the sun's rays reflected towards the Earth - as a way of transmitting data. Today it is impossible to imagine astronautics without all related applied sciences. In those days, the imagination of a number of scientists was really amazing. In addition to communication methods, they also touched on topics such as the Tsiolkovsky formula for a multi-stage rocket.
Is it possible to single out any discipline among the whole variety as the main one? It is the theory of motion of cosmic bodies. It is she who serves as the main link, without which cosmonautics is impossible. This area of science is called cosmodynamics. Although it has many identical names: celestial or cosmic ballistics, space flight mechanics, applied celestial mechanics, the science of the motion of artificial celestial bodies, etc. All of them denote the same field of study. Cosmodynamics formally enters into celestial mechanics and uses its methods, but there is an extremely important difference. Celestial mechanics only study orbits, it has no choice, but cosmodynamics is designed to determine the optimal trajectories of the achievement of certain celestial bodies by spacecraft. And the Tsiolkovsky equation for jet propulsion allows ships to determine how it is possible to influence the flight path.
Cosodynamics as a science
Since K.E. Tsiolkovsky deduced the formula, the science of the motion of celestial bodies has become firmly established as cosmodynamics. It allows spacecraft to use the methods of finding the optimal transition between different orbits, which is called orbital maneuvering, and is the basis of the theory of movement in space, just like aerodynamics is the basis for flights in the atmosphere. However, it is not the only science dealing with this issue. In addition to it, there is also rocket dynamics. Both of these sciences form a solid foundation for modern space technology and both are included in the section of celestial mechanics.
Cosodynamics consists of two main sections:
- The theory of the motion of the center of inertia (mass) of an object in space, or the theory of trajectories.
- The theory of the motion of a cosmic body relative to its center of inertia, or the theory of rotation.
To understand what the Tsiolkovsky equation is, you need a good understanding of mechanics, i.e., Newton's laws.
Newton's first law
Any body moves uniformly and rectilinearly or is at rest until external forces applied to it force it to change this state. In other words, the velocity vector of such a motion remains constant. This behavior of bodies is also called inertial motion.
Any other case in which there is any change in the velocity vector means that the body has acceleration. An interesting example in this case is the movement of a material point in a circle or any satellite in orbit. In this case, a uniform movement occurs, but not rectilinear, because the velocity vector constantly changes direction, which means that the acceleration is not equal to zero. This change in speed can be calculated by the formula v 2 / r, where v is a constant value of speed, and r is the radius of the orbit. The acceleration in this example will be directed to the center of the circle at any point on the path of the body.
Based on the definition of the law, the cause of the change in the direction of the material point can only be force. In its role (in the case of the satellite) is the gravity of the planet. The attraction of planets and stars, as one can easily guess, is of great importance in cosodynamics in general and when using the Tsiolkovsky equation, in particular.
Newton's second law
Acceleration is directly proportional to force and inversely proportional to body weight. Or in mathematical form: a = F / m, or more familiarly, F = ma, where m is the coefficient of proportionality, which is a measure of the inertia of the body.
Since any rocket is represented as the movement of a body with a variable mass, the Tsiolkovsky equation will change every unit of time. In the above example of a satellite moving around a planet, knowing its mass m, one can easily find out the force under which it rotates in orbit, namely: F = mv 2 / r. Obviously, this force will be directed to the center of the planet.
The question arises: why does the satellite not fall on the planet? It does not fall, because its trajectory does not intersect with the surface of the planet, because nature does not force it to move along the action of the force, because only the acceleration vector, and not the velocity, is directed to it.
It should also be noted that in conditions where the force acting on the body and its mass is known, one can determine the acceleration of the body. And by it mathematical methods determine the path along which this body moves. Here we come to two main tasks that cosdynamics deals with:
- The identification of forces with which you can manipulate the movement of the spacecraft.
- Determination of the motion of this ship, if the forces acting on it are known.
The second task is a classic question for celestial mechanics, while the first shows the exclusive role of cosodynamics. Therefore, in this field of physics, in addition to the Tsiolkovsky formula for jet propulsion, it is extremely important to understand Newtonian mechanics.
Newton's Third Law
The cause of the force acting on a body is always another body. But the opposite is also true. This is the essence of Newton’s third law, which states that every action has an action that is equal in magnitude, but oppositely directed, called opposition. In other words, if body A acts with force F on body B, then body B acts on body A with force -F.
In the example of a satellite and a planet, Newton’s third law leads us to understand that with what force a planet attracts a satellite, it is with the same satellite that attracts a planet. This gravity is responsible for accelerating the satellite. But it also gives acceleration to the planet, but its mass is so great that this change in speed is negligible for it.
Tsiolkovsky’s formula for jet propulsion is entirely based on an understanding of Newton’s last law. Indeed, it is precisely due to the ejected mass of gases that the main body of the rocket acquires acceleration, which allows it to move in the right direction.
A little bit about reference systems
When considering any physical phenomena, it is difficult not to touch upon a topic such as a frame of reference. The motion of a spaceship, like any other body in space, can be recorded in different coordinates. There are no wrong frames of reference; there are only more convenient and less. For example, the motion of bodies in the solar system is best described in the heliocentric reference frame, that is, in coordinates associated with the sun, also called the Copernican system. However, the movement of the moon in this system is less convenient to consider, so it is studied in geocentric coordinates - the reference is relative to the Earth, this is called the Ptolemy system. But, if the question is whether the asteroid passing by will fall into the moon, it will be more convenient to use heliocentric coordinates again. It is important to be able to use all coordinate systems and be able to look at a task from different points of view.
Rocket movement
The main and only way to travel in outer space is a rocket. For the first time this principle was expressed, according to the site "Habr", the formula Tsiolkovsky in 1903. Since then, astronautical engineers have invented dozens of types of rocket engines using the most diverse types of energy, but they are all united by one principle of operation: throwing part of the mass from the reserves of the working fluid for acceleration. The force that is formed as a result of this process is usually called the traction force. Here are some conclusions that will allow us to come to the Tsiolkovsky equation and derive its main form.
Obviously, the traction force will increase depending on the volume of mass ejected from the rocket per unit time and the speed that this mass manages to communicate. Thus, the relation F = w * q is obtained, where F is the traction force, w is the velocity of the rejected mass (m / s) and q is the mass spent per unit time (kg / s). It is worth noting separately the importance of a frame of reference related specifically to the missile itself. Otherwise, it is impossible to characterize the thrust of a rocket engine if you measure everything relative to the Earth or other bodies.
Studies and experiments have shown that the ratio F = w * q remains valid only for cases when the ejected mass is a liquid or a solid. But rockets use a jet of hot gas. Therefore, a number of corrections must be introduced into the relation, and then we obtain an additional term of the relation S * (p r - p a ), which is summed up with the original w * q. Here p r is the pressure exerted by the gas at the nozzle exit; p a is atmospheric pressure and S is the area of the nozzle. Thus, the refined formula will look like this:
F = w * q + Sp r - Sp a.
It can be seen that as the rocket climbs, the atmospheric pressure will become less, and the thrust force will increase. However, physicists love convenient formulas. Therefore, a formula is often used that is similar to its original form F = w e * q, where w e is the effective mass flow rate. It is determined experimentally during the test of the propulsion system and is numerically equal to the expression w + (Sp r - Sp a ) / q.
Consider a concept identical to w e - specific impulse of traction. Specific - means related to something. In this case, it is the gravity of the Earth. To do this, in the above formula, the right side is multiplied and divided by g (9.81 m / s 2 ):
F = w e * q = (w e / g) * q * g or F = I beats * q * g
This value is measured I beats in N * s / kg or the same m / s. In other words, the specific impulse of thrust is measured in units of speed.
Tsiolkovsky's formula
As you can easily guess, in addition to the engine thrust, many other forces act on the rocket: the Earth’s gravity, the gravity of other objects of the Solar system, atmospheric resistance, light pressure, etc. Each of these forces gives its acceleration to the rocket, and the total effect affects the final acceleration. Therefore, it is convenient to introduce the concept of jet acceleration or a r = F t / M, where M is the mass of the rocket in a certain period of time. Reactive acceleration is the acceleration with which a rocket would move in the absence of forces acting on it from outside. Obviously, as the mass is consumed, the acceleration will increase. Therefore, there is another convenient characteristic - the initial reactive acceleration a r0 = F t * M 0 , where M 0 is the mass of the rocket at the time the movement begins.
The logical question will be what speed a rocket can develop in such an empty space after a certain amount of working fluid mass is used up. Let the mass of the rocket changed from m 0 to m 1 . Then the speed of the rocket after uniform use of the mass to a value of m 1 kg will be determined by the formula:
V = w * ln (m 0 / m 1 )
This is nothing more than a formula for the motion of bodies with variable mass or the Tsiolkovsky equation. It characterizes the energy resource of the rocket. And the speed obtained by this formula is called ideal. You can write this formula in another identical version:
V = I beats * ln (m 0 / m 1 )
It is worth noting the application of the Tsiolkovsky Formula for calculating fuel. More precisely, the mass of the carrier rocket, which will be required to bring a certain weight into the Earth’s orbit.
In the end, it should be said about such a great scientist as Meshchersky. Together with Tsiolkovsky they are the forefathers of astronautics. Meshchersky made a huge contribution to the creation of the theory of motion of objects of variable mass. In particular, the formula of Meshchersky and Tsiolkovsky is as follows:
m * (dv / dt) + u * (dm / dt) = 0,
v - , u - . , .