Acceleration in space: how does gravity help you fly into the distance? Gravity assist for spacecraft What is gravity assist

Thinking about gravity as a phenomenon. As always, a purely personal opinion.

A little information

When exactly people learned about the forces of gravity will remain a mystery, obviously, for a very long time. Officially, it is believed that Isaac Newton came to grips with the phenomena of universal gravitation, after he received an occupational injury with an apple while walking.

Apparently, as a result of his injury, Isaac Newton received a revelation from our Lord, which resulted in the corresponding equation:

F = G (m 1 * m 2) / r 2 (Equation # 1)

Where, respectively: F- the required interaction force (gravitational force), m 1, m 2 - masses of interacting bodies, r- distance between bodies, G- gravitational constant.

I will not touch on the philosophy of Isaac Newton, direct authorship or some other things not related to the facts of observation, if anyone is interested, you can see investigation Vadim Lovchikov or something similar.

And so, let's first analyze what we are offered under the guise of this simple equation.

First What should be paid attention to, equation No. 1 has radial (spherical symmetry), which means that gravity does not have distinguished directions of interaction and all interactions that it provides are strictly symmetric.

Second What you should pay attention to, in equation # 1 there is neither time nor any speeds, that is, interaction is provided immediately, without delay at any distance.

Third, Newton pointed to the divine nature of gravity, that is, all things in the world interact by the will of God - gravity is no exception. Why the interaction takes place this way is the will of God, he did not have any physical picture of the world in our understanding.

As you can see, the principles of gravity are simple and understandable, they are set out in all school textbooks and are broadcast by all irons (with the exception of perhaps the third principle), but as we remember Francis Bacon bequeathed us to comprehend nature through observations (empirically), do the above laws correspond to this rule?

Few facts

Inertia, is a natural phenomenon that occurs when any bodies move. Despite the general spread of this phenomenon, physicists still (if anyone knows, let them correct me) cannot clearly say with what inertia is physically connected, with the body or with the space around it. Newton knew very well about the existence of this phenomenon, and the fact that it affects the forces of interaction of gravitating bodies, but if you look at the equation №1, you will not find there traces of inertia, as a consequence the problem of "Three bodies" has not been solved rigorously.

All irons, of all stripes convince me that Newton de calculated the orbits of the planets based on his divine equation, of course I believe them, because not long before that Johannes Kepler did everything empirically, however, none of the irons explains, as Isaac did in his calculations Newton took into account inertia, no one will tell you this in any textbook, even a university one.

The consequence of this is very simple, British scientists fitted the results of calculations to the works of Kepler, equation No. 1 does not take into account the inertia and velocities of bodies, therefore it is completely useless for calculating specific orbits of celestial bodies. It is not even funny to say that Newton's philosophy somehow describes the mechanism of inertia physically.

Gravity maneuver- a phenomenon of nature, when, during the interaction of gravitating bodies, one of them is accelerated, the other slows down. Considering the perfect radial symmetry of equation No. 1, as well as the instantaneous velocity of gravity propagation according to this equation, this physical effect is impossible, all the added momentum will be taken away when the bodies move apart and the interacting bodies will remain "at their own". They learned to work with gravitational maneuvers based on empirical observations (flights into space), according to Newton's theory, in this case only a change in the direction of motion of bodies, but not their momentum, is possible, which clearly contradicts experimental data.

Disc-like structures- most of the visible universe is occupied by disk-like structures, these are galaxies, and disks of planetary systems, planetary rings. Considering the complete symmetry of equation # 1, this is a very strange physical fact... According to this equation, the overwhelming majority of structures should have a spherical symmetric shape, astronomical observations directly contradict this statement. The official cosmogonic theory of the condensation of planets from a dust cloud does not explain in any way the presence of flat disks of planetary systems around stars. The same exception is the rings of Saturn, which were supposedly formed by the impact of certain bodies in the orbit of Saturn, why was it a flat and not a spherical structure that was formed?

The astronomical phenomena we observe directly contradict the basic postulates of the symmetry of Newton's theory of gravitation.

Tidal activity- as claims modern science, tidal waves in the seas of the Earth are formed by the joint gravitational influence of the Moon and the Sun. Of course, the influence of the Moon and the Sun on the tides is, but this is what it is, in my opinion, a rather controversial question, I would like to see an interactive simulation where the positions of the Moon and the Sun, as well as the tides, would be superimposed, something I have not yet seen such good simulations, which is very strange given the love of modern scientists for computer simulations.

There are much more questions about tides than answers, to start at least with the formation of a "tidal ellipse", I understand that gravity causes an "antinode" of the waters on the side closest to the Moon or the Sun, and what causes a similar "antinode" on back side Earth, if you look at equation No. 1, this, in principle, cannot be.

The good physicists agreed that the leading value in the tidal forces is not the modulus of force, but its gradient, such as the gradient of the force of the Moon more, it more affects the tides, the Sun has a smaller gradient, it less affects the tides, but forgive in equation No. 1 there is nothing like that, but Newton never said anything like that, how to understand this? Obviously, as another fit for a well-known result from the British "scientists". When the seething of the tidal substance reached a certain level, the British "scientists" decided even more confuse grateful listeners, which of this is true is not at all clear.

I have no opinion on the correct algorithm for calculating the tides, but all indirect signs indicate that no one has it.

Cavendish experiment- determination of the "gravitational constant" using a torsion balance. This is a real shame of modern physical science, moreover, the fact that this is a shame was clear even in the days of Cavendish (1790), but he would not be a real "British" scientist if he paid attention to the dull external world, an ugly experiment from a physical point of view entered all possible physics textbooks and has been arriving there ever since. Only recently have the "luminaries" from science begun to show slight concern about its reproducibility.

Experience is fundamentally non-reproducible under Earth conditions. The question is not even in the "Casimir effect", which was predicted long before Casimir, not in thermal distortions of the structure, and the electromagnetic interaction of loads. The main issue is the long-period natural oscillations of the installation; it is impossible to eliminate this distortion in terrestrial conditions in any way.

I personally do not presume to say what numbers the British scientists intended, I can only say that, in accordance with the latest physical studies, this is all rubbish that has nothing to do with real gravitational interactions. Thus, this experience cannot serve to prove or disprove something, it is just rubbish with which nothing worthwhile can be done, and even more so it is impossible to find out the value of the "gravitational constant".

A little cursing

It would be possible to list many more facts, but I do not see any special meaning in this - it still does not affect anything, the "physicists" from gravity have been treading in one place for four hundred years, apparently they are much more important not what happens in nature, and what some Anglican theologian said, obviously, Nobel prizes are given only for this.

Now it is very fashionable to lament that young people "ignore" physics, do not have respect for authorities and other nonsense. What respect can there be if the manipulations of our British partners are visible without contact lenses? Physical data directly contradict all the postulates of science, but the owl continues to be regularly pulled on the globe and the end-edge of this fascinating activity is not visible. Young people see how our deeds are done before the Lord, taking into account the modern information security, and I am sure they draw appropriate conclusions.

I think that the biggest secret of modern physics is the specific values ​​of the gravitational forces in the solar system, otherwise why so many accidents when landing (lunar landing, landing, landing) satellites, but everyone continues to read the mantra about the "great scientist" and his laws obviously do not want to give out their know-how, earned by sweat and blood.

Even more annoying is modern cosmology, people essentially do not have any facts about gravity, but they have already invented dark matter, dark energy and black holes and gravitational waves. Maybe let's first deal with at least the surroundings of the Earth and the Sun, launch test probes and find out what by what, and therefore we will already fence various schizophrenia, but no British "scientists" are not like that. As a result, we have a shaft of "scientific" publications, the total value of which is somewhere in the nadir.

Then they will object to me, well, of course, there is also Einstein and his clique. You know, these kind people surpassed Newton himself, Newton at least said that there are gravitational forces, albeit by God's will, Einstein declared them imaginary, bodies, they say, fly because I (Einstein) so want, and nothing else, in his studies he contrived lose even God. Therefore, I will not even condemn these agnostic quirks of the sick consciousness, I simply cannot consider it scientific data. This is a fairy tale, essay, philosophy, whatever, but not empiricism.

conclusions

All available history, especially the latest, convincingly proves that our British partners do not give anything for free, and then they suddenly became generous with a whole theory of gravity, this is at least suspicious.

Personally, I do not believe at all in their good intentions, all physical data, especially received from our partners, need a thorough centralized audit, otherwise we will scratch the ego for another thousand years with all sorts of disgusting obscurantists, and they will drag us into endless troubles with human and material victims.

The main conclusion of the article is that gravity as a phenomenon is at the same level of research, at least in the field of public knowledge, as 400 years ago. Let's finally get down to exploring the real world, and not kissing the British relics.

However, everyone is free to form their own opinion based on the available facts.

There is another way to accelerate an object to a speed close to the speed of light - to use the "sling effect". When sending space probes to other planets, NASA sometimes forces them to maneuver around a neighboring planet in order to use the "sling effect" to further accelerate the apparatus. This is how NASA conserves valuable rocket fuel. This is how the Voyager 2 spacecraft managed to reach Neptune, whose orbit lies at the very edge of the solar system.

Freeman Dyson, a physicist from Princeton, has an interesting proposal. If sometime in the distant future mankind manages to detect in space two neutron stars revolving around a common center at a high speed, then an earth ship, flying very close to one of these stars, can, due to a gravitational maneuver, gain a speed equal to almost a third the speed of light. As a result, the ship would be accelerated to near-light speeds due to gravity. In theory, this could happen.

But in reality, this way of accelerating with the help of gravity will not work. (The law of conservation of energy says that a roller coaster cart, accelerating on a descent and slowing down on an ascent, ends up at the top at exactly the same speed as at the very beginning - no energy increment occurs. In the same way, turning around the motionless sun , we will end at exactly the same speed as we started the maneuver.) Dyson's two-neutron-star method could work in principle, but only because neutron stars are moving rapidly. A spacecraft using gravity assist is gaining energy from the motion of a planet or star. If they are motionless, such a maneuver will do nothing.

And Dyson's proposal, while it may work, will not help today's earth scientists in any way - after all, in order to visit the rapidly rotating neutron stars, you will need to build a starship first.

From the cannon to the heavens

Another clever way to launch a ship into space and accelerate to fantastic speeds is to shoot it from the rail electromagnetic "cannon", which was described in their works by Arthur Clarke and other science fiction authors. This project is currently being seriously considered as a possible part of the anti-missile shield of the Star Wars program.

The method consists in using the energy of electromagnetism to accelerate the rocket to high speeds instead of propellant or gunpowder.

In the simplest case, a rail gun is two parallel wires or rails; the missile, or missile, sits on both rails in a U-shape. Even Michael Faraday knew that a force acts on a frame with an electric current in a magnetic field. (Generally speaking, all electric motors work on this principle.) If you pass through the rails and the projectile electricity With a force of millions of amperes, an extremely powerful magnetic field will arise around the entire system, which, in turn, will drive the projectile along the rails, accelerate it to tremendous speed and throw it into space from the end of the rail system.

During the tests, electromagnetic rail guns successfully fired metal objects at tremendous speeds, accelerating them at a very short distance. What is remarkable, in theory, a conventional rail gun is capable of firing a metal projectile at a speed of 8 km / s; that's enough to put it into low-earth orbit. In principle, the entire rocket fleet of NASA could be replaced by rail cannons, which would shoot payload directly from the surface of the Earth into orbit.

The rail gun has significant advantages over chemical guns and missiles. When you fire a gun, the maximum speed at which the expanding gases can push the bullet out of the barrel is limited by the speed of the shockwave. Jules Berne in the classic novel "From Earth to the Moon" fired a projectile with astronauts to the Moon with gunpowder, but in fact it is easy to calculate that the maximum speed that a powder charge can give a projectile is many times less than the speed required for flight to the Moon ... The rail gun does not use the explosive expansion of gases and therefore does not depend in any way on the speed of propagation of the shock wave.

But the rail gun has its own problems. Objects on it accelerate so quickly that they tend to collapse due to collision ... with air. The payload turns out to be highly deformed during the "shot" from the muzzle of the rail gun, because when the projectile hits the air, it's like hitting a brick wall. In addition, during acceleration, the projectile experiences tremendous acceleration, which in itself is capable of severely deforming the load. The rails must be replaced regularly, since the projectile also deforms them when moving. Moreover, the overload in a rail gun is fatal to humans; human bones simply cannot withstand such acceleration and collapse.

One solution is to mount a rail gun on the moon. There, outside of the earth's atmosphere, the projectile will be able to accelerate unhindered in the vacuum of outer space. But even on the Moon, the projectile will experience tremendous overloads during acceleration, which can damage and deform the payload. In a sense, the rail gun is the antipode of the laser sail, which picks up speed gradually over time. The limitations of a rail gun are determined precisely by the fact that it transfers enormous energy to the body at a short distance and in a short time.

A rail cannon capable of firing an apparatus towards nearby stars would be a very expensive structure. So, one of the projects provides for the construction of a rail gun in outer space two-thirds of the distance from the Earth to the Sun. This cannon will have to store solar energy, and then expend it at once, accelerating a ten-ton payload to a speed equal to a third of the speed of light. In this case, the "projectile" will experience an overload of 5000 g. Of course, only the most enduring robotic ships will be able to "survive" such a launch.

Gravitational maneuver to accelerate an object Gravitational maneuver to slow down an object Gravitational maneuver acceleration, deceleration or change in the direction of flight of a spacecraft, under the action of the gravitational fields of celestial bodies. ... ... Wikipedia

Gravitational maneuver to accelerate an object Gravitational maneuver to slow down an object Gravitational maneuver acceleration, deceleration or change in the direction of flight of a spacecraft, under the action of the gravitational fields of celestial bodies. ... ... Wikipedia

- ... Wikipedia

This is one of the main geometric parameters of objects formed by means of a conical section. Contents 1 Ellipse 2 Parabola 3 Hyperbola ... Wikipedia

An artificial satellite is an orbital maneuver, the purpose of which (in the general case) is to transfer the satellite to an orbit with a different inclination. There are two types of such a maneuver: Changing the inclination of the orbit to the equator. Produced by turning on ... ... Wikipedia

Section of celestial mechanics that studies the motion of artificial cosmic bodies: artificial satellites, interplanetary stations and others spaceships... The scope of tasks of astrodynamics includes the calculation of the orbits of spaceships, the determination of parameters ... ... Wikipedia

The Obert effect in astronautics is an effect in which a rocket engine moving at high speed generates more usable energy than a similar engine moving slowly. The Obert effect is caused by the fact that when ... ... Wikipedia

Customer ... Wikipedia

And the equipotential surfaces of the system of two bodies Lagrange points, libration points (lat. Librātiō wobble) or L points ... Wikipedia

Books

• Things of the twentieth century in drawings and photographs. Forward into space! Discoveries and achievements. A set of 2 books,. "Forward into space! Discoveries and achievements" Since ancient times, man dreamed of getting off the ground and conquering the sky, and then space. More than a hundred years ago, inventors were already thinking about creating ...
• Forward into space! Discoveries and achievements, Klimentov Vyacheslav Lvovich, Sigorskaya Yulia Aleksandrovna. Since ancient times, man dreamed of getting off the ground and conquering the sky, and then space. More than a hundred years ago, inventors were already thinking about creating spaceships, but the beginning of space ...

, Earth, Mars and even the Moon.

The physical essence of the process

Consider the trajectory of a spacecraft flying near some large celestial body, for example, Jupiter. In the initial approximation, we can neglect the action on the spacecraft of gravitational forces from other celestial bodies.

A complex combination of gravitational maneuvers was used by the AMS Cassini (for acceleration, the apparatus used the gravitational field of three planets - Venus (twice), Earth and Jupiter) and Rosetta (four gravitational maneuvers near Earth and Mars).

In art

An artistic description of such a maneuver can be found in the science fiction novel by A. Clarke "2010: Odyssey 2".

In the sci-fi movie Interstellar, the Orbital Station Endurance does not have enough fuel to reach the third planet, located near the black hole Gargantua (named after the literary giant glutton). The main character Cooper takes a risky move: Endurance must pass close to Gargantua's event horizon, thereby giving the station acceleration due to the black hole's gravity.

In the science fiction novel The Martian and the movie of the same name, using gravity assist around the Earth, the team accelerates the Hermes spacecraft for a re-flight to Mars.

see also

Write a review on the article "Gravity Maneuver"

Notes (edit)

Links

• // crydee.sai.msu.ru
• (navigation calculations for the space simulator "Orbiter", allows you to calculate, including gravity assist maneuvers)
• // novosti-kosmonavtiki.ru

Orbits
Types The main Parameters

Laws and objectives Celestial sphere Orbit parameters Movement celestial bodies Astrodynamics Space flight Spacecraft orbits

Excerpt from Gravity Maneuver

- Oh my God!
- What are you pushing, - is there a fire about you, or what? See ... fell apart.
Because of the silence that was being established, snoring was heard of some who had fallen asleep; the rest turned and warmed themselves, occasionally talking. From a distant fire, a hundred paces away, a friendly, cheerful laughter was heard.
“See, they are rumbled in the fifth company,” said one soldier. - And what a passion for the people!
One soldier got up and walked towards the fifth company.
“Sometimes it’s laughing,” he said, returning. - Two guardians have joined. One is frozen at all, and the other is so courageous, byada! The songs are playing.
- Oh oh? go see ... - Several soldiers headed for the fifth company.

The Fifth Company stood close to the forest itself. A huge bonfire burned brightly in the middle of the snow, illuminating the branches of the trees weighed down with frost.
In the middle of the night, the soldiers of the fifth company heard footsteps in the snow and the grunt of branches in the forest.
“Guys, witch,” said one soldier. Everyone raised their heads, listened, and out of the forest, into the bright light of the fire, appeared two, holding each other, strangely dressed human figures.
They were two Frenchmen hiding in the forest. Hoarsely speaking something in a language incomprehensible to the soldiers, they approached the fire. One was taller, wearing an officer's hat, and seemed quite weak. Approaching the fire, he wanted to sit down, but fell to the ground. Another, small, stocky, tied with a kerchief over the cheeks of a soldier, was stronger. He raised his comrade and, pointing to his mouth, said something. The soldiers surrounded the French, spread an overcoat to the sick man, and brought cereals and vodka to both of them.
The weakened French officer was Rambal; his batman Morel was tied with a handkerchief.
When Morel drank vodka and finished the pot of porridge, he suddenly became painfully cheerful and began to say something to the soldiers who did not understand him. Rambal refused to eat and silently lay on his elbow by the fire, looking at the Russian soldiers with meaningless red eyes. From time to time he uttered a drawn-out groan and fell silent again. Morel, pointing to his shoulders, inspired the soldiers that he was an officer and that he needed to be warmed up. A Russian officer, who approached the fire, sent to ask the colonel if he would take a French officer to warm him up; and when they returned and said that the colonel had ordered an officer to be brought in, Rambal was told to go. He got up and wanted to walk, but he staggered and would have fallen if the soldier standing beside him had not supported him.
- What? You will not? - With a mocking wink, said one soldier, referring to Rambal.
- Eh, you fool! What are you lying awkwardly! That is a man, really, a man, - reproaches were heard from different sides to the joking soldier. Rambal was surrounded, two men were raised in their arms, intercepted by them, and carried into the hut. Rambal put his arms around the necks of the soldiers and, when they carried him, spoke plaintively:
- Oh, nies braves, oh, mes bons, mes bons amis! Voila des hommes! oh, mes braves, mes bons amis! [Oh well done! Oh my good, good friends! Here are the people! Oh my good friends!] - and, like a child, leaned his head on the shoulder of one soldier.
Meanwhile, Morel was sitting in a better place, surrounded by soldiers.
Morel, a small stocky Frenchman with sore, watery eyes, tied in a woman's scarf over his cap, was dressed in a woman's fur coat. He, apparently drunk, embracing the soldier who was sitting next to him, sang a French song in a hoarse, breaking voice. The soldiers were holding their sides, looking at him.
- Well, well, well, teach me how? I'll take it quickly. How? .. - said the joker songwriter, whom Morel hugged.
Vive Henri Quatre,
Vive ce roi vaillanti -
[Long live Henry the Fourth!
Long live this brave king!
etc. (French song)]
sang Morel, winking an eye.
Сe diable a quatre ...
- Vivarika! Beth Seruvaru! sedentary ... - repeated the soldier, waving his hand and really catching the melody.
- See, cleverly! Go go go go! .. - Rough, joyful laughter rose from different sides. Morel grimaced and laughed too.
- Well, go on more, more!
Qui eut le triple talent,
De boire, de battre,
Et d "etre un vert galant ...
[Who had triple talent,
drink, fight
and be nice ...]
- But it's also foldable. Well, well, Zaletaev! ..
- Kyu ... - with an effort uttered Zaletaev. - Kyu yu yu ... - he stretched out, diligently protruding his lips, - letriptala, de boo de ba and detravagala, - he sang.
- Ay, important! That's a guardian! oh ... go go go! - Well, you still want to eat?
- Give him some porridge; After all, it will not soon be full of hunger.
They gave him porridge again; and Morel, chuckling, set to work on the third bowler hat. Joyful smiles were on all the faces of the young soldiers who looked at Morel. The old soldiers, who considered it indecent to engage in such trifles, lay on the other side of the fire, but from time to time, propping themselves up on their elbows, glanced at Morel with a smile.
“People, too,” said one of them, dodging his overcoat. - And wormwood grows on its root.
- Oo! Lord, Lord! How stellar passion! By the frost ... - And everything was quiet.
The stars, as if knowing that now no one would see them, played out in the black sky. Either flashing, now extinguished, now shuddering, they were busy whispering about something joyful but mysterious among themselves.

NS
The French troops gradually melted away in a mathematically correct progression. And that crossing over the Berezina, about which so much has been written, was only one of the intermediate stages of the destruction of the French army, and not at all a decisive episode of the campaign. If so much was written and written about Berezina, then on the part of the French it happened only because on the Berezinsky bridge that was broken through, the disasters that the French army had suffered evenly before, here suddenly grouped together in one moment and into one tragic spectacle, which everyone remembered. On the part of the Russians, they talked and wrote so much about the Berezina only because, far from the theater of war, in St. Petersburg, a plan was drawn up (by Pfulm) to capture Napoleon in a strategic trap on the Berezina River. Everyone was convinced that everything would be in fact exactly as in the plan, and therefore insisted that it was the Berezinskaya crossing that killed the French. In essence, the results of the Berezinskaya crossing were much less disastrous for the French in the loss of guns and prisoners than Krasnoye, as the figures show.
The only meaning of the Berezinskaya crossing is that this crossing obviously and undoubtedly proved the falsity of all plans for cutting off and the validity of the only possible course of action required by Kutuzov and all the troops (mass) - only to follow the enemy. The crowd of Frenchmen fled with an ever-increasing force of speed, with all the energy aimed at achieving the goal. She ran like a wounded animal, and she could not stand on the road. This was proved not so much by the device of the crossing as by the movement on the bridges. When the bridges were broken, unarmed soldiers, Moscow residents, women with children who were in the French train - everything did not give up under the influence of inertia, but ran forward into boats, into the frozen water.
This aspiration was reasonable. The position of both the fleeing and the pursuing was equally bad. Remaining with his own people, each in distress hoped for the help of a comrade, for a certain place he occupied among his own. Having surrendered himself to the Russians, he was in the same position of disaster, but he was on a lower level in the section of satisfying the needs of life. The French did not need to have accurate information that half of the prisoners with whom they did not know what to do, despite all the Russians' desire to save them, were dying of cold and hunger; they felt it could not be otherwise. The most compassionate Russian chiefs and hunters before the French, the French in the Russian service could not do anything for the prisoners. The French were destroyed by the disaster in which the Russian army was located. It was impossible to take away bread and clothes from hungry, necessary soldiers, so that they could not be given to the harmful, not hated, not guilty, but simply unnecessary French. Some have done it; but that was just an exception.

If a rocket flies close to a planet, its speed will change. Either it will decrease or it will increase. It depends on which side of the planet it will fly from.

When the American Voyager spacecraft made their famous Grand Tour of the Solar system, they performed several so-called gravity assist maneuvers near the giant planets.
Most fortunate was Voyager 2, which flew past all four major planets. See the figure for its speed graph:

The graph shows that after each approach to the planet (except for Neptune), the speed of the spacecraft increased by several kilometers per second.

At first glance, this may seem strange: an object flies into the gravitational field and accelerates, then flies out of the field and decelerates. The arrival speed must be equal to the departure speed. Where does the extra energy come from?
Additional energy appears because there is a third body - the Sun. When flying near a planet, the spacecraft exchanges momentum and energy with it. If with such an exchange the gravitational energy of the planet in the field of the Sun decreases, then the kinetic energy of the spacecraft (SC) increases, and vice versa.

How should a spacecraft fly past the planet in order for its speed to increase? It is not difficult to answer this question. Let the spacecraft traverse the orbit of the planet directly in front of it. In this case, having received an additional impulse in the direction of the planet, it will give it an additional impulse in the opposite direction, that is, in the direction of its motion. As a result, the planet will move into a slightly higher orbit, and its energy will increase. In this case, the spacecraft energy will correspondingly decrease. If the spacecraft crosses the orbit behind the planet, then, slightly slowing down its movement, it will transfer the planet to a lower orbit. In this case, the speed of the spacecraft will increase.

Of course, the mass of the spacecraft is incommensurate with the mass of the planet. Therefore, the change in the orbital parameters of the planet during a gravitational maneuver is an infinitely small quantity that cannot be measured. Nevertheless, the energy of the planet changes, and we can be convinced of this by performing a gravitational maneuver and seeing that the speed of the spacecraft is changing. For example, here is how Voyager 2 flew near Jupiter on July 9, 1979 (see fig.). When approaching Jupiter, the speed of the spacecraft was 10 km / sec. At the moment of closest approach, it increased to 28 km / s. And after Voyager 2 flew out of the gas giant's gravitational field, it decreased to 20 km / sec. Thus, as a result of gravity assist, the speed of the spacecraft doubled and became hyperbolic. That is, it exceeded the speed required to leave the solar system. In Jupiter's orbit, the departure speed from the solar system is about 18 km / sec.

This example shows that Jupiter (or another planet) can accelerate any body to hyperbolic speed. This means that he can "throw" this body out of the solar system. Maybe modern cosmogonists are right? Maybe the giant planets really threw ice blocks to the distant outskirts of the solar system and, thus, formed the Oort comet cloud.
Before answering this question, let's see what gravitational maneuvers are capable of the planets?

2. Principles of gravity assist

For the first time I got acquainted with gravity assist in 9th grade at the regional Olympiad in physics. The task was as follows. A rocket launches from Earth at a speedV(enough to fly out of the field of attraction). The rocket has a thrust engine F that can run time t... At what point in time do you need to turn on the engine so that the final velocity of the rocket is at its maximum? Neglect air resistance.

At first it seemed to me that it didn’t matter when to turn on the engine. Indeed, due to the law of conservation of energy, the final speed of the rocket must be the same in any case. It remained to calculate the final speed of the rocket in two cases: 1. turn on the engine at the beginning, 2. turn on the engine after leaving the Earth's gravitational field. Then compare the results and make sure that the final velocity of the rocket is the same in both cases. But then I remembered that the power is equal: the thrust times the speed. Therefore, the power of the rocket engine will be maximum if the engine is turned on immediately at the start, when the rocket speed is at its maximum. So, the correct answer: we turn on the engine immediately, then the final speed of the rocket will be maximum.

And although I solved the problem correctly, the problem remained. The final speed, and, therefore, the energy of the rocket DEPENDS on the moment at which the engine is turned on. It seems to be a clear violation of the law of conservation of energy. Or not? What's the matter here? Energy must be conserved! I tried to answer all these questions after the Olympiad.

Let us have a rocket of mass M with an engine that creates thrust by force F... Place this rocket in empty space (away from stars and planets) and turn on the engine. With what acceleration will the rocket move? We know the answer from Newton's Second Law: acceleration a equals:

a=F / M

Now let's go to another inertial frame of reference, in which the rocket moves at a high speed, say, 100 km / s. What is the acceleration of a rocket in this frame of reference?
Acceleration DOES NOT DEPEND on the choice of the inertial reference system, so it will be the SAME:

a=F / M

The mass of the rocket also does not change (100 km / s is not yet a relativistic case), therefore the thrust force F will be the SAME. And, therefore, the power of the rocket DEPENDS on its speed. After all, power is equal to force multiplied by speed. It turns out that if a rocket moves at a speed of 100 km / s, then the power of its engine is 100 times more powerful than EXACTLY the same engine on a rocket moving at a speed of 1 km / s.

At first glance, this may seem strange and even paradoxical. Where does the huge extra power come from? Energy must be conserved!

Let's take a look at this issue.

The rocket always moves on jet propulsion: it throws various gases into space at high speed. For definiteness, let us assume that the rate of gas emission is 10 km / sec. If a rocket moves at a speed of 1 km / s, then its engine accelerates mainly not the rocket, but the propellant. Therefore, the power of the engine to accelerate the rocket is not high. But if the rocket is moving at a speed of 10 km / s, then the ejected fuel will REMAIN relative to an external observer, that is, all the engine power will be spent on accelerating the rocket. And if the rocket is moving at a speed of 100 km / s? In this case, the ejected fuel will move at a speed of 90 km / s. That is, the fuel speed WILL REDUCE from 100 to 90 km / sec. And ALL the difference in the kinetic energy of the fuel by virtue of the law of conservation of energy will be transferred to the rocket. Therefore, the power of the rocket engine at such speeds will increase significantly.

Simply put, in a fast-moving rocket, its propellant has tremendous kinetic energy. And from this energy additional power is drawn to accelerate the rocket. Now it remains to figure out how this property of the rocket can be used in practice.

3. Practical application

Suppose, in the near future, you are going to fly in a rocket to the Saturn system on Titan:

to research anaerobic life forms.

Flew to the orbit of Jupiter and it turned out that the speed of the rocket had dropped to almost zero. The flight path was not calculated properly or the fuel turned out to be counterfeit. Or maybe a meteorite hit the fuel compartment, and almost all of the fuel was lost. What to do?

The rocket has an engine and a small supply of fuel remains. But the maximum that the engine is capable of is to increase the rocket speed by 1 km / sec. This is clearly not enough to fly to Saturn. And now the pilot offers this option.

“We enter the gravitational field of Jupiter and fall on it. As a result, Jupiter accelerates the rocket to a tremendous speed - about 60 km / sec. When the rocket reaches this speed, turn on the engine. The engine power at this speed will increase many times over. Then we fly out of the gravitational field of Jupiter. As a result of such a gravitational maneuver, the rocket speed does not increase by 1 km / sec, but much more. And we can fly to Saturn. "

But someone objects.

“Yes, the power of the rocket near Jupiter will increase. The rocket will receive additional energy. But, flying out of the gravitational field of Jupiter, we will lose all this additional energy. The energy must remain in the potential pit of Jupiter, otherwise there will be something like a perpetual motion machine, which is impossible. Therefore, there will be no benefit from gravity assist. But we’ll waste our time ”.

What do you think of it?

So, the rocket is not far from Jupiter and is almost motionless relative to it. The rocket has an engine with enough fuel to increase the rocket speed by only 1 km / sec. To improve the efficiency of the engine, it is proposed to perform a gravitational maneuver: "drop" the rocket onto Jupiter. It will move in its field of attraction along a parabola (see photo). And at the lowest point of the trajectory (marked with a red cross in the photo), turn on the engine. The rocket speed near Jupiter will be 60 km / sec. After the engine accelerates it further, the rocket speed will increase to 61 km / s. What speed will the rocket have when it flies out of Jupiter's gravitational field?

This task is within the power of a high school student, if, of course, he knows physics well. First, you need to write a formula for the sum of potential and kinetic energies. Then recall the formula for the potential energy in the gravitational field of the ball. Look in the handbook to see what the gravitational constant is equal to, as well as the mass of Jupiter and its radius. Using the law of conservation of energy and performing algebraic transformations, obtain a general final formula. And finally, substituting all the numbers into the formula and doing the calculations, get the answer. I understand that no one (almost no one) wants to delve into any formulas, so I will try, without straining you with any equations, to explain the solution of this problem “on the fingers”. I hope it works!

If the rocket is stationary, its kinetic energy is zero. And if the rocket is moving at a speed of 1 km / sec, then we will assume that its energy is 1 unit. Accordingly, if the rocket moves at a speed of 2 km / sec, then its energy is 4 units, if 10 km / sec, then 100 units, etc. This is clear. We have already solved half of the problem.

At the point marked with a cross:

the rocket speed is 60 km / sec, and the energy is 3600 units. 3600 units are enough to fly out of Jupiter's gravitational field. After the rocket accelerated, its speed became 61 km / s, and the energy, respectively, 61 squared (take the calculator) 3721 units. When a rocket leaves Jupiter's gravitational field, it only spends 3600 units. There are 121 units left. This corresponds to a speed (take the square root) of 11 km / s. The problem has been solved. This is not an approximate, but EXACT answer.

We see that gravity assist can be used to gain additional energy. Instead of accelerating the rocket to 1 km / s, it can be accelerated to 11 km / s (energy 121 times more, efficiency - 12 thousand percent!) If there is some massive body like Jupiter nearby.

How did we get a HUGE energy gain? Due to the fact that they left the spent fuel not in an empty space near the rocket, but in a deep potential hole created by Jupiter. The consumed fuel has received a large potential energy with the MINUS sign. Therefore, the rocket received a large kinetic energy with a PLUS sign.

4. Rotation of the velocity vector near the planet

Suppose we are flying a rocket near Jupiter and want to increase its speed. But we have NO fuel. Let's just say we have some fuel to correct our course. But it is clearly not enough to noticeably accelerate the rocket. Can we noticeably increase the speed of the rocket using gravity assist?

In the very general view this task looks like this. We fly into the gravitational field of Jupiter at some speed. Then we fly out of the field. Will our speed change? And how much can it change? Let's solve this problem.

From the point of view of an observer who is on Jupiter (or rather, motionless relative to its center of mass), our maneuver looks like this. At first, the rocket is at a great distance from Jupiter and moves towards it at a speed V... Then, approaching Jupiter, it accelerates. In this case, the trajectory of the rocket is curved and, as is known, in its most general form is a hyperbola. The maximum rocket speed will be at the closest approach. The main thing here is not to crash into Jupiter, but to fly next to it. After the closest approach, the rocket will begin to move away from Jupiter, and its speed will decrease. Finally, the rocket will fly out of Jupiter's gravitational field. What speed will it have? Exactly the same as it was upon arrival. The rocket flew into Jupiter's gravitational field at a speed V and flew out of it at exactly the same speed V... Nothing changed? No, it has changed. The DIRECTION of speed has changed. It is important. Thanks to this, we can make a gravity assist.

Indeed, for us, after all, it is not the speed of the rocket relative to Jupiter that is important, but its speed relative to the Sun. This is the so-called heliocentric speed. At this speed, the rocket moves through the solar system. Jupiter also moves through the solar system. The vector of the heliocentric velocity of the rocket can be decomposed into the sum of two vectors: the orbital velocity of Jupiter (approximately 13 km / sec) and the velocity of the rocket RELATIVELY to Jupiter. There is nothing difficult here! This is the usual triangle rule for vector addition taught in 7th grade. And this rule is ENOUGH to understand the essence of gravity assist.

We have four speeds. V 1 is the speed of our rocket relative to the Sun BEFORE the gravity assist. U 1 is the speed of the rocket relative to Jupiter BEFORE the gravity assist. U 2 is the speed of the rocket relative to Jupiter AFTER the gravity assist. The largest U 1 and U 2 EQUAL, but in direction they are DIFFERENT. V 2 is the speed of the rocket relative to the Sun AFTER gravity assist. To see how all these four speeds are related to each other, take a look at the figure:

The green arrow AO is the speed at which Jupiter moves in its orbit. The red arrow AB is V 1: The speed of our rocket relative to the Sun BEFORE the gravity assist. The yellow OV arrow is the speed of our rocket relative to Jupiter BEFORE the gravitational maneuver. The yellow OS arrow is the speed of the rocket relative to Jupiter AFTER the gravity assist. This speed MUST lie somewhere on the yellow circle of radius OB. Because in its coordinate system Jupiter CANNOT change the value of the rocket's speed, but can only rotate it by a certain angle (alpha). And finally, AC is what we need: rocket speed V 2 AFTER gravity assist.

See how simple it is. The speed of the rocket AFTER the gravity assist is equal to the speed of the rocket BEFORE the gravity assist AB plus the aircraft vector. And the BC vector is the CHANGE of the rocket speed in the Jupiter frame of reference. Because OS - OB = OS + VO = VO + OS = VS. The more the rocket's velocity vector turns relative to Jupiter, the more effective the gravitational maneuver will be.

So, a rocket WITHOUT fuel flies into the gravitational field of Jupiter (or another planet). The magnitude of its speed BEFORE and AFTER the maneuver relative to Jupiter DOES NOT CHANGE. But due to the rotation of the velocity vector relative to Jupiter, the speed of the rocket relative to Jupiter still changes. And the vector of this change is simply added to the vector of the missile speed BEFORE the maneuver. I hope I explained everything clearly.