Pulses along the axis of motion affect the shape and orientation* of the orbit and do not change its inclination.
Gravitational maneuver as a natural phenomenon was first discovered by astronomers of the past, who realized that significant changes in the orbits of comets, their period (and therefore their orbital speed) occur under the gravitational influence of the planets. Thus, after the transition of short-period comets from the Kuiper belt to the inner part solar system, a significant transformation of their orbits occurs precisely under the gravitational influence of massive planets, when exchanging angular momentum with them, without any energy costs.
Samu the idea to use gravity maneuver for spaceflight purposes was developed by Michael Minovich in the 60s, when, as a student, he interned at JPL*. The idea was quickly picked up and implemented in many space missions. But at first glance, the possibility of significantly accelerating the movement of the device without spending energy seems strange and requires explanation.
We often hear about the “capture” of asteroids and comets by the field of planets. Strictly speaking, capture without loss of energy is impossible: if some body approaches massive planet, the module of its velocity first increases as it approaches, and then decreases by the same amount as it moves away. But the body can still move into the orbit of the planet’s satellite if it is decelerated at the same time (for example, there is deceleration in the upper layers of the atmosphere, if the approach is close enough; or if significant tidal dissipation of energy occurs; or, finally, if the body is destroyed within the limit Roche with different velocity vectors acquired by debris). At the stage of formation of the Solar System, an important factor was also the deceleration of the body in the gas-dust nebula. As for spacecraft, then only in the case of launching a satellite into orbit, braking in the upper layers of the atmosphere (aerobraking) is used. In a “pure” gravitational maneuver, the rule of equality of the velocity module before and after approaching the planet is strictly preserved (as intuition suggested: what you came with is what you left with). What's the gain?
The gain becomes obvious if we move from planetocentric to heliocentric coordinates.
The most beneficial maneuvers are near the giant planets, and they significantly reduce the flight duration. Maneuvers are also used Earth and Venus, but this significantly increases the duration of space travel. All data given in the table refers to a passive maneuver. But in some cases, at the pericenter of the flyby hyperbola, the device, with the help of its propulsion system, is given a small reactive impulse, which gives a significant additional gain.
In flight, the device often requires deceleration rather than acceleration. It is easy to choose such a rendezvous geometry when the speed of the vehicle in heliocentric coordinates drops. This depends on the position of the velocity vectors during the exchange of angular momentum. Simplifying the problem, we can say that the approach of the device to the planet with inside its orbit leads to the fact that the device gives up part of its angular momentum to the planet and slows down; and vice versa, getting closer to outside orbit leads to an increase in the moment and speed of the apparatus. It is interesting that it is impossible to register changes in the speed of the vehicle during maneuvers with any accelerometers on board - they constantly record the state of weightlessness.
Advantages of gravity maneuver compared to Homan flight to the giant planets are so large that the payload of the device can be doubled. As already mentioned, the time to reach the target during a gravitational maneuver for massive giant planets is reduced very significantly. The development of the principles of the maneuver showed that it is possible to use less massive bodies (Earth, Venus and, in special cases, even the Moon). Only the mass, in a sense, is exchanged for the flight time, which forces researchers to wait 2-3 extra years. However, the desire to reduce costs for expensive space program makes you come to terms with such a waste of time. Now the choice of flight route is, as a rule, multi-purpose, covering several planets. In 1986, a gravitational maneuver near Venus allowed the Soviet spacecraft VEGA-1 and VEGA-2 to meet Halley's comet.
A gravity maneuver is a way to change the direction of a spacecraft's motion, as well as increase or decrease its speed, using the gravity of massive objects and without using valuable fuel on board the spacecraft.
Probably, the possibility of such a gravitational maneuver was already suspected by ancient astronomers and stargazers of ancient Babylon, when they observed the movements of comets changing their trajectory and speed when they flew near other celestial bodies.
The principle of operation of the gravity maneuver can be described as follows: if the spacecraft approaches the inner side of the planet’s orbit, then its speed slows down. If the device passes from the outer side of the planet’s orbit, then its speed will increase. This principle of operation resembles the work of a slinger throwing projectiles. This is why the gravity maneuver is often called a “gravity slingshot.”
Using Gravity Braking Maneuver | www.commons.wikimedia.org/wiki/File:Swingby_dec_anim.gif 
Using Gravity Maneuver to Accelerate | www.commons.wikimedia.org/wiki/File:Swingby_acc_anim.gif It should be understood that in the reference frame associated with the celestial object that is used for the gravitational maneuver (for example, the probe passes near Venus), no positive effect for the spacecraft is observed will be, except for changing its flight path. However, relative to other celestial bodies (for example, the Sun), the spacecraft will move faster/slower.
The advantages of the gravity maneuver are obvious. It allows you to increase/decelerate without having to turn on the engines, leading to great fuel savings. Less fuel means more payload. Accordingly, one spacecraft can carry as much payload as would be carried by two spacecraft that did not use the “gravitational sling” effect. The money saved as a result can be distributed to other space projects.
Probably the most famous device that used a gravity maneuver was the American Voyager 2. Thanks to the system of acceleration and deceleration, he flew on a tour of the solar system along the route “Earth-Jupiter-Saturn-Uranus-Neptune”. And now, having received acceleration from the planets, it has already gone beyond the boundaries of the solar system.
No less interesting is the Voyager 1 apparatus. Its current speed of 17 km/s, achieved using gravitational maneuvers, is the highest among all man-made objects, although at launch it was an order of magnitude less.
The Cassini interplanetary station was forced to resort to a combination of gravitational maneuvers. Having used the gravitational field of Venus twice and once each of Earth and Jupiter, the device accelerated to the required speed, while using 25 times (!) less fuel than it would have needed without the use of gravitational maneuvers.
This is interesting: GThe gravity maneuver is best used near objects with higher speed and greater gravity. The ideal candidate for such an object is obvious: stars. The minds of scientists have long been excited by the idea of flying a spacecraft near neutron stars. According to calculations, such a maneuver could accelerate the ship to 1/3 the speed of light. What a size! At this speed, intergalactic flights no longer seem so impossible...
Illustration: bigstockphoto | 3DSculptor
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Gravity maneuver to accelerate an object Gravity maneuver to decelerate an object Gravity maneuver acceleration, deceleration or change of flight direction of a spacecraft under the influence of gravitational fields of celestial bodies.... ... Wikipedia
Gravity maneuver to accelerate an object Gravity maneuver to decelerate an object Gravity maneuver acceleration, deceleration or change of flight direction of a spacecraft under the influence of gravitational fields of celestial bodies.... ... Wikipedia
- ... Wikipedia
This is one of the main geometric parameters objects formed by a conic 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 into 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
A branch of celestial mechanics that studies the movement of artificial cosmic bodies: artificial satellites, interplanetary stations and other spacecraft. The scope of astrodynamics tasks includes the calculation of spacecraft orbits, determination of parameters... ... Wikipedia
The Oberth effect in astronautics is the effect in which a rocket engine moving at high speed produces more useful energy than the same engine moving slowly. The Oberth effect is caused by the fact that when... ... Wikipedia
Customer... Wikipedia
And equipotential surfaces of a system of two bodies Lagrange points, libration points (lat. librātiō swinging) or L points ... Wikipedia
Books
- Things of the 20th century in drawings and photographs. Forward to space! Discoveries and achievements. Set of 2 books, . "Forward, into space! Discoveries and achievements" Since ancient times, man has 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...
- Let's go to space! Discoveries and achievements, Klimentov Vyacheslav Lvovich, Sigorskaya Yulia Aleksandrovna. Since ancient times, man has dreamed of breaking away from the earth 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...
At the beginning of the 20th century, when the fundamental feasibility of space flights was scientifically substantiated, the first thoughts about their possible trajectories appeared. A straight flight from Earth to another planet is energetically extremely unfavorable. In 1925, the German engineer Walter Hohmann showed that the minimum energy required for a flight between two circular orbits is achieved when the trajectory is a “half” ellipse tangent to the initial and final orbits. In this case, the spacecraft engine must produce only two pulses: at the perigee and apogee (if we are talking about near-Earth space) of the transition ellipse. This scheme is widely used, for example, when launching into geostationary orbit. In interplanetary flights, the task is somewhat complicated by the need to take into account the gravity of the Earth and the destination planet, respectively, at the initial and final sections of the trajectory. Nevertheless, flights to Venus and Mars are carried out in orbits close to Hohmann’s.
Perhaps the first example of a more complex space navigation technique can be bielliptic trajectories. As one of the first theorists, cosmonaut Ari Abramovich Sternfeld, proved, they are optimal for transferring a satellite between circular orbits with different inclinations. Changing the orbital plane is one of the most expensive operations in astronautics. For example, to rotate 60 degrees, the device needs to add the same speed with which it is already moving in orbit. However, you can do it differently: first, issue an accelerating impulse, with the help of which the device will move to a highly elongated orbit with a high apogee. In her top point the speed will be very low, and the direction of movement will change at the cost of relatively small fuel costs. At the same time, you can adjust the perigee altitude by slightly changing the speed in magnitude. Finally, at the bottom point of the elongated ellipse, a braking impulse is given, which transfers the device to a new circular orbit.
This maneuver, called “high apogee interorbital transfer,” is especially relevant when launching geostationary satellites, which are initially launched into a low orbit with an inclination to the equator equal to the latitude of the launch site, and then transferred to a geostationary orbit (with zero inclination). The use of a bielliptic trajectory allows significant savings on fuel.
Gravity maneuvers
Many interplanetary missions with modern technical capabilities are simply not feasible without resorting to exotic navigation techniques. The fact is that the rate of flow of the working fluid from chemical rocket engines is about 3 km/s. Moreover, according to the Tsiolkovsky formula, every 3 km/s of additional acceleration triples the launch mass of the space system. To go from low Earth orbit (speed 8 km/s) to Mars along the Hohmann trajectory, you need to gain about 3.5 km/s, to Jupiter - 6 km/s, to Pluto - 8-9 km/s. It turns out that the payload during a flight to distant planets is only a few percent of the mass launched into orbit, and that, in turn, is only a few percent of the launch mass of the rocket. That's why the 700-pound Voyagers were launched toward Jupiter by a 600-ton Titan IIIE rocket. And if the goal is to enter orbit around the planet, then it becomes necessary to take with you a supply of fuel for braking, and the launch mass increases even more.
But ballistics experts do not give up - to save fuel, they adapted the same gravity, which takes a significant part of the energy to overcome at launch. Gravity, or in professional language, perturbation maneuvers require virtually no fuel consumption. All that is needed is the presence of a celestial body near the flight path that has sufficiently strong gravity and a position suitable for the purposes of the mission. When approaching a celestial body, the spacecraft accelerates or decelerates under the influence of its gravitational field. Here the attentive reader may notice that the apparatus, having been accelerated by the planet’s gravity, is also slowed down by it after approaching the celestial body and that as a result there will be no acceleration. Indeed, the velocity relative to the planet used as a “gravitational sling” will not change in magnitude. But she will change direction! And in the heliocentric (associated with the Sun) frame of reference, it turns out that the speed changes not only in direction, but also in magnitude, since it consists of the speed of the vehicle relative to the planet and, at least partially, the speed of the planet itself relative to the Sun. In this way, it is possible to change the kinetic energy of the interplanetary station without wasting fuel. When flying to the distant, outer planets of the Solar System, the gravitational maneuver is used for acceleration, and on missions to the inner planets, on the contrary, to dampen the heliocentric speed.
DISTURBANCES AND CORRECTIONS |
In the pictures, the trajectories of interplanetary flights look very simple: from the Earth, the station moves along an elliptical arc, the far end of which abuts the planet. The ellipticity of the orbit around the Sun is dictated by Kepler's first law. Even a schoolchild can calculate it, but if a real spacecraft is launched at it, it will miss the target by many thousands of kilometers. The fact is that the motion of the apparatus, in addition to the Sun, is influenced by the gravity of the planets orbiting it. Therefore, it is possible to accurately calculate where the device will end up after months, or even years of flight, only through complex numerical modeling. The initial position and speed of the apparatus are set, it is determined how the planets are located relative to it and what forces act on their part. They are used to calculate where the device will be after a short time, say, an hour, and how its speed will change. Then the calculation cycle is repeated, and so the entire trajectory is calculated step by step. Most likely, it will not end up exactly where it needs to go. |
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The idea of a gravitational maneuver was first expressed by Friedrich Arturovich Zander and Yuri Vasilyevich Kondratyuk back in the 1920-1930s. It is officially believed that the first such maneuver was performed in 1974 by the American station Mariner 10, which, after flying near Venus, headed towards Mercury. However, the primacy of the Americans is disputed Russian historians cosmonautics who consider the first gravitational maneuver to be the flyby of the Moon, which was carried out in 1959 by the Soviet station Luna-3, which first photographed reverse side our natural satellite.
Jupiter will help us
Many interplanetary probes used Jupiter's gravity for acceleration. The first were Pioneer 10 and Pioneer 11, followed by Voyager 1 and Voyager 2. In 1992, Jupiter helped Ulysses, a probe exploring the polar regions of the Sun, move out of the ecliptic plane, around which it revolves in an orbit almost perpendicular to the Earth's. There is simply no other way to launch a vehicle into such an orbit at the current level of development of space technology. The New Horizons probe, launched by the United States to Pluto on January 19, 2006, also performed a perturbation maneuver at Jupiter. By increasing its speed by 4 km/s and deviating 2.5 degrees from the ecliptic plane, it could arrive at its target in 2015, before the atmosphere on Pluto (which is moving away from the Sun this century) begins to freeze, thereby reducing the value of future exploration .
Of course, to perform gravity maneuvers, the launch date must be kept very precisely. Ballistics experts use the concept of a “launch window” - this is the date interval within which the effectiveness of planned gravity maneuvers is maximum. Closer to the edges of the “window” the effect becomes smaller, and the need for fuel becomes greater. If you go beyond its boundaries, the carrier simply will not be able to launch the device into the desired orbit, which will lead to a failure of the flight or an unacceptable increase in its duration. For example, the launch of New Horizons was repeatedly postponed due to weather and technical reasons. If the launch had been delayed for a few more days, the probe would have set off without relying on Jupiter’s “gravitational assistance” and with less chance of success. It is most convenient to perform maneuvers around giant planets. Thanks to their large mass, it is possible to turn around them in a wide, smooth arc, and the requirements for navigation accuracy remain quite mild. However, Venus, Earth, Mars and even the Moon are often used as a “sling”. You can’t make mistakes here, otherwise the device will leave the planet in a completely different direction than it was planned.
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The ISEE-3/ICE probe studied the Sun for four years (1978-1982) from orbit around the Lagrange point L1, and then, through complex gravitational maneuvers near the Earth and the Moon, it was sent to meet comets Giacobini-Zinner (1985) and Halley (1986) . The probe will return to Earth in 2012. Rice. NASA |
The launch window is the date interval within which the effectiveness of the planned gravity maneuvers is maximum. |
Homan ellipses touching the orbit of the Earth and the destination planet are the most economical interplanetary trajectories, if you do not resort to gravitational maneuvers. A flight to Mars in a Hohmann orbit takes about 240-280 days, to Venus - about 150 days. |
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Space gravsurfing
The most difficult - but that’s why they’re interesting! - trajectories with perturbation maneuvers not for one, but for several celestial bodies. For example, the Galileo station, in order to get to Jupiter, carried out a gravitational maneuver in the gravitational field of Venus, and then two more near the Earth. Such flights are not always possible, but only with a certain arrangement of planets. The most famous such “grand tour” was made by Voyager 2, which successively flew near Jupiter, Saturn, Uranus and Neptune. Its twin, Voyager 1, could also have taken a similar route, but scientists chose to take a closer look at Saturn’s mysterious moon Titan, and its gravity irreversibly deviated the station’s trajectory away from Uranus. It was a difficult but right decision. It was the data from Voyager 2 that allowed the Huygens probe to land on Titan 24 years later.
Nowadays, an even more complex flight is carried out by the MESSENGER station. Its main task is to enter orbit around Mercury for a detailed study of its characteristics. The mission, designed for a seven-year journey, reached The final stage. The device has already performed four gravitational maneuvers: one near the Earth, two near Venus and one near Mercury itself, and between them the engines were maneuvered in order to correctly enter the gravitational “funnel” of the planet each time. Messenger will have to perform five more maneuvers (two gravitational and three by engines) before it becomes a satellite of the planet closest to the Sun. During this time, it will “wrap” 8 billion kilometers around the Sun - more than to Pluto! However, if the trajectory were not so complex, with the current state of rocket and space technology, this flight could not have taken place at all.
LAGRANGE'S STAIRCASE |
Despite corrections and gravitational maneuvers, the orbits of most interplanetary stations are still close to the classical arcs of ellipses and hyperbolas. But in Lately celestial navigators are increasingly using much more sophisticated trajectories that lie in those areas of space where the attraction of two celestial bodies at once has to be equally taken into account. |
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With little attraction to small bodies
But gravity maneuvers are not the only way to save fuel. Back in the 1930s, one of the pioneers of domestic rocket engine construction, Valentin Petrovich Glushko, proposed the use of electric rocket engines (EP). Compared to traditional liquid-propellant rocket engines (LPRE), their working fluid flow rate is an order of magnitude higher, which means they require hundreds of times less fuel. Unfortunately, the thrust of electric propulsion engines is calculated on the order of several grams of force, so they are not suitable for launching vehicles into orbit. These are “outer space engines,” designed for slow but continuous acceleration lasting months, and for interplanetary flights, years. “Low-thrust missions” only became popular when electronics made giant leaps to extend the service life of spacecraft from a few months to several years, or even decades.
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The low-thrust flight path is not at all like a classic ellipse; it represents a slowly unfolding Archimedes spiral. The transition from low Earth orbit to geostationary orbit along such a trajectory takes six months. This is truly torture for the owner of a satellite selling space communications services: every day of waiting costs tens of thousands of dollars. We also have to take into account such an unpleasant circumstance as multiple flights through the Earth's radiation belts. Fine electronics really don't like cosmic radiation. But on the other hand, a satellite equipped with an electric propulsion engine can be launched into geostationary orbit by a Soyuz rocket (300 tons), while a vehicle with a conventional liquid propellant engine already needs a mighty Proton (700 tons). The difference in launch costs is two to three times. So the spacecraft customer is scratching his head: which option to choose? Usually, they still settle on what is faster: modern communications satellites begin to “recoup” the money spent on their launch within a couple of weeks after being launched into the target orbit. So in near-Earth space, low-thrust engines are used mainly for small orbital corrections.
Another thing is flights, say, to asteroids. Electric propulsion engines will make it possible to relatively easily transfer an interplanetary station from one object to another, and not just fly past, but linger for a long time at each one. Due to their insignificant (compared to planets) mass, asteroids have negligible gravity. Their flyby bears little resemblance to the usual orbital motion around large planets. Orbital speeds here they are measured in centimeters per second, and periods are measured over many days. To fly around an asteroid faster, you have to almost constantly “work with the engines.” If you turn them off, the device will simply fly away from the planetoid. But the almost complete absence of gravity allows you to land on the surface of an asteroid and take off from it at minimum costs fuel.
By by and large the word “landing” can be used here only conditionally: the mooring of an interplanetary probe to an asteroid is more reminiscent of the docking of two spacecraft than a classic landing on the surface of a planet. This trick was performed by the Japanese with their Hayabusa probe, which twice descended to the surface of the Itokawa asteroid and rose from it. By the way, this same flight showed how difficult it is to control a vehicle near the surface of an asteroid. Exchange of signals with the device takes tens of minutes, so it is impossible to give commands to it in real time, despite the low speeds. Therefore, testing autonomous navigation near uneven surface asteroid was one of the main tasks of Hayabusa.
The American probe Dawn, launched in September 2007 to the asteroids Ceres and Vesta, is equipped with ion engines with a thrust of less than one tenth of Newton (the weight of a 10-sided load). Over the course of a day's work, they accelerate a vehicle weighing about a ton by 25 km/h. This is not as little as it might seem: in a year at a similar pace you can gain 2.5 km/s. The full supply of fuel on board (425 kilograms) is enough to change the speed of the vehicle by 10 km/s - this is not possible for any interplanetary spacecraft with chemical engines.
Planetary engines
Let's try to fantasize and imagine that it has finally been decided to send a crew consisting of people, say, to the Saturn system. You can choose a fast flight with high thrust: assemble an interplanetary spacecraft in low-Earth orbit, use a liquid-propellant rocket engine to generate a powerful acceleration impulse, and hyperbolically set off on a journey. It will still take a long time to fly - several years. The amount of fuel needed is enormous. This means that equipping a giant ship will require more than a dozen super-heavy missiles. Supplies of oxygen, water, food and everything that is needed in an interplanetary flight are lost against the background of a huge mass of fuel, necessary not only for acceleration near the Earth, but also for braking at the destination of the journey, and for returning to the home planet...
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What if you try low deadlifts? The insane amount of fuel will be significantly reduced, and the travel time, oddly enough, may remain the same! After all, the ship's engines will work the whole way - halfway to accelerate, and halfway to decelerate. True, the thrust of electric propulsion engines will have to be increased hundreds of times compared to those on the Zarya probe. But firstly, such developments are already underway, and secondly, there can be many engines.
To power the electric propulsion engine you will need several megawatts of energy. Near the Earth, it could be obtained for free - from huge solar panels with an area of thousands, if not tens of thousands. square meters. But with distance from the Sun, their efficiency quickly decreases: for Mars - by 60%, for Jupiter - 30 times. So for flights to the giant planets you will have to use nuclear reactor. And yet, most likely, liquid rocket engines will still be needed in order to quickly pass through dangerous radiation belts near the Earth. Apparently, it is the combined propulsion systems that will be used in interplanetary manned missions of the future.
Not just gravity
Deep space is fraught with many mysteries. It would seem that what could be more accurate than ballistic calculations, which are based on the laws of celestial mechanics? Not so! There are many forces acting on the space probe that are difficult to account for in advance. Pressure solar radiation and the solar wind, magnetic fields planets and the outflow of gas from the apparatus itself - all this affects the speed of its movement. Even the thermal radiation from the probe and the radio signal sent to Earth by the highly directional antenna cause recoil, which must be taken into account for precise navigation. And what happened to the already mentioned “Pioneers” has not yet received a proper explanation. Russian astrophysicist Vyacheslav Turyshev, who works at NASA, discovered about 10 years ago that the probes experience very little anomalous braking. Over the 20 years of flight, the Pioneer anomaly led to the fact that, approaching the boundaries of the solar system, the spacecraft deviated from the calculated position by 400 thousand kilometers! What hypotheses have not been put forward to explain the anomaly? From the already mentioned magnetic fields and the evaporation of residual fuel from fuel lines to the presence of massive invisible objects on the borders of the Solar system. Some physicists consider the anomaly to be an indication of the inaccuracy of the modern theory of gravity, while others see it as a manifestation of cosmological factors such as dark matter and dark energy. There is no comprehensive explanation yet, and Turyshev’s group continues to process data on the Pioneer flight. Be that as it may, when designing new trajectories of interplanetary flights, the possibility of such unexpected phenomena will have to be taken into account.
In general, the work of a space ballistician balances on the verge of art and exact sciences. He always has to solve a problem with many unknowns, aggravated by the customer’s desire to do everything “faster and cheaper”, without going beyond the boundaries of physical laws. So, undoubtedly, we will continue to witness the birth of many new non-trivial space trajectories.
, Earth, Mars and even the Moon.
Physical essence of the process
Let's consider the trajectory of a spacecraft flying near some large celestial body, for example, Jupiter. In the initial approximation, we can neglect the effect of gravitational forces from other celestial bodies on the spacecraft.
A complex combination of gravitational maneuvers was used by the Cassini spacecraft (for acceleration, the device used 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 “2010: Odyssey 2” by A. Clark.
In the science fiction film Interstellar, the Endurance orbital station does not have enough fuel to reach the third planet, located next to the black hole Gargantua (named after the literary giant glutton). Main character Cooper takes a risky step: Endurance must pass close to Gargantua's event horizon, thereby giving the station acceleration due to the attraction of the black hole.
In the science fiction novel “The Martian” and the film of the same name, using a gravitational maneuver around the Earth, the team accelerates the Hermes ship for a second flight to Mars.
see also
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Notes
Links
- // crydee.sai.msu.ru
- (navigation calculations for space simulator"Orbiter", allows you to calculate, including gravity maneuvers)
- // novosti-kosmonavtiki.ru
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An excerpt characterizing the Gravity Maneuver
- Oh my God!- Why are you pushing, is the fire about you alone, or what? See... it fell apart.
From behind the established silence, the snoring of some who had fallen asleep was heard; the rest turned and warmed themselves, occasionally talking to each other. A friendly, cheerful laugh was heard from the distant fire, about a hundred paces away.
“Look, they’re roaring in the fifth company,” said one soldier. – And what a passion for the people!
One soldier got up and went to the fifth company.
“It’s laughter,” he said, returning. - Two guards have arrived. One is completely frozen, and the other is so courageous, dammit! Songs are playing.
- Oh oh? go have a look... - Several soldiers headed towards the fifth company.
The fifth company stood near the forest itself. A huge fire burned brightly in the middle of the snow, illuminating the tree branches weighed down with frost.
In the middle of the night, soldiers of the fifth company heard footsteps in the snow and the crunching of branches in the forest.
“Guys, it’s a witch,” said one soldier. Everyone raised their heads, listened, and out of the forest, into bright light fire, two strangely dressed human figures appeared, holding each other.
These were two Frenchmen hiding in the forest. Hoarsely saying something in a language incomprehensible to the soldiers, they approached the fire. One was taller, wearing an officer's hat, and seemed completely weakened. Approaching the fire, he wanted to sit down, but fell to the ground. The other, small, stocky soldier with a scarf tied around his cheeks, was stronger. He raised his comrade and, pointing to his mouth, said something. The soldiers surrounded the French, laid out an overcoat for the sick man, and brought porridge and vodka to both of them.
The weakened French officer was Rambal; tied with a scarf was his orderly Morel.
When Morel drank vodka and finished a pot of porridge, he suddenly became painfully cheerful and began to continuously 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. Occasionally he would let out a long groan and then fall silent again. Morel, pointing to his shoulders, convinced the soldiers that it was an officer and that he needed to be warmed up. The Russian officer, who approached the fire, sent to ask the colonel if he would take the French officer to warm him up; and when they returned and said that the colonel had ordered an officer to be brought, Rambal was told to go. He stood up and wanted to walk, but he staggered and would have fallen if the soldier standing next to him had not supported him.
- What? You will not? – one soldier said with a mocking wink, turning to Rambal.
- Eh, fool! Why are you lying awkwardly! “It’s a man, really, a man,” they heard from different sides reproaches to the soldier who joked. They surrounded Rambal, lifted him into his arms, grabbed him, and carried him to the hut. Rambal hugged 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! O my good, good friends! Here are the people! O my good friends!] - and, like a child, he leaned his head on the shoulder of one soldier.
Meanwhile Morel sat on best place surrounded by soldiers.
Morel, a small, stocky Frenchman, with bloodshot, watery eyes, tied with a woman's scarf over his cap, was dressed in a woman's fur coat. He, apparently drunk, put his arm around the soldier sitting next to him and sang a French song in a hoarse, intermittent voice. The soldiers held their sides, looking at him.
- Come on, come on, teach me how? I'll take over quickly. How?.. - said the joker songwriter, who was hugged by Morel.
Vive Henri Quatre,
Vive ce roi vaillanti –
[Long live Henry the Fourth!
Long live this brave king!
etc. (French song)]
sang Morel, winking his eye.
Se diable a quatre…
- Vivarika! Vif seruvaru! sit-down... - the soldier repeated, waving his hand and really catching the tune.
- Look, clever! Go go go go!.. - rough, joyful laughter rose from different sides. Morel, wincing, laughed too.
- Well, go ahead, go ahead!
Qui eut le triple talent,
De boire, de batre,
Et d'etre un vert galant...
[Having triple talent,
drink, fight
and be kind...]
– But it’s also complicated. Well, well, Zaletaev!..
“Kyu...” Zaletaev said with effort. “Kyu yu yu...” he drawled, carefully protruding his lips, “letriptala, de bu de ba and detravagala,” he sang.
- Hey, it’s important! That's it, guardian! oh... go go go! - Well, do you want to eat more?
- Give him some porridge; After all, it won’t be long before he gets enough of hunger.
Again they gave him porridge; and Morel, chuckling, began to work on the third pot. Joyful smiles were on all the faces of the young soldiers looking at Morel. The old soldiers, who considered it indecent to engage in such trifles, lay on the other side of the fire, but occasionally, raising themselves on their elbows, they looked at Morel with a smile.
“People too,” said one of them, dodging into his overcoat. - And wormwood grows on its root.
- Ooh! Lord, Lord! How stellar, passion! Towards the frost... - And everything fell silent.
The stars, as if knowing that now no one would see them, played out in the black sky. Now flaring up, now extinguishing, now shuddering, they busily whispered among themselves about something joyful, but mysterious.
X
The French troops gradually melted away in a mathematically correct progression. And that crossing of the Berezina, about which so much has been written, was only one of the intermediate stages in the destruction of the French army, and not at all a decisive episode of the campaign. If so much has been and is being written about the Berezina, then on the part of the French this happened only because on the broken Berezina Bridge, the disasters that the French army had previously suffered evenly here suddenly grouped together at one moment and into one tragic spectacle that remained in everyone’s memory. On the Russian side, 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 Pfuel) to capture Napoleon in a strategic trap on the Berezina River. Everyone was convinced that everything would actually happen exactly as planned, and therefore insisted that it was the Berezina crossing that destroyed the French. In essence, the results of the Berezinsky crossing were much less disastrous for the French in terms of the loss of guns and prisoners than Krasnoye, as the numbers show.
The only significance of the Berezina crossing is that this crossing obviously and undoubtedly proved the falsity of all plans for cutting off and the justice of the only possible course of action demanded by both Kutuzov and all the troops (mass) - only following the enemy. The crowd of Frenchmen fled with an ever-increasing force of speed, with all their energy directed towards achieving their goal. She ran like a wounded animal, and she could not get in the way. This was proven not so much by the construction of the crossing as by the traffic on the bridges. When the bridges were broken, unarmed soldiers, Moscow residents, women and children who were in the French convoy - all, under the influence of the force of inertia, did not give up, but ran forward into the boats, into the frozen water.
This aspiration was reasonable. The situation of both those fleeing and those pursuing was equally bad. Remaining with his own, each in distress hoped for the help of a comrade, for a certain place he occupied among his own. Having given himself over to the Russians, he was in the same position of distress, but he was on a lower level in terms of satisfying the needs of life. The French did not need to have correct information that half of the prisoners, with whom they did not know what to do, despite all the Russians’ desire to save them, died from cold and hunger; they felt that it could not be otherwise. The most compassionate Russian commanders and hunters of the French, the French in 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 clothing from hungry, necessary soldiers in order to give it to the French who were not harmful, not hated, not guilty, but simply unnecessary. Some did; but this was only an exception.
