It is hard to imagine how much fuel space vehicles have saved gravitational maneuvers. They help to reach the vicinity of the giant planets and even go forever beyond the solar system. Even for the study of comets and asteroids relatively close to us, the most economical trajectory can be calculated using gravitational maneuvers. When did the idea of ​​the "cosmic sling" come about? And when was it first implemented?

The 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, consequently, their orbital speed) occur under the gravitational influence of the planets. So, after the transition of short-period comets from the Kuiper belt to the inner part of the solar system, a significant transformation of their orbits occurs precisely under the gravitational influence of massive planets, during the exchange of angular momentum with them, without any energy costs.

The very idea of ​​using gravitational maneuvers to achieve the goal of space flight was developed by Michael Minovich in the 60s, when, as a student, he did an internship at NASA's Jet Propulsion Laboratory. For the first time, the idea of ​​a gravitational maneuver was realized in the flight path of the automatic interplanetary station "Mariner-10", when the gravitational field of Venus was used to reach Mercury.

In a "pure" gravitational maneuver, the rule of equality of the modulus of velocities before and after approaching a celestial body is strictly preserved. The gain becomes obvious if we pass from planetocentric coordinates to heliocentric ones. This is clearly seen in the scheme shown here, adapted from V. I. Levantovsky's book "Space Flight Mechanics". The trajectory of the vehicle is shown on the left, as it is seen by an observer on the planet R. The speed v in at "local infinity" is equal in absolute value to v out. All that the observer will notice is a change in the direction of the apparatus. However, an observer located in heliocentric coordinates will see a significant change in the speed of the apparatus. Since only the modulus of the spacecraft's velocity relative to the planet is preserved, and it is comparable to the modulus of the orbital velocity of the planet itself, the resulting vector sum of the velocities can become both greater and lesser than the velocity of the vehicle before approaching. On the right is a vector diagram of such an exchange of angular momentum. V in and v out denote equal entry and exit velocities of the spacecraft relative to the planet, and V sbl, V remote, and V pl denote the speeds of approach and removal of the spacecraft and the orbital velocity of the planet in heliocentric coordinates. The ΔV increment is that speed impulse that the planet reported to the apparatus. Of course, the moment that the apparatus itself transmits to the planet is negligible.

Thus, by an appropriate choice of the rendezvous path, one can not only change the direction, but also significantly increase the speed of the apparatus without any expenditure of its energy sources.

This diagram does not show that at first the speed increases sharply, and then drops to a final value. Ballisticians do not usually care about this, they perceive the exchange of angular momentum as a "gravitational impact" from the planet, the duration of which is negligible compared to the total duration of the flight.

Critical in the gravitational maneuver are the mass of the planet M, the target range d and the speed v in. Interestingly, the velocity increment ΔV is maximum when v in is equal to the circular velocity near the planet's surface.

Thus, the maneuvers of the giant planets are most advantageous, and they noticeably shorten the duration of the flight. Maneuvers near the Earth and Venus are also used, but this significantly increases the duration of space travel.

Since the success of the Mariner 10 mission, gravity assist maneuvers have been used in many space missions. For example, the mission of the Voyager spacecraft was exceptionally successful, with the help of which studies of the giant planets and their satellites were carried out. The vehicles were launched in the US in the fall of 1977 and reached the mission's first target, the planet Jupiter, in 1979. After completing the research program around Jupiter and exploring its satellites, the vehicles performed a gravitational maneuver (using Jupiter's gravitational field), which allowed them to be sent on slightly different trajectories to Saturn, which they reached in 1980 and 1981, respectively. Next, Voyager 1 performed a complex maneuver to pass within 5,000 km of Saturn's moon Titan, and then ended up on an exit trajectory from the solar system.

Voyager 2 also performed another gravitational maneuver and, despite some technical problems, was directed towards the seventh planet, Uranus, which was encountered in early 1986. After approaching Uranus, another gravitational maneuver was performed in its field, and Voyager 2 headed towards Neptune. Here, the gravitational maneuver allowed the device to get close enough to Neptune's satellite Triton.

In 1986, a gravitational maneuver near Venus enabled the Soviet spacecraft VEGA-1 and VEGA-2 to encounter Halley's comet.

At the very end of 1995, Jupiter was reached by a new apparatus, Galileo, whose flight path was chosen as a chain of gravitational maneuvers in the gravitational fields of the Earth and Venus. This allowed the device to visit the asteroid belt twice in 6 years and get close to the fairly large bodies Gaspra and Ida, and even return to Earth twice. After being launched in the USA in the fall of 1989, the spacecraft was sent to Venus, which it approached in February 1990, and then returned to Earth in December 1990. Again, a gravitational maneuver was performed, and the device went to the inner part of the asteroid belt. In order to reach Jupiter, in December 1992, Galileo returned to Earth again and, finally, laid down on a flight course to Jupiter.

In October 1997, also in the USA, the Cassini spacecraft was launched to Saturn. The program of his flight provides for 4 gravitational maneuvers: two near Venus and one each near the Earth and Jupiter. After the first Venus rendezvous maneuver (in April 1998), the spacecraft went to the orbit of Mars and again (without the participation of Mars) returned to Venus. The second Venus maneuver (June 1999) returned Cassini to Earth, where a gravity assist maneuver was also performed (August 1999). Thus, the spacecraft gained sufficient speed for a fast flight to Jupiter, where at the end of December 2000 its last maneuver on the way to Saturn will be performed. The device should reach the goals in July 2004.

L. V. Ksanfomality, Doctor of Phys.-Math. Sci., Head of the Laboratory of the Space Research Institute.

conventional view

There are special bodies in the solar system - comets.
A comet is a small body several kilometers in size. Unlike an ordinary asteroid, the comet includes various ices: water, carbon dioxide, methane, and others. When the comet enters the orbit of Jupiter, these ices begin to evaporate rapidly, leave the surface of the comet together with dust and form the so-called coma - a gas and dust cloud surrounding the solid core. This cloud extends hundreds of thousands of kilometers from the core. Thanks to the reflected sunlight, the comet (not itself, but only a cloud) becomes visible. And due to light pressure, part of the cloud is pulled into the so-called tail, which stretches from the comet for many millions of kilometers (see photo 2). Due to very weak gravity, all the substance of the coma and tail is irretrievably lost. Therefore, flying near the Sun, a comet can lose several percent of its mass, and sometimes more. The time of her life by astronomical standards is negligible.
Where do new comets come from?

According to traditional cosmogony, they come from the so-called Oort cloud. It is generally accepted that at a distance of one hundred thousand astronomical units from the Sun (half the distance to the nearest star) there is a huge reservoir of comets. The nearest stars periodically disturb this reservoir, and then the orbits of some comets change so that their perihelion is near the Sun, the gases on its surface begin to evaporate, forming a huge coma and tail, and the comet becomes visible through a telescope, and sometimes even with the naked eye. Pictured is the famous Great Comet Hale-Bopp, in 1997.

How did the Oort cloud form? The generally accepted answer is this. At the very beginning of the formation of the solar system in the region of the giant planets, many icy bodies with a diameter of ten or more kilometers formed. Some of them became part of the giant planets and their satellites, and some were ejected to the periphery of the solar system. Jupiter played the main role in this process, but Saturn, Uranus and Neptune also applied their gravitational fields to it. In the most general terms, this process looked like this: a comet flies near the powerful gravitational field of Jupiter, and it changes its speed so that it ends up on the periphery of the solar system.

True, this is not enough. If the comet's perihelion is inside the orbit of Jupiter, and the aphelion is somewhere on the periphery, then its period, as it is easy to calculate, will be several million years. During the existence of the solar system, such a comet will have time to approach the Sun almost a thousand times and all of its gas that can evaporate will evaporate. Therefore, it is assumed that when the comet is on the periphery, then the perturbations from the nearest stars will change its orbit so that the perihelion will also be very far from the Sun.

So there is a four step process. 1. Jupiter throws a piece of ice to the periphery of the solar system. 2. The nearest star changes its orbit so that the perihelion of the orbit is also far from the Sun. 3. In such an orbit, a piece of ice stays safe and sound for almost several billion years. 4. Another passing star again perturbs its orbit so that the perihelion is near the Sun. As a result, a piece of ice flies towards us. And we see it like a new comet.

All this seems quite plausible to modern cosmogonists. But is it? Let's take a closer look at all four steps.

GRAVITY MANEUVER

First meeting

I first got acquainted with the gravitational maneuver in the 9th grade at the regional Olympiad in physics. The task was this.
A rocket is launched from the Earth at a speed V (sufficient to fly out of the field of gravity). The rocket has an engine with thrust F, which can operate for a time t. At what point in time must the engine be turned on so that the final speed of the rocket is maximum? Ignore air resistance.

At first it seemed to me that it did not matter when to turn on the engine. After all, 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. we turn on the engine at the beginning, 2. we turn on the engine after leaving the Earth's gravity field. Then compare the results and make sure that the final speed of the rocket is the same in both cases. But then I remembered that power is equal to: traction force times 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 maximum. So, the correct answer is: we turn on the engine immediately, then the final speed of the rocket will be maximum.

And although I solved the problem correctly, but the problem remained. The final speed, and, therefore, the energy of the rocket DEPENDS on at what point in time 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.

Rocket thrust DEPENDS on its speed. This is an important point and worth discussing.
Suppose we have a rocket of mass M with an engine that creates thrust with force F. Let's place this rocket in empty space (away from stars and planets) and turn on the engine. How fast will the rocket move? We know the answer from Newton's Second Law: the acceleration A is equal to:
A = F/M

Now let's move on to another inertial frame of reference, in which the rocket moves at a high speed, say, 100 km/sec. What is the acceleration of the rocket in this frame of reference?
Acceleration DOES NOT DEPEND on the choice of inertial frame of reference, 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), so the thrust force F will be the SAME.
And, therefore, the power of the rocket DEPENDS on its speed. After all, power equals force times speed. It turns out that if a rocket is moving at a speed of 100 km / s, then the power of its engine is 100 times more powerful than EXACTLY THE SAME engine located 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 look into this issue.
A rocket always moves on jet thrust: it throws various gases into space at high speed. For definiteness, we assume that the speed of the emission of gases is 10 km/sec. If a rocket is moving at a speed of 1 km/sec, then its engine accelerates mainly not the rocket, but the propellant. Therefore, the engine power 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 be at rest relative to the external observer, that is, the entire engine power will be spent on rocket acceleration. 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/sec. That is, the speed of the fuel WILL DECREASE from 100 to 90 km/s. And the ALL difference in the kinetic energy of the fuel, due to 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, a fast-moving rocket has a lot of kinetic energy in its propellant. 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.

An attempt at practical application

Suppose, in the not too distant future, you are going to fly a rocket into the Saturn system to Titan (see photos 1-3) to study anaerobic life forms. They 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 bay, and almost all the fuel was lost. What to do?

The rocket has an engine and a small amount of fuel left. But the maximum that the engine is capable of is to increase the speed of the rocket by 1 km / s. This is clearly not enough to fly to Saturn. And now the pilot offers such an option.
“We enter the field of attraction of Jupiter and fall on it. As a result, Jupiter accelerates the rocket to a tremendous speed - about 60 km / s. When the rocket accelerates to this speed, turn on the engine. Engine power at this speed will increase many times. Then we take off from the field of attraction of Jupiter. As a result of such a gravitational maneuver, the speed of the rocket increases not by 1 km / s, 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 Jupiter's field of attraction, we will lose all this additional energy. The energy must remain in the potential well of Jupiter, otherwise there will be something like a perpetual motion machine, and this is impossible. Therefore, there will be no benefit from the gravitational maneuver. We're just wasting our time."

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's speed by only 1 km/sec. To increase the efficiency of the engine, it is proposed to perform a gravitational maneuver: "drop" the rocket on Jupiter. She will move in his field of attraction along a parabola (see photo). And at the lowest point of the trajectory (marked with a red cross in the photo) will turn on l engine. The speed of the rocket near Jupiter will be 60 km/sec. After the engine further accelerates it, the speed of the rocket will increase to 61 km / s. What speed will the rocket have when it leaves Jupiter's field of gravity?

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 remember the formula for the potential energy in the gravitational field of the ball. Look in the reference book, what is the gravitational constant, 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 some formulas, so I will try, without straining you with any equations, to explain the solution of this problem “on the fingers”. Hope it works! :) .

If the rocket is stationary, its kinetic energy is zero. And if the rocket moves at a speed of 1 km / s, then we will assume that its energy is 1 unit. Accordingly, if the rocket moves at a speed of 2 km / s, then its energy is 4 units, if 10 km / s, then 100 units, etc. This is clear. We have already solved half of the problem.
At the point marked with a cross (see photo), the speed of the rocket is 60 km / s, and the energy is 3600 units. 3600 units is enough to fly out of Jupiter's field of gravity. After the rocket accelerated, its speed became 61 km / s, and the energy, respectively, 61 squared (we take the calculator) 3721 units. When a rocket flies out of Jupiter's field of gravity, it only consumes 3600 units. There are 121 units left. This corresponds to a speed (take the square root) of 11 km/sec. Problem solved. This is not an approximation, but an EXACT answer.

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

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

Vector rotation

Suppose we are flying a rocket near Jupiter and we want to increase its speed. But we don't have fuel. Let's just say we have some fuel to correct our course. But it is clearly not enough to noticeably disperse the rocket. Can we noticeably increase the speed of a rocket using gravity assist?
In its most general form, this task looks like this. We fly into Jupiter's gravitational field 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, stationary relative to its center of mass), our maneuver looks like this. 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 rocket trajectory is curved and, as is known, in its most general form is a hyperbole. The maximum speed of the rocket will be at the minimum approach. The main thing here is not to crash into Jupiter, but to fly next to it. After the minimum approach, the rocket will begin to move away from Jupiter, and its speed will decrease. Finally, the rocket will fly out of Jupiter's field of gravity. What will her speed be? Exactly the same as it was on arrival. The rocket flew into the gravitational field of Jupiter at a speed V and flew out of it at exactly the same speed V. Has anything changed? No has changed. The DIRECTION of speed has changed. It is important. Thanks to this, we can perform a gravitational maneuver.

Indeed, what is important for us is not the speed of the rocket relative to Jupiter, but its speed relative to the Sun. This is the so-called heliocentric velocity. With such a speed, the rocket moves through the solar system. Jupiter also moves around the solar system. The rocket's heliocentric velocity vector can be decomposed into the sum of two vectors: Jupiter's orbital velocity (about 13 km/sec) and the rocket's velocity RELATIVE to Jupiter. There is nothing complicated here! This is the usual triangle rule for vector addition, which is taught in 7th grade. And this rule is ENOUGH to understand the essence of the gravity maneuver.

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

The green arrow AO is the speed of Jupiter in its orbit. The red arrow AB is U(1): the speed of our rocket relative to the Sun BEFORE the gravity assist. The yellow arrow OB 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 OB radius. 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: U(2) rocket speed AFTER the gravity assist.

See how simple it is. The speed of the rocket AFTER the gravity assist AC is equal to the speed of the rocket BEFORE the gravity assist AB plus the vector BC. And the BC vector is a CHANGE in the speed of the rocket in Jupiter's frame of reference. Because OS - OB = OS + IN = IN + OS = BC. The more the rocket's velocity vector rotates 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 rocket's velocity relative to Jupiter still changes. And the vector of this change is simply added to the velocity vector of the rocket BEFORE the maneuver. I hope I explained everything clearly.

To better understand the essence of the gravitational maneuver, we will analyze it using the example of Voyager 2, which flew near Jupiter on July 9, 1979. As can be seen from the graph (see photo), he flew up to Jupiter at a speed of 10 km / s, and flew out of his gravitational field at a speed of 20 km / s. Only two numbers: 10 and 20.
You will be surprised how much information can be extracted from these numbers:
1. We will calculate what speed Voyager 2 had when it left the Earth's gravitational field.
2. Let's find the angle at which the apparatus approached Jupiter's orbit.
3. Calculate the minimum distance that Voyager 2 flew to Jupiter.
4. Let's find out what its trajectory looked like relative to an observer located on Jupiter.
5. Find the angle by which the spacecraft deviated after the encounter with Jupiter.

We will not use complex formulas, but will do the calculations, as usual, “on the fingers”, sometimes using simple drawings. However, the answers we get will be accurate. Let's just say they might not be exact, because the numbers 10 and 20 are most likely not exact. They are taken from the chart and rounded. In addition, other numbers that we will use will also be rounded. After all, it is important for us to understand the gravitational maneuver. Therefore, we will take the numbers 10 and 20 as exact, so that there is something to build on.

Let's solve the 1st problem.
Let's agree that the energy of Voyager-2 moving at a speed of 1 km/sec is 1 unit. The minimum departure speed from the solar system from the orbit of Jupiter is 18 km/sec. The graph of this speed is in the photo, but it is located like this. It is necessary to multiply the orbital speed of Jupiter (about 13 km / s) by the root of two. If Voyager 2, when approaching Jupiter, had a speed of 18 km / s (energy 324 units), then its total energy (the sum of kinetic and potential) in the gravitational field of the Sun would be EXACTLY equal to zero. But the speed of Voyager 2 was only 10 km / s, and the energy was 100 units. That is, less than:
324-100 = 224 units.
This lack of energy is CONTAINED as Voyager 2 travels from Earth to Jupiter.
The minimum departure speed from the solar system from the Earth's orbit is approximately 42 km / s (slightly more). To find it, you need to multiply the orbital speed of the Earth (about 30 km / s) by the root of two. If Voyager 2 were moving away from Earth at a speed of 42 km/sec, its kinetic energy would be 1764 units (42 squared) and the total would be ZERO. As we have already found out, the energy of Voyager 2 was less than 224 units, that is, 1764 - 224 = 1540 units. We take the root of this number and find the speed with which Voyager 2 flew out of the Earth's gravity field: 39.3 km / s.

When a spacecraft is launched from the Earth into the outer part of the solar system, then it is launched, as a rule, along the orbital velocity of the Earth. In this case, the speed of the Earth's movement is ADDED to the speed of the apparatus, which leads to a huge gain in energy.

And how is the issue with the DIRECTION of speed solved? Very simple. They wait until the Earth reaches the desired part of its orbit so that the direction of its speed is the one that is needed. Say, when launching a rocket to Mars, there is a small “window” in time in which it is very convenient to launch. If, for some reason, the launch failed, then the next attempt, you can be sure, will not be earlier than two years later.

When at the end of the 70s of the last century the giant planets lined up in a certain order, many scientists - specialists in celestial mechanics suggested taking advantage of a happy accident in the location of these planets. A project was proposed on how to carry out the Grand Tour at minimal cost - a trip to ALL the giant planets at once. Which was done with success.
If we had unlimited resources and fuel, we could fly wherever we want, whenever we want. But since energy has to be saved, scientists carry out only energy-efficient flights. You can be sure that Voyager 2 was launched along the direction of the Earth's motion.
As we calculated earlier, its speed relative to the Sun was 39.3 km/sec. When Voyager 2 flew to Jupiter, its speed dropped to 10 km / s. Where was she sent?
The projection of this velocity onto Jupiter's orbital velocity can be found from the law of conservation of angular momentum. The radius of Jupiter's orbit is 5.2 times that of the Earth's orbit. So, you need to divide 39.3 km / s by 5.2. We get 7.5 km / s. That is, the cosine of the angle we need is 7.5 km / s (Voyager velocity projection) divided by 10 km / s (Voyager velocity), we get 0.75. The angle itself is 41 degrees. At this angle, Voyager 2 flew into the orbit of Jupiter.

Knowing the speed of Voyager 2 and the direction of its movement, we can draw a geometric diagram of the gravity assist. It is done like this. We select point A and draw from it the vector of Jupiter's orbital velocity (13 km / s on the selected scale). The end of this vector (green arrow) is denoted by the letter O (see photo 1). Then from point A we draw the velocity vector of Voyager 2 (10 km / s on the selected scale) at an angle of 41 degrees. The end of this vector (red arrow) is denoted by the letter B.
Now we build a circle (yellow color) with a center at point O and radius |OB| (see photo 2). The end of the velocity vector both before and after the gravitational maneuver can lie only on this circle. Now we draw a circle with a radius of 20 km/sec (in the chosen scale) centered at point A. This is Voyager's speed after the gravity assist. It intersects with the yellow circle at some point C.

We have drawn the gravity assist that Voyager 2 performed on July 9, 1979. AO is Jupiter's orbital velocity vector. AB is the velocity vector at which Voyager 2 approached Jupiter. Angle OAB is 41 degrees. AC is the velocity vector of Voyager 2 AFTER the gravity assist. It can be seen from the drawing that the angle OAC is approximately 20 degrees (half the angle OAB). If desired, this angle can be calculated exactly, since all the triangles in the drawing are given.
OB is the velocity vector at which Voyager 2 was approaching Jupiter, FROM THE POINT OF VIEW of an observer on Jupiter. OS - Voyager's velocity vector after the maneuver relative to the observer on Jupiter.

If Jupiter were not rotating and you were in the subsolar side (the Sun is at its zenith), then you would see Voyager 2 moving from West to East. First, it appeared in the western part of the sky, then, approaching, reached the Zenith, flying near the Sun, and then disappeared behind the horizon in the East. Its velocity vector has turned, as can be seen from the drawing, by about 90 degrees (angle alpha).

The Voyager spacecraft is the furthest man-made object from Earth. It has been rushing through space for 40 years, having long fulfilled its main goal - the study of Jupiter and Saturn. Photos of distant planets of the solar system, the famousPale blue dotand "Family Photo", a golden disc with information about the Earth - all these are glorious pages in the history of Voyager and world astronautics. But today we will not sing hymns to the famous device, but we will analyze one of the technologies, without which the forty-year flight simply would not have taken place. Meet: His Majesty the gravity maneuver.

The gravitational interaction, the least understood of the four available, sets the tone for all astronautics. One of the main expense items during the launch of a spacecraft is the cost of the forces that are needed to overcome the Earth's gravitational field. And every gram of payload on a spacecraft is extra fuel in a rocket. It turns out a paradox: to take more, you need more fuel, which also weighs. That is, to increase the mass, you need to increase the mass. Of course, this is a very generalized picture. In reality, accurate calculations allow you to take the necessary load and increase it as necessary. But gravity, as Sheldon Cooper said, is still a heartless, ahem, bitch.

As is often the case, in any phenomenon lies a dual nature. The same is true in relation to gravity and astronautics. Man managed to use the gravitational pull of the planets to the benefit of his space flights, and due to this, Voyager has been plowing interstellar space for forty years without spending fuel.

It is not known who first came up with the idea of ​​a gravitational maneuver. If you think about it, you can reach the first astronomers of Egypt and Babylon, who, on starry southern nights, watched how comets change their trajectory and speed, passing by the planets.

The first formalized idea of ​​a gravitational maneuver came from the lips of Friedrich Arturovich Zander and Yuri Vasilyevich Kondratyuk in the 1920s and 30s, in the era of theoretical cosmonautics. Yuri Vasilyevich Kondratyuk (real name - Alexander Ivanovich Shargey) - an outstanding Soviet engineer and scientist who, independently of Tsiolkovsky, himself created the schemes of an oxygen-hydrogen rocket, proposed using the planet's atmosphere for braking, developed a project for a descent vehicle for landing on a celestial body , which was subsequently used by NASA for the lunar mission. Friedrich Zander is one of those people who stood at the origins of Russian astronautics. He was, and for some years chaired, the GIRD - Rocket Propulsion Research Group, a community of enthusiastic engineers who built the first liquid-propellant rocket prototypes. In the complete absence of any material interest, GIRD was sometimes jokingly deciphered as a Group of Engineers Working for Nothing.

Yuri Vasilievich Kondratyuk
Source: wikimedia.org

About fifty years passed between the proposals made by Kondratyuk and Zander and the practical implementation of the gravity maneuver. It is not possible to accurately establish the first apparatus accelerated by gravity - the Americans claim that this is Mariner 10 in 1974. We say that it was Luna 3 in the year 1959. This is a matter of history, but what exactly is a gravity maneuver?

The essence of the gravitational maneuver

Imagine an ordinary carousel in the yard of an ordinary house. Then mentally spin it up to a speed of x kilometers per hour. Then take a rubber ball in your hand and throw it into the spinning carousel at a speed of y kilometers per hour. Just take care of your head! And what will we get as a result?

It is important to understand here that the total speed will not be determined absolutely, but relative to the observation point. From the carousel, and from your position, the ball will bounce off the carousel at a speed x + y - the total for the carousel and the ball. Thus, the carousel transfers part of its kinetic energy (more precisely, momentum) to the ball, thereby accelerating it. Moreover, the amount of energy lost from the carousel is equal to the amount of energy transferred to the ball. But due to the fact that the carousel is large and cast iron, and the ball is small and rubber, the ball flies at high speed to the side, and the carousel only slows down a little.

Now let's transfer the situation to space. Imagine a normal Jupiter in a normal solar system. Then mentally spin it ... although, stop, this is not necessary. Just imagine Jupiter. A spacecraft flies past him and, under the influence of the giant, changes its trajectory and speed. This change can be described as a hyperbola - the speed first increases as you approach, and then decreases as you move away. From the point of view of a potential inhabitant of Jupiter, our spacecraft returned to its original speed by simply changing direction. But we know that the planets revolve around the Sun, and even at high speed. Jupiter, for example, at a speed of 13 km/s. And when the device flies by, Jupiter catches it with its gravity and drags it along, throwing it forward at a greater speed than it was before! This is if you fly behind the planet relative to the direction of its movement around the Sun. If you fly in front of it, then the speed, respectively, will fall.

gravity maneuver. Source: wikimedia.org

Such a scheme is reminiscent of throwing stones from a sling. Therefore, another name for the maneuver is "gravity sling". The greater the speed of the planet and its mass, the more you can accelerate or slow down on its gravitational field. There is also a little trick - the so-called Orbet effect.

Named after Hermann Orbet, this effect can be described in the most general terms as follows: a jet engine moving at high speed does more useful work than the same one moving slowly. That is, the spacecraft's engine will be most efficient at the "lowest" point of the trajectory, where gravity will pull it the most. Turned on at this moment, it will receive a much greater impulse from the burned fuel than it would receive away from gravitating bodies.

Putting all this into a single picture, we can get a very good acceleration. Jupiter, for example, with its own speed of 13 km / s, can theoretically accelerate the ship by 42.7 km / s, Saturn - by 25 km / s, smaller planets, Earth and Venus - by 7-8 km / s. Here the imagination immediately turns on: what will happen if we launch a theoretical fireproof apparatus towards the Sun and accelerate away from it? Indeed, this is possible, since the Sun revolves around the center of mass. But let's think more broadly - what will happen if we fly past a neutron star, as McConaughey's hero flew past Gargantua (a black hole) in Interstellar? There will be an acceleration of about 1/3 of the speed of light. So if we had a suitable ship and a neutron star at our disposal, then such a catapult could launch a ship to the Proxima Centauri region in just 12 years. But this is still only a wild fantasy.

Voyager maneuvers

When I said at the beginning of the article that we would not sing hymns to Voyager, I was lying. The fastest and most distant apparatus of mankind, which is also celebrating 40 years this year, you see, is worthy of mention.

The very idea of ​​going to distant planets was made possible by gravitational maneuvers. It would be unfair not to mention then-UCLA graduate student Michael Minovich, who calculated the effects of a gravitational sling and convinced professors at the Jet Propulsion Laboratory that even with the technology available in the 60s, it was possible to fly to distant planets.

Photograph of Jupiter taken by Voyager

Gravity maneuver to accelerate an object Gravity maneuver to slow down an object Gravity maneuver to accelerate, decelerate or change the direction of the flight of a spacecraft, under the influence of gravitational fields of celestial bodies ... ... Wikipedia

Gravity maneuver to accelerate an object Gravity maneuver to slow down an object Gravity maneuver to accelerate, decelerate or change the direction of the flight of a spacecraft, under the influence of gravitational fields of celestial bodies ... ... Wikipedia

- ... Wikipedia

This is one of the main geometric parameters of objects formed by means of 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 inclusion ... ... Wikipedia

A branch of celestial mechanics that studies the movement of artificial space bodies: artificial satellites, interplanetary stations and other spacecraft. The scope of tasks of astrodynamics includes the calculation of the orbits of spacecraft, the determination of parameters ... ... Wikipedia

The Oberth effect in astronautics is the effect that a rocket engine moving at high speed produces more usable energy than the same engine moving slowly. The Oberth effect is caused by the fact that when ... ... Wikipedia

Customer ... Wikipedia

And the equipotential surfaces of a system of two bodies Lagrange points, libration points (lat. librātiō rocking) or L points ... Wikipedia

Books

• Things of the twentieth century in drawings and photographs. Forward into space! Discoveries and achievements. Set of 2 books, . "Forward, into space! Discoveries and achievements" 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 ...
• Onward to space! Discoveries and achievements, Klimentov Vyacheslav Lvovich, Sigorskaya Yulia Alexandrovna. 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 ...

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 makes them maneuver around a neighboring planet in order to use the "sling effect" to further disperse the device. This is how NASA saves valuable rocket fuel. This is how the Voyager 2 spacecraft managed to fly to Neptune, whose orbit lies at the very edge of the solar system.

Freeman Dyson, a physicist at Princeton, made an interesting suggestion. If someday in the distant future, mankind manages to detect in space two neutron stars revolving around a common center at high speed, then an Earth ship, flying very close to one of these stars, can, due to a gravitational maneuver, pick up a speed equal to almost a third the speed of light. As a result, the ship would accelerate to near-light speeds due to gravity. Theoretically, this could happen.

Only 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 the descent and slowing on the ascent, ends up at the top at exactly the same speed as at the very beginning - there is no increase in energy. Similarly, wrapping around the stationary Sun , we will finish at exactly the same speed as we started the maneuver.) The Dyson method with two neutron stars could in principle work, but only because neutron stars move fast. A spacecraft using a gravitational maneuver receives an increase in energy due to the movement of a planet or star. If they are motionless, such a maneuver will not work.

And Dyson's suggestion, while it might work, won't help today's scientists on Earth, because visiting fast-rotating neutron stars would first require building a starship.

From the gun to the sky

Another ingenious way to launch a ship into space and accelerate it to fantastic speeds is to shoot it from a rail electromagnetic “gun”, which Arthur C. Clarke and other science fiction authors described in their works. This project is currently being seriously considered as a possible part of the Star Wars missile shield.

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

At its simplest, a rail gun is two parallel wires or rails; the rocket projectile, or missile, "sits" on both rails, forming a U-shaped configuration. 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 an electric current of millions of amperes is passed through the rails and the projectile, 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 tests, rail-mounted electromagnetic guns successfully fired metal objects at tremendous speeds, accelerating them over a very short distance. Remarkably, in theory, an ordinary rail gun is capable of firing a metal projectile at a speed of 8 km / s; this is enough to put it into low Earth orbit. In principle, the entire NASA rocket fleet could be replaced by rail guns, which would fire a payload into orbit directly from the surface of the Earth.

The railgun has significant advantages over chemical guns and rockets. 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 shock wave. Jules Berne in the classic novel "From the Earth to the Moon" shot a projectile with astronauts to the Moon using 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 needed to fly to the Moon . The railgun, on the other hand, 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 railgun has its own problems. Objects on it are accelerating so fast that they tend to be flattened due to collision... with air. The payload is severely deformed when the railgun is fired from the muzzle, 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 greatly deforming the load. The rails must be replaced regularly, as the projectile also deforms them when moving. Moreover, overloads in a rail gun are fatal to humans; human bones simply can not withstand such acceleration and collapse.

One solution is to put a railgun on the Moon. There, outside 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 during acceleration will experience enormous overloads that can damage and deform the payload. In a sense, a railgun is the antithesis of a laser sail, which picks up speed gradually over time. The limitations of the 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 railgun capable of firing a craft at the nearest stars would be a very expensive construction. Thus, one of the projects provides for the construction in open space of a rail gun with a length of two-thirds of the distance from the Earth to the Sun. This gun would have to store solar energy and then expend it all 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 robot ships will be able to “survive” such a launch.