How do we fly away from Earth: a short guide for traveling beyond the orbit

Recently on Habré there was news about the planned construction of a space elevator . For many, this seemed to be something fantastic and incredible, like a huge Halo ring or a Dyson sphere . But the future is closer than it seems, the stairway to the sky is quite possible, and maybe we will even see it in our lifetime.
Now I will try to show why we cannot go and buy the Earth-Moon ticket at the price of the Moscow-Peter ticket, how the elevator will help us and what it will hold so as not to fall to the ground.

From the very beginning of the development of rocket science, the headache of engineers was fuel. Even in the most advanced missiles, fuel takes up about 98% of the ship’s mass.
If we want to transfer to the cosmonauts on the ISS a bag of gingerbreads weighing 1 kilogram , then this will require, roughly speaking, 100 kilograms of rocket fuel . The booster is disposable, and will return to Earth only in the form of burnt debris. Dear get gingerbread. The mass of the ship is limited, and hence the payload per launch is strictly limited. And each launch requires expenses.
And if we want to fly somewhere further Earth orbit?

Engineers from all over the world sat down and began to think: what should a spacecraft be in order to carry more on it and fly further on it?
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Where will the rocket fly to?

While the engineers were thinking, their children found saltpeter and cardboard somewhere and started making toy rockets . Such rockets did not reach the roofs of high-rise buildings, but the children rejoiced. Then the cleverest thought: “let's push more saltpeter into the rocket, and it will fly higher”.
But the rocket did not fly higher, as it became too heavy. She could not even rise into the air. After a number of experiments, the children found the optimal amount of nitrate, in which the rocket flies above everything. If you add more fuel, the mass of the rocket pulls it down. If less - fuel ends earlier.

Engineers also quickly realized that if we want to fill in more fuel, it means that the thrust should be greater. Options to increase the range a bit:

• increase engine efficiency to minimize fuel loss ( Laval nozzle )
• increase the specific impulse of the fuel so that with an equal mass of fuel the thrust force would be greater

Although engineers are constantly moving forward, almost the entire mass of the ship takes fuel. Since, besides the fuel, I want to send something useful to space, the entire path of the rocket is carefully calculated, and the minimum amount of fuel is laid in the rocket. At the same time, they actively use the gravitational help of celestial bodies and centrifugal forces. The astronauts after the completion of the mission do not say: "guys, there is still some fuel left in the tank, let's fly to Venus."

But how to determine how much fuel is needed so that the rocket does not fall into the ocean with an empty tank, and reach Mars?

Second cosmic velocity

The children also tried to make the rocket fly higher. They even got a textbook on aerodynamics, read about the Navier-Stokes equations, but did not understand anything and just attached a sharp nose to the rocket.
Their familiar old Hottabych passed by and asked what the guys were sad about.
- Eh, grandfather, if we had a rocket with infinite fuel and low mass, it would probably have flown to the skyscraper, or even to the very top of the mountain.
“It doesn't matter, Kostya ibn-Edward,” answered Hottabych, pulling out the last hair, “let this rocket never run out of fuel.”
Joyful children launched a rocket and waited for her to return to the ground. The rocket flew up to the skyscraper, and to the top of the mountain, but did not stop and flew further until it disappeared from view. If you look into the future, this rocket left the earth, flew out of the solar system, our galaxy, and flew at sublight speed to conquer the vastness of the universe.

The children were surprised how their little rocket could fly so far. After all, the school said that in order not to fall back to Earth, the speed should be no less than the second space (11.2 km / s). Could their little rocket be able to develop such a speed?
But their parents, engineers, explained that if a rocket has an infinite supply of fuel, then it can fly anywhere, if the thrust force is greater than the gravitational and friction forces. Since the rocket is able to take off, the thrust force is enough, and in open space it is even easier.

The second cosmic velocity is not the velocity that a rocket should have. This is the speed with which you need to throw the ball from the surface of the earth so that it does not return to it. A rocket, unlike a ball, has engines. For her, not speed, but total impulse is important.
The most difficult thing for a rocket is to overcome the initial part of the path. First, the gravity at the surface is stronger. Secondly, the Earth has a dense atmosphere in which it is very hot to fly at such speeds. Yes, and jet rocket engines work in it worse than in a vacuum. Therefore, they are now flying on multi-stage rockets: the first stage quickly consumes its fuel and is separated, while the lighter ship flies on other engines.

Konstantin Tsiolkovsky thought about this problem for a long time, and came up with a space elevator (as far back as 1895). Then, of course, they laughed at him. However, they laughed at him because of the rocket, the satellite, and the orbital stations, and generally considered him not of this world: “we still have cars here not completely invented, but he was going to space”.
Then the scientists thought and penetrated, the rocket flew, launched a satellite, built orbital stations, in which they settled people. Nobody laughs at Tsiolkovsky, on the contrary, he is highly respected. And when the ultra-strong graphene nanotubes were discovered, they seriously thought about the “stairs to the sky”.

Why satellites do not fall down?

Everyone knows about centrifugal force. If you quickly turn the ball on a string, it does not fall to the ground. Let's try to quickly spin the ball, and then gradually slow down the speed of rotation. At some point, it will stop spinning and fall. This will be the minimum speed at which centrifugal force balances the force of gravity of the earth. If you turn the ball faster, the rope will tighten more (and at some point it will burst).
There is also a “rope” between the Earth and the satellites - gravity. But unlike the usual rope, it can not stretch. If the satellite is “turned” faster than necessary, it will “detach” (and go into an elliptical orbit, or fly away altogether). The closer the satellite is to the surface of the earth, the faster it must be “twisted”. The ball on a short rope also turns faster than on a long one.
It is important to remember that the satellite’s orbital (linear) speed is not speed relative to the surface of the earth . If it is written that the satellite's orbital speed is 3.07 km / s, this does not mean that it rushes over the surface like mad. The orbital speed of points at the equator of the earth , by the way, is 465 m / s (the Earth rotates, as claimed by the stubborn Galileo).
In fact, for a ball on a string and for a satellite, it is not linear speeds that are calculated, but angular (how many revolutions per second the body makes).
It turns out that if we find such an orbit that the angular velocities of the satellite and the surface of the earth coincide, then the satellite will hang above one point on the surface. Such an orbit was found, and it is called the geostationary orbit (GSO). Satellites hang over the equator motionless, and people do not have to turn the plates and "catch the signal."

Beanstalk

But what if you pull a rope from such a satellite to the ground, because it hangs over one point? To tie the load to the other end of the satellite, the centrifugal force will increase and will hold both the satellite and the rope. After all, the ball does not fall if it is well unwound. Then it will be possible to lift loads along this rope directly into orbit, and forget, like a nightmare, multistage rockets, which are devouring fuel in kilotons with a small payload.
The speed of movement in the atmosphere at the cargo will be small, it means it will not heat up, unlike a rocket. And energy to lift will need less, since there is a fulcrum.

The main problem is the weight of the rope. To the geostationary orbit of the Earth 35 thousand kilometers . If a steel line with a diameter of 1 mm is reached to a geostationary orbit, its mass will be 212 tons (and it must be pulled much further in order to balance the elevator with centrifugal force). However, it must withstand its weight, and the weight of the load.
Fortunately, in this case it helps a little what the physics teachers often criticize the students for: weight and mass are different things. The further the cable stretches from the ground, the more it loses weight. Although the specific strength of the cable should still be huge.
Engineers had hope with carbon nanotubes. Now this is a new technology, and we cannot yet twist these tubes into a long cable. And it is impossible to achieve their maximum design strength. But who knows what will happen next?