Earth Escape Plan: A Brief Guide for Out of Orbit

2024 Author: Seth Attwood | [email protected]. Last modified: 2023-12-16 15:55

Recently on Habré there was news about the planned construction of a space elevator. For many, it seemed like something fantastic and incredible, like a huge ring from Halo or a Dyson sphere. But the future is closer than it seems, a stairway to heaven 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 an Earth-Moon ticket at the price of a Moscow-Peter ticket, how the elevator will help us and what it will hold onto so as not to collapse to the ground.

From the very beginning of the development of rocketry, fuel was a headache for engineers. Even in the most advanced rockets, fuel occupies about 98% of the ship's mass.

If we want to give the astronauts on the ISS a bag of gingerbread weighing 1 kilogram, then this will require, roughly speaking, 100 kilograms of rocket fuel. The launch vehicle is disposable and will return to Earth only in the form of burnt debris. Expensive gingerbreads are obtained. The mass of the ship is limited, which means that the payload for one launch is strictly limited. And every launch comes at a cost.

What if we want to fly somewhere beyond the near-earth orbit?

Engineers from all over the world sat down and began to think: what should a spaceship be like in order to take more on it and fly on it further?

Where will the rocket fly?

While the engineers were thinking, their children found saltpeter and cardboard somewhere and started making toy rockets. Such missiles did not reach the roofs of high-rise buildings, but the children were happy. Then the smartest thought came to mind: "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 couldn't even get up into the air. After some experimentation, the children found the optimal amount of saltpeter at which the rocket flies the highest. If you add more fuel, the mass of the rocket pulls it down. If less - fuel ends earlier.

The engineers also quickly realized that if we want to add more fuel, then the traction force must also be greater. There are few options to increase the flight range:

• increase engine efficiency so that fuel losses are minimal (Laval nozzle)
• increase the specific impulse of the fuel so that the thrust force is greater for the same fuel mass

Although engineers are constantly moving forward, almost the entire mass of the ship is taken up by fuel. Since besides fuel, you want to send something useful into space, the entire path of the rocket is carefully calculated, and the very minimum is put into the rocket. At the same time, they actively use the gravitational help of celestial bodies and centrifugal forces. After completing the mission, the astronauts do not say: "Guys, there is still a little fuel 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, but fly to Mars?

Second space speed

The children also tried to make the rocket fly higher. They even got hold of a textbook on aerodynamics, read about the Navier-Stokes equations, but did not understand anything and simply attached a sharp nose to the rocket.

Their familiar old man 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 a skyscraper, or even to the very top of a mountain.

- It doesn't matter, Kostya-ibn-Eduard, - Hottabych answered, pulling out the last hair, - let this rocket never run out of fuel.

The joyful children launched a rocket and waited for it to return to earth. The rocket flew both to the skyscraper and to the top of the mountain, but did not stop and flew further until it disappeared from sight. If you look into the future, then 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 wondered how their little rocket could fly so far. After all, at school they said that in order not to fall back to Earth, the speed should be no less than the second cosmic speed (11, 2 km / s). Could their small rocket reach that speed?

But their engineering parents explained that if a rocket has an infinite supply of fuel, then it can fly anywhere if the thrust is greater than gravitational forces and friction forces. Since the rocket is capable of taking off, the thrust force is sufficient, and in open space it is even easier.

The second cosmic speed is not the speed that a rocket should have. This is the speed at which the ball must be thrown from the surface of the ground so that it does not return to it. A rocket, unlike a ball, has engines. For her, it is not speed that is important, but the total impulse.

The most difficult thing for a rocket is to overcome the initial section of the path. First, surface gravity is stronger. Secondly, the Earth has a dense atmosphere in which it is very hot to fly at such speeds. And jet rocket engines work worse in it than in a vacuum. Therefore, they fly now on multistage rockets: the first stage quickly consumes its fuel and is separated, and the lightweight ship flies on other engines.

Konstantin Tsiolkovsky thought about this problem for a long time, and invented the space elevator (back in 1895). Then, of course, they laughed at him. However, they laughed at him because of the rocket, and the satellite, and the orbital stations, and generally considered him out of this world: "We have not yet fully invented cars here, but he is going into space."

Then the scientists thought about it and got into it, a rocket flew, launched a satellite, built orbital stations, in which people were populated. Nobody laughs at Tsiolkovsky anymore; on the contrary, he is greatly respected. And when they discovered super-strong graphene nanotubes, they seriously thought about the "stairway to heaven."

Why don't the satellites fall down?

Everyone knows about centrifugal force. If you quickly twist the ball on the string, it does not fall to the ground. Let's try to spin the ball quickly, and then gradually slow down the rotation speed. At some point, it will stop spinning and fall. This will be the minimum speed at which centrifugal force will counterbalance the earth's gravity. If you spin the ball faster, the rope will stretch more (and at some point it will break).

There is also a "rope" between the Earth and the satellites - gravity. But unlike a regular rope, it cannot be pulled. If you "spin" the satellite faster than necessary, it will "come off" (and go into an elliptical orbit, or even fly away). The closer the satellite is to the surface of the earth, the faster it needs to be "turned". The ball on a short rope also spins faster than on a long one.

It is important to remember that the orbital (linear) speed of a satellite is not speed relative to the earth's surface. If it is written that the orbital speed of a satellite is 3.07 km / s, this does not mean that it is hovering over the surface like mad. The orbital speed of points on the equator of the earth, by the way, is 465 m / s (the earth rotates, as the stubborn Galileo claimed).

In fact, for a ball on a string and for a satellite, not linear velocities are calculated, but angular velocities (how many revolutions per second the body makes).

It turns out that if you find an orbit such that the angular velocities of the satellite and the earth's surface coincide, the satellite will hang over one point on the surface. Such an orbit was found, and it is called the geostationary orbit (GSO). The satellites hang motionless over the equator, and people do not have to turn their plates and “catch the signal”.

Bean stem

But what if you lower a rope from such a satellite to the very ground, because it hangs over one point? Attach a 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 you spin it well. Then it will be possible to lift loads along this rope directly into orbit, and forget, like a nightmare, multistage rockets, devouring fuel in kilotons at a low carrying capacity.

The speed of movement in the atmosphere of the cargo will be small, which means that it will not heat up, unlike a rocket. And less energy is required to climb, since there is a fulcrum.

The main problem is the weight of the rope. The geostationary orbit of the Earth is 35 thousand kilometers away. If you stretch a steel line with a diameter of 1 mm to the geostationary orbit, its mass will be 212 tons (and it needs to be pulled much further to balance the lift with centrifugal force). At the same time, it must withstand its own weight, and the weight of the load.

Fortunately, in this case, something helps a little, for which physics teachers often scold students: weight and weight are different things. The further the cable stretches from the surface of the earth, the more it loses in weight. Although the strength-to-weight ratio of the rope should still be enormous.

With carbon nanotubes, engineers have hope. Now this is a new technology, and we cannot yet twist these tubes into a long rope. And it is not possible to achieve their maximum design strength. But who knows what will happen next?