What is the maximum speed a rocket can reach?

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This is one of the fairly frequently asked questions. Sometimes they ask if it is possible to accelerate a rocket to the speed of light and the like. In this article, I will answer this question in detail.

The problem with the rocket as a mode of travel is that the rocket must carry all of its fuel with it. Moreover, what fuel will be spent not only on accelerating the spacecraft itself, but also on accelerating the fuel itself. Those. if we want to take an additional ton of fuel, then in reality we will need to take more — since this ton will also need to be carried with us.

All this is described by the rocket equation, which was derived by Konstantin Tsiolkovsky.

Where Δ

The maximum specific impulse of modern rocket engines is approximately 5000 m / s. Let us take the mass of the rocket’s payload as 15,000 kilograms. That is how much the lunar module weighed:

Thus, the total mass of the spacecraft at launch is

For warm-up, let’s calculate the speed that can be achieved if the mass of the fuel is equal to the mass of the payload, i.e.

It is easy to make sure that in this case it will be possible to achieve a speed of only 3465.74 m / s.

Let’s increase the amount of fuel 10 times. Substituting it into the formula and we can easily make sure that with the amount of fuel 150,000 kg the rocket will be able to reach a speed of 11 989.5 — practically the second space speed!

Okay, these are all half measures. Let’s increase the amount of fuel 10,000 times! We substitute the values into the formula and we get: 46 052 m / s.

Let’s add more fuel. Suppose we use all the proven reserves of hydrocarbons on Earth as fuel. Then we have 182 × 10¹² kg of fuel and they give us the speed

If you use the entire mass of the Earth as fuel, you can achieve the speed

Because the specific impulse of rocket engines is very small compared to the speed of light. In order to achieve relativistic speeds, we need motors whose specific impulse will be comparable to the speed of light. A fusion rocket engine, for example, might be a good candidate. According to theoretical calculations, its specific impulse will be approximately in the region of 10-11% of the speed of light.

Another possible option is to use the reaction of annihilation of matter and antimatter and the energy released during this to obtain an impulse. An engine running on antimatter could give a specific impulse in the region of 90-95% of the speed of light.

Another possible way to overcome the limitation of Tsiolkovsky’s rocket formula is to prevent the spacecraft from carrying fuel with it.

For example, it is proposed to accelerate spacecraft with light sails using stationary lasers or to «refuel» the spacecraft with interstellar gas and dust encountered in flight. This approach is used in the currently theoretically developed interstellar ramjet engine Bassard, although in my opinion there are several theoretical problems that can hardly be avoided.