Interstellar ships on gravitational springs (fantastic project)

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Even the closest stars are very far away. There is still a long way to go to other galaxies. From the Andromeda galaxy, light takes about a million years to reach us.

Is it conceivable to get there in, say, a week? According to Earth time, it does not add up to Andromeda so soon. The light goes on for years and years. But the ship cannot move faster than light. Another thing is the time of the interstellar traveler himself, if his ship flies at a sufficiently high speed. When moving at high speeds, all processes are replaced by the same number of times. The higher the speed, the greater the replacement.

How should we fly if we want to travel to the Andromeda Nebula in a week? A distance of 10⁶ light years must be covered in $\frac{1}{52}$ years. Calculations using the formula of the relative theory result: it is necessary to fly with constant acceleration $a=700\text{ g}$! (g is the acceleration of free fall).

But what about overloads? With an acceleration of 700 g, our weight will increase 700 times! It’s like driving over a starlet with an asphalt roller. Our blood also becomes 700 times thicker. And it must circulate throughout the body. The heart cannot cope with such a significant load. Pilots sometimes go blind during sharp turns - the blood does not rise to the brain, although here the acceleration $a$ does not exceed $5\div 10\text{ g}$. You can lie down to reduce the load on the heart - then you need to raise the blood to a lower height. But even a tenfold overload in this position can only be withstood for three to five minutes.

Is it possible to come up with a better way that allows you to move at any acceleration without any overload?

Is it possible to propose a design for a ship depicting an astronaut under any kind of overload?

Before rushing at an enemy, it is useful to study it.

Where does the weight come from?

If you stand up the external scale, the needle will deviate from the zero position. The earth attracts the body, and since we are motionless relative to the scales, this force must be balanced by the elastic force of the arms. The arrow will show us the weight $P=mg(m-\text{ масса})$. Let us change the weight (readings of external scales) in an elevator rising with acceleration. The arrow will show $m(a+g)$, a re-

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load: elastic force not only balances the Earth’s gravity, but also gives the body acceleration $a$. If the elevator falls freely, then the weight will be zero - all bodies fall with the same acceleration, our movement will be exactly the same as the movement of the spring, and the spring will not be aware of it. Taking an apple, we will not feel its weight; it does not press on our hand, but falls freely along with our hand.

So, the weight $P=m(a+g)$, if $a$ is directed in the same direction as the acceleration of free fall $g$ and $|a|=|g|$ (free fall), a state of weightlessness occurs. This condition is experienced by astronauts when flying with their engines turned off, or when they are moving with the acceleration of gravity.

It is important that weight is due to both acceleration and gravitational attraction. It became possible to compensate one thing for another. It is possible to create weightlessness because the acceleration of gravity does not depend on either the mass or the substance of the falling bodies. This property was discovered by Galileo. But even now, researchers sometimes cannot resist the temptation to test this property. In 1964, Roll, Krotkov and Dicke established the equality of acceleration for gold and aluminum with an accuracy of 0.00000000001!

We will meet weightlessness in the cabin of a free-fall elevator. There are no overloads. Let us take a massive body created by the acceleration of gravity $a$, equal in magnitude to the desired acceleration of travel. Let’s install an engine on it that can provide just this acceleration. The traveler is accommodated with all comforts in a separate cabin, freely falling onto this body. The cabin falls with acceleration $a$, but the engine is running and the body leaves with the same acceleration.

At zero initial speed, the distance between the cabin and the massive body will remain unchanged. In a freely falling cabin there is weightlessness, but at the same time it rushes with the necessary acceleration.

But before the halfway point, you need to start slowing down. The coordination of the acceleration of the body and the free fall acceleration of the cabin will be disrupted, and the cabin will crash into a massive body. In addition, there is a danger of standing up or falling on the body with any change in the acceleration of the ship (massive body). This means that we need to better think through the design of the ship.

Let’s drill a shaft in the direction of acceleration through the center of a massive body, which has been shaped into a ball. The acceleration of gravity will vary depending on the distance to the center of the ball. Let us denote the acceleration on the surface of the ball by $a_0$ and the radius of the ball by $r_0$. Let’s plot the acceleration $a$ at a distance $r$ from the center of the ball (see figure *).

At distances from $-r_0$ to $r_0$ (that is, inside the ball), the acceleration of gravity changes according to the law $a=a_0 \frac{r}{r_0}$, and at $r<-r_0$ and $r>r_0$

*) This problem is discussed in detail in the article by Ya. A. Smorodinsky “Similar movements”. The dependence of the force of attraction of a body on the distance to the center of the ball was found with the solution problem F43 («Kvant» No. 5, 1971).