Shulou(Shulou.com)11/24 Report--

If astronauts are on long-term space missions, they need to rotate the spacecraft to produce artificial gravity, but this is not as easy as you might think.

Although it is great for people to live in space, the "weightlessness" environment brings some serious challenges. Human beings are affected by constant gravity on the earth and can exert the best physical performance. However, if long-term exposure to microgravity environment, the human body will be affected by many, including bone loss and muscle atrophy.

Therefore, if human beings want to live in space, they need to create an artificial gravity environment. There is only one way to do this: build a vehicle that moves at a constant acceleration. The most common concept is to build a rotating spacecraft, but this is not as easy as it sounds, and there are many difficulties.

First of all, let's review the basics of gravity and feel the meaning of gravity.

Gravity is the attraction between objects with mass. Because both the human body and the earth have mass, gravity constantly pulls you toward the earth and keeps you on the ground. But even if this force is constantly acting on you, you can't feel it, because the earth is pulling all parts of your body at the same time, making the effect imperceptible.

I know what you're thinking: "when I sit in a chair, of course I can feel the effect of gravity." In fact, what you feel is not gravity, but the force of the chair (and the ground) pushing you up, which we call "apparent weight".

We can get a good understanding of the concept of visual weight by taking the elevator. In a stationary elevator, when you press the up button, the elevator begins to move up. This means that it (at least for a short time) must have an upward acceleration until the elevator reaches its speed. In the process of accelerating upward, you feel a little heavy. Then, once the elevator approaches its intended floor, it must slow down. This means that it accelerates down, and in the meantime, you will feel a little light.

However, your actual weight will not fluctuate. Your true weight measures the force gravity exerts on your body, which is the result of the interaction between your mass (m) and the earth's mass and your distance from the center of the earth. On Earth, gravity exerts a force of 9.8 newtons per kilogram. Mass and weight are different, and on planets with different gravitation, even if the mass is the same, the weight will be different. )

The elevator will change the weight, not your weight or mass. This may seem strange, but this effect is very useful for spacecraft.

Linear acceleration assumes that you are in gravity-free space-or in low-Earth orbit with microgravity (microgravity represents weightlessness). What happens if the spacecraft has a giant elevator that is accelerating upward? If the acceleration of the elevator is the same as the gravity field on the earth's surface, then the gravity you feel is exactly the same as on the earth.

Of course, a spaceship with an infinite elevator is impractical. It would be easier to accelerate the entire spacecraft, which would definitely create artificial gravity. In fact, this is the main way gravity is generated on a spaceship in the science fiction series "the vastness of the Sky" (The Expanse).

But there is a problem here: in order to produce continuous gravity, the spacecraft needs to accelerate continuously, and the engine cannot be turned off, otherwise the acceleration will drop to zero, which requires a lot of fuel. Artificial gravity costs a lot of money (they invented "Epstein drive technology" in the vastness of the sky, which can be seen as magic).

For humans of our time, another method of acceleration will be needed to generate artificial gravity.

The acceleration of circular motion is defined as the rate of change of velocity. If a car accelerates from 10 m / s to 20 m / s in 1 second, the acceleration of the car is 10 m / s. We usually write it as. )

But velocity is actually a vector. This means that speed can indicate not only how fast an object is moving, but also the direction in which it is moving.

Suppose a car is heading west at a speed of 20 m / s, then turning, and a second later it is heading north at a speed of 20 m / s. From the definition of speed, even if the car travels at the same speed, it will have acceleration because it changes direction. If we know the radius (R) and speed (v) of the path the car takes in this turn, we can calculate the acceleration:

You don't really need this math. You can intuitively know that turning is a kind of acceleration, because when you turn, you can feel something pushing you to the side of the car, just like you feel the acceleration in a moving elevator. That's why we can use rotating objects to produce artificial acceleration. You don't need to make a spacecraft or space station go around like a car. Instead, imagine a huge rotating object with people standing in it. It looks like this:

Illustration: RHETT ALLAIN three people standing inside a rotating cylinder. Because they all move in a circular path, each of them feels a bit like the upward acceleration of gravity. For them, the "up" direction is toward the center of the cylinder. It has been proved that the angular velocity (ω) rather than the velocity (v) of spacecraft can be used to describe their motion. Everyone has an acceleration:

Angular velocity (ω) is measured in radians per second. If the value of this acceleration is the same as the gravity field on the earth's surface, then that person will almost feel that he is standing on the earth's surface. We will talk about differences soon. )

The biggest advantage of a rotating spacecraft or space station is that once it starts spinning, it no longer needs to use any rocket fuel to keep it running. Unless affected by an external force, it will continue to rotate. That's why you often see this artificial gravity method in science fiction TV dramas and movies (such as the Martian, Babylon V, 2001: space Odyssey, Interstellar, etc.).

This equation illustrates the importance of designing spaceships. You can make a small vehicle (R is smaller) and spin it very fast (ω is larger), or you can make a large ship with a smaller rotation speed.

If the smallest rotating spacecraft reduces the radius of the rotating spacecraft, it must increase its angular velocity in order to obtain the desired acceleration. (suppose you need to reach, which is 1 g, which means the same acceleration as standing on the surface of the earth. )

But here's the problem again-- this time it's human. Yes, we have some problems in dealing with rotation. Personally, I can't play with any of the rotating equipment in the amusement park, such as the crazy tea party at Disneyland. I feel a little sick just thinking about it. ) according to laboratory tests, most people can tolerate a rotation speed of about 1 rpm per minute. Other data show that an angular velocity of up to 4 rpm is also possible. Another study concluded that through constant rotation training, humans may be able to work at a speed of 26 rpm.

Suppose we have some astronauts who are very good at spinning and can't turn their stomach, and they can put up with a rotation rate of 26 rpm. How small spacecraft do you need to build to produce 1g of artificial gravity?

First of all, we need to convert the angular velocity from revolutions per minute to radians per second to get a value of ω = 2.72 radians per second. (remember: 1 circle equals 2 π radians. )

Next, we only use the acceleration and solve the R (radius), and we will get a circular spacecraft with a radius of 1.3 meters and a diameter of 2.6 meters. This is super small, even smaller than the diameter of the module of the International Space Station (the latter is about 4.2 meters). With a more reasonable angular speed of 4 rpm, the diameter of the spacecraft would be 111.7 meters, or about 112m, the size of a football or football field.

If you don't want to build a 112-meter rotating spaceship, you can use a trick: you can replace a large container with two smaller containers and connect them so that the two smaller parts rotate around a common center of mass. Humans can be in one (or both) of these parts in order to experience artificial gravitational fields. You can see an example of this rotating boat in the movie Stowaway.

Even under such conditions, the gravity difference is different from how you feel on Earth: first, the artificial gravity field above your head may have a different value from the strength of the field under your feet. To understand why this happens, let's imagine a person standing in a fairly small rotating spacecraft.

Illustration: RHETT ALLAIN because people are in a rotating space, their heads and feet have the same angular velocity (ω). However, they do not move in circles of the same size. The head is closer to the center of the rotating aircraft than the foot, so the circular path radius of the head () is smaller than that of the foot (). Keep in mind that the acceleration value (that is, artificial gravity) decreases as the radius of motion decreases, so it feels a bit strange that the head is subjected to a smaller gravity field than the foot.

The actual situation may be even worse. Imagine that ultra-small spaceship with a radius of only 1.3 meters. This is smaller than the average person's height-the astronaut's head will exceed the center of rotation. In this case, their heads will be pulled to one side of the ship (we call it the ceiling) and their feet will be pulled to the other side, which we can call the floor. Even if high-speed rotation is not enough to make astronauts sick, this gravity difference will affect astronauts.

This "gravity difference" is not a big problem for larger rotating spacecraft. Let's consider an example of a rotating aircraft with a diameter of 112 meters. It has a radius of 55.8m and an angular velocity of 4 rpm. The gravity field at the floor is the same as on Earth. If the astronauts are 1.75 meters tall, their heads will move within a circular radius of 54.1 meters. This means that at their heads, the gravitational field will be zero. It's only 3.2% less than the field under their feet-so it's no big deal.

There is another force in the rotating vehicle called the Coriolis force. This force is a bit complicated, so let's start with an example of using a merry-go-round. Suppose there are two people (labeled An and B) standing on the merry-go-round, one at the edge and one near the middle. The top view is as follows:

Illustration: RHETT ALLAIN notice that both people are moving around the circular path at the same angular speed. However, B must travel farther in the same circle time as A, which means that B has a greater linear velocity (v) than A.

It's no big deal unless B decides to move toward the center of the circle. By moving to a new circular path with a smaller radius, B must accelerate to a new orbit, and this additional acceleration is called the Coriolis force.

If a ball rolls from B to A, it moves along the curved path, as follows:

Illustration: the magnitude of the RHETT ALLAIN Coriolis force depends on the speed of the moving object (relative to the rotating object) and the angular velocity of the merry-go-round. The same thing will happen to spacecraft.

The calculation of Coriolis force involves many factors, which is complicated. Here, it is written as an equation:

It is important to note that the force is always perpendicular to the velocity and is zero if the body is at rest in the rotating coordinate system.

What effect will this have on the astronauts in the rotating spacecraft? If the man had just sat still, nothing would have happened. But what if they stand up? In the process of standing up, they will have a speed toward the center of the circle, because the center of mass moves upward from sitting to standing.

Relative to their speed, the Coriolis force pushes them sideways. Depending on the direction of the chairs, this force may push them in different directions. If the chair rotates in the same direction as the spacecraft, the Coriolis force pushes it forward when the person stands up. If the chairs are facing back, it will push them back. If the chairs face to one side, they are pushed to the other side. And not just stand up, if you move your hand, there will be a lateral force acting on it. If you try to pour the drink into the glass, there will always be a lateral force on the liquid. Maybe you can adapt to the lateral force of every action, but it's always very uncomfortable.

Is there anything you can do about the Coriolis force? Yes, you can minimize this lateral thrust by designing a spacecraft with a lower angular velocity, which means it takes longer to complete a rotation. It also means less artificial gravity.

If you want your spaceship to have artificial gravity that simulates the Earth and a smaller Coriolis effect, you only need a bigger spaceship. It's a tough choice: you can build a small, cheap spaceship to withstand the annoying Coriolis force, or you can build a large, expensive spaceship that will make you feel at home-but it will be big and expensive.

Original link: The problem with spinning spacecraft

The content of the translation only represents the author's point of view, not the position of the Institute of Physics of the Chinese Academy of Sciences.

This article comes from the official account of Wechat: Institute of Physics, Chinese Academy of Sciences (ID:cas-iop), author: RHETT ALLAIN, translator: Nuor, revision: zhenni, Editor: Tibetan idiot

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