Just keep it simple: To achieve an artificial gravity of 0.5 g, you will need a radius of 450 meters and a spacecraft-to-counterweight distance of twice that (900 meters).
Just fun, the The Wikipedia page lists the tether distance as 450 meters. It will be given a rotational radius of 225 meters. Using the same velocity angle, the astronauts have an artificial gravity of only 0.25 g.
I mean, that’s not terrible. In fact, the gravitational field on Mars is 0.38 g’s, so it’s almost enough to prepare astronauts for work on Mars. But I will keep my artificial gravity of 0.5 g and a tether length of 900 meters.
What Is It Like To Slide A Tether?
Before going into detail, let’s think about what happens when an astronaut climbs a cable from the spacecraft to the counterweight on the other side for some reason. Maybe life is better on the other side – who knows?
If the astronaut starts the cable (I call “up” the direction opposite to artificial gravity), physics dictates that they feel the same weight as the other astronauts in the spacecraft. However, as they lift the cable, their circumferential radius (their distance from the center of rotation) decreases, which also reduces the artificial gravity. They continue to feel light until they reach the center of the tether, where they feel no weight. As they continue their journey to the other side, their apparent weight will begin to increase-but in the opposite direction, pulling them toward the counterweight on the other end of the tether.
But that’s not very exciting for a movie. So here’s something even more dramatic. Suppose an astronaut starts near the center of rotation with little artificial gravity. Instead of slowly climbing “down” the tether, what if he just let go of the fake gravity pull nya down? How fast will he go to the end of the line? (It’s like falling to Earth, unless he “falls,” the gravitational force increases as his distance from the center. That is, the more he falls, the more energy he has.)
Because the astronaut’s strength changed as he continued to move, it became an even more challenging problem. But don’t worry, there is a simple way to get a solution. It may sound like a hoax, but it will work. The key to breaking the movement in small hours.
If we consider his movement at a time interval of only 0.01 seconds, then he will not move very much. This means that the artificial force of gravity is mostly constant, since its circumferential radius is also approximated constantly. However, if we maintain a constant force over the entire time interval, then we can use much simpler kinematic equations to find the astronaut’s position and speed after 0.01 seconds. Then we use his new position to find new forces and also repeat the whole process. This method is called a numerical calculation.
If you want the model to move after 1 second, you need 100 at about 0.01 time intervals. You can do this calculation on paper, but it is much easier for a computer program to do it. I will take the quick way and use Python. You can find my code here, but this is what it will look like. (Note: I increased the size of the astronaut so you can see him, and this movement runs at 10x speed.)
For sliding under the cable, it takes the astronaut about 44 seconds to slide with a final speed (in the direction of the cable) of 44 meters per second, or 98 miles per hour. As such, it is not a safe thing to do.