Let’s simply make it easy: To obtain a man-made gravity of 0.5 g, you’ll want a radius of 450 meters and a spacecraft-to-counterweight distance of twice that (900 meters).

Just for enjoyable, the Wikipedia page lists the tether distance at 450 meters. This would give a rotational radius of 225 meters. Using the identical angular velocity, the astronauts would have a man-made gravity of simply 0.25 g’s.

I imply, that is not horrible. In truth, the gravitational discipline on Mars is 0.38 g’s, so this is able to be nearly adequate for the astronauts to arrange for work on Mars. But I’m going to stay with my synthetic gravity of 0.5 g’s and a tether size of 900 meters.

What Would It Be Like to Slide Down a Tether?

Without going into an excessive amount of element, let’s think about what would occur if an astronaut was going to climb certainly one of the cables from the spacecraft to the counterweight on the different aspect for some cause. Maybe life’s simply higher on the different aspect—who is aware of?

When the astronaut begins up the cable (I’m calling “up” the path that’s reverse the synthetic gravity), physics dictates that they are going to really feel the identical obvious weight as the different astronauts on the spacecraft. However, as they get increased on the cable, their round radius (their distance from the heart of rotation) decreases, making the synthetic gravity additionally lower. They would preserve feeling lighter till they obtained to the heart of the tether, the place they might really feel weightless. As they continued their journey to the different aspect, their obvious weight would begin to improve—however in the other way, pulling them towards the counterweight at the different finish of the tether.

But that is not very thrilling for a film. So right here is one thing very dramatic as an alternative. Suppose an astronaut begins close to the heart of rotation with little or no synthetic gravity. Instead of slowly climbing “down” the tether, what if she simply lets the faux gravity pull her down? How quick would she be going when she will get to the finish of the line? (This would kind of be like falling on Earth, besides that as she “falls,” the gravitational drive would improve as her distance from the heart does. In different phrases, the additional she falls, the larger the drive on her.)

Since the drive on the astronaut adjustments as she strikes down, this turns into a more difficult downside. But don’t fret, there is a easy strategy to get an answer. It would possibly seem to be a cheat, however it works. The secret is to interrupt the movement into tiny items of time.

If we think about her movement throughout a time interval of simply 0.01 seconds, then she would not transfer very far. This implies that the synthetic gravity drive is usually fixed, since her round radius can be roughly fixed. However, if we assume a relentless drive throughout that brief time interval, then we will use easier kinematic equations to seek out the place and velocity of the astronaut after 0.01 seconds. Then we use her new place to seek out the new drive and repeat the complete course of once more. This technique is named a numerical calculation.

If you need to mannequin the movement after 1 second, you would wish 100 of those 0.01 time intervals. You may do that calculation on paper, however it’s simpler to make a pc program do it. I’ll take the straightforward manner out and use Python. You can see my code here, however that is what it could appear to be. (Note: I made the measurement of the astronaut bigger so you would see her, and this animation is working at 10x pace.)

For this slide down the cable, it takes the astronaut round 44 seconds to slip with a ultimate pace (in the path of the cable) of 44 meters per second, or 98 miles per hour. So, that is not a secure factor to do.