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Friday, July 30, 2021

Might You Actually Climb the Spinning Ship’s Cable in Stowaway?

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

Only for enjoyable, the Wikipedia web page lists the tether distance at 450 meters. This might give a rotational radius of 225 meters. Utilizing the identical angular velocity, the astronauts would have a synthetic gravity of simply 0.25 g’s.

I imply, that is not horrible. In reality, the gravitational subject on Mars is 0.38 g’s, so this may be nearly ok for the astronauts to arrange for work on Mars. However I will stick to my synthetic gravity of 0.5 g’s and a tether size of 900 meters.

What Would It Be Wish to Slide Down a Tether?

With out going into an excessive amount of element, let’s take into account what would occur if an astronaut was going to climb one of many cables from the spacecraft to the counterweight on the opposite facet for some purpose. Possibly life’s simply higher on the opposite facet—who is aware of?

When the astronaut begins up the cable (I am calling “up” the route that’s reverse the unreal gravity), physics dictates that they may really feel the identical obvious weight as the opposite astronauts on the spacecraft. Nevertheless, as they get larger on the cable, their round radius (their distance from the middle of rotation) decreases, making the unreal gravity additionally lower. They’d hold feeling lighter till they obtained to the middle of the tether, the place they’d really feel weightless. As they continued their journey to the opposite facet, their obvious weight would begin to improve—however in the other way, pulling them towards the counterweight on the different finish of the tether.

However that is not very thrilling for a film. So right here is one thing very dramatic as a substitute. Suppose an astronaut begins close to the middle of rotation with little or no synthetic gravity. As a substitute of slowly climbing “down” the tether, what if she simply lets the pretend gravity pull her down? How briskly would she be going when she will get to the tip of the road? (This might type of be like falling on Earth, besides that as she “falls,” the gravitational drive would improve as her distance from the middle does. In different phrases, the additional she falls, the larger the drive on her.)

For the reason that drive on the astronaut adjustments as she strikes down, this turns into a tougher drawback. However don’t fret, there is a easy method to get an answer. It would look like a cheat, nevertheless it works. The bottom line is to interrupt the movement into tiny items of time.

If we take into account her movement throughout a time interval of simply 0.01 seconds, then she does not transfer very far. Because of this the unreal gravity drive is generally fixed, since her round radius can also be roughly fixed. Nevertheless, if we assume a relentless drive throughout that quick time interval, then we will use easier kinematic equations to search out the place and velocity of the astronaut after 0.01 seconds. Then we use her new place to search out the brand new drive and repeat the entire course of once more. This technique is named a numerical calculation.

If you wish to mannequin the movement after 1 second, you would want 100 of those 0.01 time intervals. You could possibly do that calculation on paper, nevertheless it’s simpler to make a pc program do it. I’ll take the simple means out and use Python. You possibly can see my code right here, however that is what it might appear like. (Observe: I made the dimensions of the astronaut bigger so you may see her, and this animation is working at 10x velocity.)

Video: Rhett Allain

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

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