Spin Gravity Compared

Spinning to make artificial gravity is  a classic element of hard sci-fi. And it’s been imagined from ringworlds the  size of the solar system, to asteroids, to tiny ships just a few meters wide. So  I wanted to see if I could put their scale into perspective but also understand the dynamics  between the different variables of spin gravity.

One of the smallest practical examples is  the Discovery One from 2001: A Space Odyssey. At the front there is a sphere that has a  centrifuge inside. That centrifuge rotates at about 5 RPM and creates 0.

17g—the  same amount of gravity as the moon. There are 4 interdependent variables for  spin gravity. And you can engineer you’re station by changing these variables.

The first  two I've already mentioned. Angular Velocity or “spin rate” shown in RPM and centripetal  acceleration or gravity level or shown in g’s. There is a maximum spin rate for human comfort,  the maximum where people won't be dizzy and sick.

And 5 to 6 RPM has been suggested by studies as  the maximum. But even that is still pretty fast, and it’s probably going to make some people  sick, which is accurately depicted in the movie Interstellar. The ship Endurance rotates  at 5.

5 RPM and poor Romley must have run out of Drmamine. (“Can we stop the spinning? ”) But  it produces more gravity than the Discovery with nearly the same RPM, because it has a larger  diameter.

When you increase the diameter, it slows down the spin rate needed  to make the same amount of gravity. That is the third variable. Math uses radius, but I will be using diameter because  it makes more sense for people.

Another way to increase the diameter is  to use a tether. And that’s what the ship Hail Mary uses in Andy Weir's book Project  Hail Mary. It flips the crew compartment 180 degrees, extends to 100 meters,  and spins at 4.

2 RPM to create 1g. But that’s still pretty fast. 1 RPM has  been suggested as a reasonable limit for the average person.

And that's what the Space  Station V, also from 2001, rotates at. Just under actually. And it produces the same  point .

17g as the Discovery at that speed. But . 17g is a little low for  comfort and maybe human health.

So to get a reasonable level of gravity and RPM’s, we have to go even bigger. The Babylon 5  space station is 800 meters in diameter and also rotates at an even 1 RPM, but produces  point . 45g because of its 800-meter diameter.

The OPAS Behemoth from the Expanse is 960 meters  in diameter, and rotates a little slower at . 75 RPM, and produces . 3g.

In the Expanse . 3g is  the standard for gravity in the outer planets and under thrust, but in real life there are  no studies showing longer term low g health implications more than one year in zero g.  So it’s not yet known what the minimum is.

Cooper station from Interstellar is never  shown from the outside and its size and specs can only be speculated on from images in  the film, and so it has been hypothesized to be 1. 6 kilometers in diameter, but if we make  it just slightly larger, we have settings for an ideal cylinder: 1. 78 kilometers in  diameter with 1 RPM and 1g of gravity.

Rama from Rendezvous with Rama by Arthur C.  Clarke is 18 kilometers in diameter on the outside (it’s 16 on the inside. ) It rotates at .

25 RPM,  completing a full rotation once every 4 minutes, which produces . 56g on the inside. From here on  out, I’m going to switch from RPM to the time it takes for one full rotation because after the  diameter get’s large enough, the RPM’s don't matter anymore.

Exactly what that diameter is is  debatable, but we’ve definitely passed it by this point with Rama. What does become the limiting  factor is the fourth variable: the rim speed, or the tangential velocity. Rama’s Tangential  Velocity is 527 miles per hour.

And this is a great example of sci-fi using science to  create drama. In the book, the tangential velocity becomes a problem. But 527 miles per  hour is small potatoes compared to what's coming.

The Elysium space station from the movie  of the same name is a Stanford Torus 60 kilometers in diameter and spins at  1g, completing a full rotation in 5 minutes 47 seconds. Its tangential  velocity is 1,213 miles per hour! Ceres is the largest object in the asteroid  belt, and in The Expanse is a space station that was spun up.

And I didn't realize  this, but it's 7 times larger than the death star at 970 kilometers in diameter. The  show really didn’t capture just how massive it is. Ceres It is the largest object in the  asteroid belt and makes up 25% of the mass of the entire asteroid belt but is not actually  an asteroid anymore it has been reclassified as a dwarf planet….

I have no comment. Ceres has a  natural gravity from its mass of point . 029g but in The Expanse, it was “spun up” by the Tycho  corporation to produce .

3g. No small feat. There is a reason why most of these are rings or  cylinders and not spheres.

When spheres spin, the centripetal acceleration is concentrated on the  rotation axis. Not only does it diminish as you move closer to the core, but it also diminishes  as you move away from that axis. In the show, there is a graphic showing the tunnels inside  Ceres in a spiral fashion, but that would be absolutely massive if they were that big, and it  doesn’t really make any sense spin gravity-wise.

It is also at this point that the tangential  velocity starts to become a problem. For man-made stations, the stresses produced by  these ludicrous velocities probably would exceed current material strengths and wouldn’t  be possible with current material science, and, as for ceres, it's questionable whether  this asteroid–planet is compact enough to maintain its structural integrity under spin  load. We don't know how dense Ceres is yet, but scientists are starting to learn that most  asteroids are loosely packed, and if you spun one up with a tangential velocity of twenty-six  hundred miles per hour it might just disintegrate.

The Moon is three thousand four  hundred and seventy-six kilometers in diameter produces gravity the old  fashion way, from mass, making 0. 17g. Alpha Halo from Halo is probably the most famous  ringworld.

It’s 10,000 kilometers in diameter, but it does not spin for  gravity. It has artificial gravity handwavium generators  that produce the gravity… Why is it a ring then? Good question.

Probably  because it looks cool… I’m done with Halo. The Earth is 12,756 km in diameter and it spins  at about 1,000 miles per hour at the equator, and its gravity is, you guessed it, 1g. And also just here for scale,  the original Halo installations, known as the Senescent array,  were 30,000 km in diameter.

If you’ve never heard of the Culture Series  by Ian Banks, it's a legend among sci-fi, and in it most of the galaxy's population  lives on what are called “orbitals. ” Which are ringworlds of various sizes. There  are two known orbitals with detail: Masaq and Vavatch.

Masaq is  only 6 thousand kilometers wide, and Vavatch is 35 thousand kilometers wide.  But Masaq is 3 million kilometers in diameter and Vavatch is 4. 46 million.

They have surface  areas equal to 118 earths and 960 respectively. And the reason why orbitals come  in different sizes is because their spin variables are scaled so that one  revolution creates one standard day and one standard gravity for the preference  of whichever species is living on them. This is because a natural day-night cycle  can be created by just tilting the ring 1 or 2 degrees off of the ecliptic plane and the  ring naturally casts a shadow on half of itself.

Only one variable, the diameter, is listed  canonically, so we can’t calculate what these are spinning at, but what if we make  a hypothetical ring with earth standards? An earth ring with a 24 hour rotation period and  1g would be 3. 7 million kilometers in diameter, and its tangential velocity would be over  three hundred thousand miles per hour.

And suspiciously Vavatch is suspiciously  20 percent larger in diameter… But all of these are small scrith compared to the  OG: Larry Niven’s Ringworld. This thing is a true behemoth, standing at 1. 6 million kilometers  wide and with a radius slightly larger than the Earth's orbit around the sun, at 1 hundred and  50 million kilometers, making a total diameter of 3 hundred million kilometers.

To produce just  under 1g, the Ringworld rotates around the star once every 9. 37 days, and its tangential  velocity is 2. 7 million miles per hour… It has a surface area of 965 trillion  square kilometers, almost a quadrillion, which is equal to over 3 million earths.

It’s  so ridiculously huge that all of the worlds from Known Space have a 1 to 1 map of themselves  on the ring… with plenty of space to spare. Also, the day-night problem couldn't be addressed  by tilting a ring that encircles the star completely. So he devised a shade system in which  20 shades, each 1 by 2.

5 million miles in size, would rotate around the inner radius of the ring  and produce a day-night cycle from their shadow Such a ridiculously huge ring is  well beyond any science we have, but nevertheless Larry Niven, like Andy Weir, got  suggestions from his fans about the scientific accuracy of the Ringworld. At the Worldcon  convention in 1971, MIT students chanted, “The Ringworld is unstable! ” Because they  identified that an object rotating around a star is not in a gravitational orbit, it  has an equal pull on all sides and wouldn’t naturally be in equilibrium.

Eventually,  it would drift one way or the other, colliding with the star. Niven then addressed this  in the next book adding Bussard Ramjets around the ring to maintain its position and creating  some drama for the story, too. I won’t spoil it.

There is one more and it’s a new contender for  the biggest boi in hard sci-fi megastructures. Heaven’s River from the Bobiverse by Dennis E  Taylor. Heaven’s River is a Topopolis.

A Topopolis is a rotating space station like the cylinders  previously shown, but stretched out all the way around a star. But Heaven’s River says, “Hold  my beer,” and ties that into what is called a Torus knot. Going around the star three times,  in a helical fashion.

And in true Bob fashion, the author says, “There was no engineering reason  for that, by the way, I just thought it was fun. ” Its diameter is slightly larger than the  ringworld, at 321 million kilometers. But it's not actually this thick.

The diameter of the cylinder  is only 180 kilometers. Which is still pretty big, but from this distance you can't see it. So  let’s zoom in.

It rotates inside a static shell, and I put Rama here for scale. And as for  the total surface area, doing the math, it would be over 600 billion square kilometers,  which is about 3,300 Earths. Still ridiculous, but not quite the ringworld.

The  Ringworld still holds the crown for the most ridiculous megastructure,  but this is still pretty cool. There are dozens, if not hundreds, of other space  stations. Let me know if I missed anything big (pun intended).

I have to thank my viewers for  recommending the Bobiverse; I didn’t know about it until I started making these videos, and  it's right up my alley as a socially isolated nerd. If you have any other sleeper sci-fi  recommendations, let me know in the comments. And don’t say Warhammer.

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