Reposting a relevant post I made on the The Expanse thread over in Cafe Society (which is itself a reworking of a post I made to a different forum more than a year ago.) Spoilered for length.
So The Expanse series by James S.A. Coey has long been in my deep “to read” pile, but with the (well received, but I’ve yet to see it) Expanse TV series, I decided to bump the books up on the list, and I’m currently around half-way through the first book, Leviathan Wakes, and even though I don’t commonly read detective mystery/police procedural type books, so far I’m more or less enjoying it. It has the problem, though, of attempting to use plausible real-world physics instead of hand-wavium, but getting the real-world physics obnoxiously wrong—wrong enough to pull me out of the narrative and make me pick up reference books and spend a couple of hours creating formulas in Excel, so I might as well inflict the math on others, too.
(Warning: the following material is in full-blown geek mode. Any mistakes in my math are entirely the fault of Barack Obama, somehow.)
In Leviathan Wakes, it asserted that the dwarf planet (formerly asteroid) Ceres has been “spun up” to provide artificial gravity for the colonists. Now, providing artificial gravity through spin is perfectly valid science—many of you have probably experienced it personally in one of those flying-saucer-shaped amusement park rides. The problem is, centrifugal gravity always pushes outward (never mind for the moment the argument that centrifugal force isn’t really a real thing) so people living on a “spun up” Ceres would have to live underground, upside down, with the bulk of the dwarf planet above their heads.
Let’s jump to Earth for a moment—Earth has an equatorial circumference of around 39,600 kilometers and completes one rotation in 24 hours. This means that the ground at the equator is moving at a rate of around 1,650 kilometers per hour. (The speed is lower as you move north or south of the equator.) The Earth isn’t exempt from outward centrifugal acceleration, but even at the equator the acceleration is around only three tenths of 1 percent of Earth’s gravity, so you don’t exactly have to worry about flying off into space.
Back to Ceres. Ceres’s natural gravity is around 2.9 percent of Earth’s. In Levithan Wakes, Ceres is said to be spun up to 30 percent of Earth gravity. But, the actual centrifugal acceleration has to be 32.9 percent—the 30 percent of outward artificial gravity you feel, plus an extra 2.9 percent to “cancel out” the natural gravity trying to yank you off the ceiling of your cave. (This is my assertion, not something from the book.) With a diameter of 946 km, to provide a centrifugal gravity of 0.329 g, Ceres’s rate of rotation would have to be accelerated from a day length of 9 hours, 4 minutes to a day length of 40 minutes, 13.6 times its current speed. (A spin-up said to have taken “half a generation.” I haven’t done the math as to how much energy this would have taken, but surely it would need to be something on the order of a Kardashev Type 2 civilization.) At this rate of rotation, a point on the surface Of Ceres’s equator is traveling at around 4,450 kilometers per hour, or more than 1 kilometer per second. This seems like it would provide a bit of a challenge to any ships attempting to land there. The surface speed would decrease as you moved north or south from the equator, but so would the apparent gravity—so the least improbable locations for landing are the most unsuitable places for living.
But it gets worse—this outward centrifugal force would be—at the equator—more than 11 times the surface gravity of Ceres. Literally everything not literally bolted, welded, or otherwise firmly attached to the surface will fly off into space at more than twice Ceres’s escape velocity. So during spin-up, either a large percentage of surface of Ceres centering on the equator would need to have been fused into solid rock, paved, or superglued down, else billions of megatons of rock and dust be hurled into space, producing an overwhelming number of high-speed projectiles for holing spacecraft and impacting planets and other occupied asteroids.
And, yes, it gets even worse than that. FSM only knows what sort of tectonic activities would be stirred up by these stresses, and I have little doubt that all of the frozen ices locked up in the crust of Ceres would quickly become gasses, along with—probably—a considerable percentage of the rocks and metals becoming liquid. Which would then also be flung off into space at higher than escape velocity. For a period likely lasting millions of years, Ceres would be just about the biggest comet of pinwheeling volcanic death that you can imagine, tossing out enough impactors to wipe out complex life on Earth and every colonized body in the solar system. So—you know—great job, engineers.
(In Leviathan Wakes–for reasons probably no more profound than poor scholarship–it is claimed that Ceres is 250 kilometers in diameter instead of the correct 946, placing fake Ceres at around 2 percent the mass of real Ceres. Not that I think the authors bothered crunching any plausibility numbers with those figures, either.)
At first, I also had issues with the use of Eros as a spun up, colonized body. While as a Near Earth Object, Eros is a convenient early target for manned missions beyond the moon, I had misremembered it as being a rubble pile (a heap of shattered rocks loosely bound together by gravity, often filled with voids.) So I pulled out my copy of Asteroid Rendezvous: Near Shoemaker’s Adventures at Eros (2002), a book collecting 9 articles written by 11 of the project scientists involved with the spacecraft that orbited Eros from 2000-2001, along with a foreword from Carolyn Shoemaker. This is an excellent book, heavily illustrated with color photographs, charts, and diagrams. Some of the articles are more technical than others but all aim more or less at an enthusiastic amateur rather than professional astronomers already well familiar with all the math and jargon. Definitely something worth picking up, if you can get your hands on a copy, and my Book Recommendation of the Day.
Anyway, refreshing my memory of the book and the asteroid, Eros seems to be solid (and thus would likely survive a spin-up) but is significantly irregularly shaped, and rotates “the wrong way”, twirling like a baton instead of rolling like a log. So first Eros would have to be stopped from spinning lengthwise before it could be spun along its long axis, and it would probably be necessary to shave down the peaks and fill in the significant craters, and something would definitely need to be done about the 100 or so meters of regolith, but it seems well within the plausible range of something that could really be done using real world science in the less than profoundly distant future (although the spin-up would probably take considerably longer than the 10 years allocated for the 140,000 times more massive Ceres.)
Eros has a width of around 11 km and a length of around 34 km, but as I mentioned, the shape is pretty irregular along the length, which would lead to problems making it rotate stably and with having consistent centrifugal gravity along the spin axis. So let’s imagine that the engineers reshape it into a smooth cylinder 8 km wide, cleaning away all loose rock and sealing all the cracks in the process (which seems a plausible enough size for the purpose of plugging in numbers.) This Eros, spun up to the 0.3 g mentioned for Ceres, would have a day length of slightly under 4 minutes and a surface speed of around 390 kilometers per hour. Nearly an order of magnitude less than the surface speed of the spun-up (molten spewing deathtrap) Ceres, but still around 100 meters per second—so ships would probably still need to dock at one of the end caps. If you wanted to spin the modified Eros to a full Earth gravity, you would end up with a day just over 2 minutes and a surface speed of around 724 kilometers per hour. Makes landing even more tricky, but without doing the mass, I’m guessing the 0.3 g and the 1.0 g options are safely within realistic structural strengths for a solid stony asteroid. In the case of cylindrical Eros, centrifugal gravity would remain the same from pole to pole, dropping only with greater depth. Each outermost layer of this hypothetical would have a surface area roughly the size of New York City. Lower levels would be theoretically possible as far down as structural integrity and tolerance of low gravity hold out—you might even be able to burrow deep enough to avoid all but the worst debris from Ceres.
