Gravity differences on asteroid with an O'Neill cylinder

In my story there is something akin to an Island Three O'Neill cylinder buried vertically into the side of the asteroid Vesta. It is 5 miles across and 20 miles long. The station is buried but is spun up inside of a cylindrical shell carved out of the asteroid. The whole of Vesta does not need to be spun. The station is buried for two purposes: to protect from cosmic radiation and to give better access to the miners.

Vesta's gravity is about 0.25 m/s^2 which (I think) is around 0.03G. For things to feel like 1G inside, the cylinder should produce 0.9995G artificially.

Now, (if I'm doing the math right) using arctan(0.03/0.9995) the inside of the cylinder would feel like it has a 1.72° slope to it, which doesn't seem like much, but...

1. Would this feel like a hill? Would walking far surface-ward wear you out faster than? Could you throw a ball further "downhill" at this angle? Or would it not even feel any different?

2. Would it make sense to build terraces periodically to level things out?

3. Would this noticeably affect air pressure or water flow across the gradient of the cylinder?

I'm trying to feel out if this would even be worth mentioning my story, or if the effect is so negligible that it wouldn't.

• Long time no see, Sam! Welcome back! I'm not much of an orbital mechanic, so could you explain where the arctan(a/(1-a)) comes from? What's its purpose?
– JBH
Commented Sep 26, 2018 at 5:11
• How can the O'Neill cylinder generate gravity if it is buried and cannot rotate?
– L.Dutch
Commented Sep 26, 2018 at 5:11
• What is the 'Island Three' thinf about? I cannot find anything on the quick neither in the linked resource nor via google Commented Sep 26, 2018 at 5:20
• A slope of 1.72° comes to 3 in 100. It would definitely feel like hill. Find a road nearby marked 3% and see how it feels. What's keeping you from making the inside walls of the cylinder into a series of suitably sloped pieces so that the combined gravitation and centrifugal force pressed exactly perpendicular on the floors? (Like this: ^^^^.) Air pressure does not have much relationship with the apparent gravitational acceleration; on the other hand, water definitely flows downhill. Commented Sep 26, 2018 at 5:47
• This is a good question, but i have to ask, why bury the cylinder into the asteroid at all? doing so means you'd need to spin the entire asteroid to generate the centrifugal force needed by the cylinder. if its so you can easily mine the asteroid, then surely having the cylinder matching orbits with Vesta and send mining parties onto and off of the asteroid would be a a lot more efficient then spinning the entire thing? Commented Sep 26, 2018 at 8:29

1 Answer

So, a force toward the more-or-less center of Vesta of 0.03g and a perpendicular force of 0.9995g. Earth experiences magnitude variations of up to 0.7% and Vesta's gravity represents 3%. I'm not sure people would feel this that all, but it is "sideways," which would be odd. Let's run with it.

OK (it's been a while since I did inclined plane physics, so I might be wrong)...

Potential Energy = mgd sin(θ)

• m = mass
• g = gravity constant
• θ = angle of the hill
• d = distance travelled (we're going to assume "1")

At 0° the contribution due to the hill is 0 J. We want a contribution equal to the affect of Vesta's gravity. F= ma.

m(0.03g) = mg sin(θ)

0.03 = sin(θ)

θ = 1.72° (which you calculated! I'm on the right track.)

So, living in your environment means feeling like you're constantly walking up and down a 1.72° hill. What's that like?

Well... that was a long and fancy way of saying you're stepping up 0.03 meters (30 cm) for every meter walked or just over an inch for every 3.28 feet walked.

It's almost nothing. I doubt people would even notice it. According to this bicycling site a 3% grade (which this represents, rise/run*100 = 0.03/1*100 = 3%) is like riding your bike into the wind (of course, they don't tell you what wind...) but not considered much of a challenge to cyclists.

OK, whether or not a 3% grade is an issue depends on what's happeneing. For a person walking, it's likely not noticable. For a car moving at 70mph, it represents a risk if a sharp turn occurs. For a train, it's a big deal. It really depends on how much mass is being moved. As mass increases, the grade of the hill becomes more important (especially downhill) because the energy needed to overcome the grade increases with it. A 3% grade won't cause my Toyota Prius to recharge. I'm just sayin'

Oooh. You had more questions. You can't "level things out" with terracing. It may feel like you're living on the side of a 3% hill, but you actually aren't. You can't change an angle to make the potential energy due to Vesta's gravity go away. You can thank the need to spin your cyclinder for that.

It does mean that if you spill a glass of water, it's going to want to dribble in the direction of Vesta's core. Remember, 3% isn't much. If you spilled it on a big sheet of glass you'd see it move, but if you spilled it on concrete you probably wouldn't.

It will mean a slight increase in air pressure toward the center of Vesta. But, once again, I doubt it would be noticable.

• Hmm. I don’t understand why the terraces idea wouldn’t work. If the station never stops spinning wouldn’t the net force on a 1.72 degree hill be the same as pointing down, or is there something about the spin that makes it different? Commented Sep 26, 2018 at 17:04
• Remember that there is no hill. On earth, the two forces (gravity and the effect of the hill) are nearly parallel. In your case, the two forces are perpendicular: 90°-1.72° = 88.28° By terracing to get rid of the Vesta gravity effect you've caused your people to walk up and down hills equal to a 100% grade. Vesta has the effect of living on a hill ... but there is no hill. You could turn your cylinder so that it's lying on the surface rather than embedded into the asteroid, but the effect is to cause a 3% variance due to the spin v. Vesta.
– JBH
Commented Sep 26, 2018 at 18:28
• Of course, if the cylinder is lying on the surface, you could adjust the spin so the effect was ±1.5% Earth-norm, which might be easier to absorb/ignore - if your story can handle the shift.
– JBH
Commented Sep 26, 2018 at 18:30
• Trying to get my head around this... Ok, so imagine you're standing inside this station. If you lay a 1 meter level on the ground oriented "surface" to "core", the bubble will shift towards the surface in a way that would look like a 3% grade on earth. Right? If that's true, if you place a 3cm block of wood under the "core" side of your 1m level, what would happen to the bubble? Commented Sep 27, 2018 at 2:05
• I’ve got it. Thanks JBH. It’s counterintuitive for an Earth dweller like myself but it makes sense now. And it might make for some interesting storytelling. Commented Sep 27, 2018 at 13:09