Can a Moon-Sized Spinning Sphere Create Livable Artificial Gravity?

[Adrovane]

Consider a hollow sphere roughly the size of the moon, spun up to produce 1g of centripetal acceleration along a band at its equator (about 15000 kph)
Big stuff, I know.
I have a few questions about the implication of such a system, and I hope someone can help me find some answers!

- How tall could a structure be on the equator? Is there a point where the structure would undergo too much stress from th difference in gravity from its base to its top?

-Travelling around the equator at speeds of about 1000 kph will increase or decrease the artificial gravity by about 0.15g if my calculations are correct, but would it be more efficient to connect various posts if the habitat with "chords" that cross through the centre of the sphere?

-What happens if you leave the equator and begin walking towards the poles? Would some kind of curved or twisted track be able to compensate for the gravity changes?

-Could the uninhabited volumes of the north and south hemispheres be filled with water? How would this affect the spin of the habitat?

-Assuming there is a kind of sun window at one pole, could the axis of rotation be made to process over a 24 hour-ish period to simuladmte a day-night cycle? Or is that kind of speed unstable?

Wow, a lot to talk about- sorry if it's a bit much, but I'd love to hear any ideas you may have!

 

[Ryan_m_b]

Consider a hollow sphere

In case you've not seen it designs for spherical rotating habitats exist in the form of Bernal spheres:
https://en.wikipedia.org/wiki/Bernal_sphere

roughly the size of the moon, spun up to produce 1g of centripetal acceleration along a band at its equator (about 15000 kph)
Big stuff, I know.

Likely too big for that acceleration. An engineer called McKendree worked out the largest diameter of a cylinder rotating at 1g using carbon nanotubes for a NASA conference years ago, IIRC they were 1000km in radius. Any bigger and the force from their rotation would rip them apart.

I have a few questions about the implication of such a system, and I hope someone can help me find some answers!

- How tall could a structure be on the equator? Is there a point where the structure would undergo too much stress from th difference in gravity from its base to its top?

Difficult question to answer given that the structure can be tapered significantly. Also if you're capable of building something that big you could string a tether between two sides.

-Travelling around the equator at speeds of about 1000 kph will increase or decrease the artificial gravity by about 0.15g if my calculations are correct, but would it be more efficient to connect various posts if the habitat with "chords" that cross through the centre of the sphere?

Going around a circle to the opposite side rather than cutting through the middle covers 1.57x the distance (half pi). So long as your elevators were capable of climbing the spoke cables at >1/1.57 times the speed of whatever vehicle averages 1000kph around the rim then yes that would be faster.

-What happens if you leave the equator and begin walking towards the poles? Would some kind of curved or twisted track be able to compensate for the gravity changes?

The ground gets steeper and you get lighter. You could have a series of switchback paths to compensate for the steepness, but you'd want to tether yourself to something to prevent floating off at altitude. You'd also want to bring a space suit because the atmosphere isn't going to extend hundreds-thousands of kilometers.

Could the uninhabited volumes of the north and south hemispheres be filled with water? How would this affect the spin of the habitat?

If you just suspend water anywhere in the center of the rotating structure it will just float there, given that it's above the atmosphere and not touching anything that will cause it to be pushed/dragged to the edges. Not sure why you'd want to do this though.

-Assuming there is a kind of sun window at one pole, could the axis of rotation be made to process over a 24 hour-ish period to simuladmte a day-night cycle? Or is that kind of speed unstable?

If you can build a megastructure of this sort you can certainly arrange a mirror at the pole that rotates at a different speed to the whole, reflecting in light for only half the day.

 

[Bandersnatch]

- How tall could a structure be on the equator? Is there a point where the structure would undergo too much stress from th difference in gravity from its base to its top?

Difficult question to answer given that the structure can be tapered significantly. Also if you're capable of building something that big you could string a tether between two sides.

The difference in gravity is not a problem, it's an advantage. You get the upper parts to weigh less, so cause less stress on the lower bits than they would on Earth. It let's you build a taller building. But, given the size of the habitat, it won't be that much of an advantage. You should assume the practicalities of building construction to be roughly the same as on Earth.
(I'm assuming you're thinking of structures built on the inside here)

 

[Adrovane]

If you just suspend water anywhere in the center of the rotating structure it will just float there, given that it's above the atmosphere and not touching anything that will cause it to be pushed/dragged to the edges. Not sure why you'd want to do this though.

I was thinking more that it would be covering the inner surface of the sphere like a lake - I was unsure whether a) the water would stay on the inner surface and b) not interfere with the habitat's spin by perhaps increasing drag

Thank you for your reply! I have seen the Bernal Sphere before, though I wasn't aware of it when I first started toying with this idea - and the tapering tower, plus Bandersnatch's comment about decreasing stress on the materials, make things a lot easier

 

[Ryan_m_b]

The difference in gravity is not a problem, it's an advantage. You get the upper parts to weigh less, so cause less stress on the lower bits than they would on Earth. It let's you build a taller building. But, given the size of the habitat, it won't be that much of an advantage. You should assume the practicalities of building construction to be roughly the same as on Earth.
(I'm assuming you're thinking of structures built on the inside here)

Sure, but this structure is 3500km in diameter. The summit of a dozen Everests stacked on top of each other has just a 3% difference in pseudo gravity to the base. It’s likely a static structure is unlikely to get up to a size that the gravitational difference is that helpful. Not unless it’s incredibly tapered or uses other clever tricks.

I was thinking more that it would be covering the inner surface of the sphere like a lake - I was unsure whether a) the water would stay on the inner surface and b) not interfere with the habitat's spin by perhaps increasing drag

The water touching the wall will be slowly spun, as that force propagates out it will cause the “lake” to disperse. Much of it will fall down the inner surface increasing in speed until it crashes to the rim. Most of it will probably spray outwards, hitting the inner rim at a later time.

 

[Adrovane]

The water touching the wall will be slowly spun, as that force propagates out it will cause the “lake” to disperse. Much of it will fall down the inner surface increasing in speed until it crashes to the rim. Most of it will probably spray outwards, hitting the inner rim at a later time.

Could this precipitate (heh) some kind of water cycle?
Is there a certain volume that will mean that parts of it would become unbound by the centripetal force and drift into the centre? That water would then fall into the rim and, if it is raised, drain back into the "seas", replenishing them?
I may not be thinking about this in quite the right way, but that's why I'm asking!
Things like this often sound good in my head but have nothing to do with real physics

 

[Ryan_m_b]

In a structure of this size I'm pretty sure you'd have rain the same as on a planet. Heat from the sunlight reflected through the poles causes water bodies to evaporate, it rises up several kilometers into the thinning atmosphere where it cools and condenses into clouds and later falls as rain.

 

[stefan r]

...

-Assuming there is a kind of sun window at one pole, could the axis of rotation be made to process over a 24 hour-ish period to simuladmte a day-night cycle? Or is that kind of speed unstable?...!

See the Banks orbital from Iain Banks' culture series. The Banks orbital is not possible with an material that exists. That is also true of your sphere.

...

- How tall could a structure be on the equator? Is there a point where the structure would undergo too much stress from th difference in gravity from its base to its top?

...

That this is sort of the wrong question. A structure like a tower can at most "only" be the radius in material (moon =1740km). The tower also gets lighter as it rises. The more difficult problem is a thin layer of dirt. All of the dirt is adding weight to the equatorial ring. So 10 cm by 10m of damp topsoil with grass is also 10,900 kilometers around the diameter. That would add 10 million tons of mass. The spheres' structural material that supports the 10 million tons of grass also adds mass which needs to also be supported.
If you switch your building architecture style to chandelier type structures(video) you use much less material. They should hang down and not touch the "ground".