How would gravity and centrifugal force interact in Dyson constructs?

I am developing an alien race whose homeworld is a Dyson sphere planetoid (they used collected planetary and asteroid matter to construct a "hollow planet" around their sun, along with "night" solar screens). The alien race has incredibly advanced bio-engineering capacity; biotech living ships, "latticework" organisms used to stitch their sphere components together, etc. They also have a younger system that currently has a Dyson ring with the same construction method.

Now, any construct that massive will have its own gravity in addition to the centrifugal force of its spin providing false gravity.

My question(s): How would gravity be perceived by inhabitants on: 1. The sphere's interior(where I am envisioning their habitation region exists)? 2. The sphere's exterior (likely their "spaceports" would be on the sphere's exterior) 3. How, if at all, would gravity/cf differ with the ring vs the sphere?

The setting is a sci-fi one and alien tech is heavily involved. So, while I am looking for plausible/realistic answers (semi-hard science?), some measure of blah-blah molecules (I like this term for sci-fi more than "hand-waving") is totally acceptable, though I'd prefer to know about things that needed such overlooking so they can have lore reasons to be non-issues.

Your question boils down to describing the gravity along the radius of an empty shell, and gets an answer in a basic lecture on gravity

1. The sphere's interior(where I am envisioning their habitation region exists)?

By the shell theorem, inside a shell the gravity given by the shell is null in every point, assuming an uniform distribution of mass. Therefore inside the shell you will have only the apparent gravity generated by the spinning. Mind that it will be radial only along the equator. Anywhere else it would be skewed.

1. The sphere's exterior (likely their "spaceports" would be on the sphere's exterior)

Here you won't have any shell theorem helping you. You will be subject to the gravity due to the mass of the sphere at a distance equal to the radius of the sphere, assuming again an uniform distribution, minus the centrifugal force. Too few mass and too high rotation and you fly off to space.

1. How, if at all, would gravity/cf differ with the ring vs the sphere?

Shell theorem doesn't hold for rings, but when you are outside you won't benefit from it anyway.

• Thanks. I was thinking that would be the case (for the sphere), but wasn't sure as my knowledge of gravity isn't extensive. I was thinking they have the mass/rotation balanced so that the interior surface is a comfortable gravity for them, and the exterior only barely overcompensates the centrifugal force, allowing them to use a "low g" environment to aid in cargo movement and ship launches. Sep 14, 2019 at 4:55
• So, on the ring, the centrifugal force AND gravity (maybe for the local segment of the ring) would apply? So, they would need the ring to spin slower for internal surface gravity to be at the race's comfortable rating? Sep 14, 2019 at 4:57
• Oops. ^ @L.Dutch Sep 14, 2019 at 7:05