As mentioned, we have no idea what the inside of Olaf is. However, if Olaf was hypothetically a hollow sphere, there would be no gravitational force due to mass on the inside surface of that sphere. There's a long explanation for this involving integrals, but the short explanation is that the net gravity from all around the sphere cancels out at any point inside the sphere. Therefore, if you wanted to generate artificial gravity on the inside by spinning the sphere, you would not have to overcome an "inwards" gravity first, you would start at zero. This of course assumes a uniform shell, or at least close enough for practical purposes (ie you likely won't care if a little extra mass on one side causes a micro-G bias toward that side). This also means you can make the inside and outside "gravities" the same (at least at the equator) by spinning the sphere up until the centripetal force is equal to half the gravitational force on the outside. Then each side will be experiencing a net force equal to half what the outside gravity would have been if the sphere was stationary. So if you imagine this line | being the shell and these <> representing the "gravity" felt on each side, if un-spun it's like |<<, you could spin the hollow sphere to half-gravity so it's like >|< (though there'd be a gradient as you move away from the equator). Now, if there was an object with gravity sitting at the center of the sphere, say, a star, then the gravity experienced inside would be equal to the force exerted by the object at the center (because the outside sphere cancels itself out). This also means that if you tunnel into a solid object of uniform density (say, a standard rocky planet, although those aren't actually "uniform" but let's just go with it), the gravity you experience would be based only on the mass that is "lower" (that is, closer to the center) than you. The gravity of everything "above" you would cancel out, just as if it was the shell of a hollow sphere. Just imagine the mass below you as being an object contained in a shell above you, that just so happens to be large enough to fill the entire shell, and you'll see how that works.

Quote:

We originally assumed the station was in orbit around Hekate, but we now believe it is parked in a stationary position, using energy from the Penrose process to counteract the black hole’s gravitational pull.

Quote:

The forceful decompression of this atmosphere into space took the explorers and their equipment with them. They are certainly dead, or rather, are eternally dying, as they stretch apart in Hekate’s event horizon.

I've scoured the book for more, but those two sections lead me to believe that there is woefully understated gravity manipulation going on with the station. There's frustratingly no mention I could find of any level of gravity or not in the station itself (though if I were designing a deathtrap of a station, I think i could get more milage out of microgravity), so it could very well be whatever you like it to be as a game master. However, the second quote suggests to me that the effect is very, very localized and once the unfortunates were ejected, Hecate's incredible gravity took over. Honestly, if you have gravity-manipulation tech, airlocking someone just seems...petty to me. But I'm not the alien that built a giant middle finger to physics, so what do I know? [Note that if you were to homerule it as an orbiting station, it would otherwise be identical to any other orbiting body. An orbit in vacuum is an orbit in vacuum, no matter how massive an object it's around. ]

This just in, I'm an idiot. I guess if the station's harnessing the Penrose effect, energy requirements aren't really a concern, but I as a tech head in-universe would be chomping at the bit to figure out how the hell that station works its magic. And would probably end up a stain on the far wall, Dead Space grav plate style.

Running some amateurish numbers through wolfram alpha, and using Sagittarius A* as a base it looks like the gravity of a black hole is actually pretty small at the edge of the ergosphere. (looks like [much] less than .1 Gs actually) Sag A*'s ergosphere is 10 light days away from the event horizon, so this seems pretty reasonable. I think a black hole with the right spin and mass could pretty easily support 1.47 Gs of acceleration at the ergosphere edge. I didn't account for relativity when I did this though, so it's probably flawed by that. (I know this is true, because classically Sagittarius A has about 28k Gs at its "surface" while relativistically it has infinite Gs at the surface) The frame dragging effect probably really messes with things as well, but I don't know how to account for that very well.

That ergosphere figure for Sag A is for the very outside edge of the ergosphere. Beyond that point the gravitational forces of the black hole don't influence bodies in those locations. Honestly, I'm not even sure what this means since gravity will influence bodies clear across the universe so my guess is that what people really mean is the force gets really, really weak (which explains the .1 g figure). Penrose, on the other hand, sits on the static limit. This is the point in which space is so badly distorted by gravity and spin that a particle moving through the distorted space at the speed of light seems to stand still to an observer. With a mass of 4000000 solar masses SGR A* would have an event horizon of about 20 light seconds. At maximum spin this would move the static limit out to 3 light minutes from the singularity, not 10 light days. At that distance you would have a force in excess of 19000 g's.

Question: would anyone standing on Olaf's surface technically be orbiting the star within?

Yeah, my thinking is if you're not orbiting proper, you'd be subject to the full gravity of the star at that distance while standing on the surface. Unless Olaf is spinning fast enough to counter all but the written surface gravity? Would that even work?

Depending on what the thing's made of, wouldn't it piggyback the interior star's magnetosphere? If so, between that and the rotational speed, yeah, the storms on that sucker are going to be nightmarish.

Some thoughts on Olaf. Would the gravity differential be explained by it being an oblate sphereoid? Then you'll be closer to the enclosed mass at the poles and experience higher gravity. I don't think it's spinning fast enough to generate significant centrifugal force to make the difference. Speaking of rotation...could anyone figure out the actual mass of the central object using the inverse-square rule? I kludged a rough guess figuring that the structure has the same diameter as Ganymedes orbit and rotates almost 3.5 times as fast so the central mass would be 3.5 Jupiter masses! That's not even a brown dwarf! Which isn't to say it wouldn't work, it actually works better this way. The internal mass would be stable - no flares or excessive energy output, you would get the planetary magnetic field to deflect solar wind, and could set up some electrodynamic tethers to draw power. Also consider that there may be all kinds of habitats orbiting inside the sphere. The orbital defense network could be there to prevent impacts and simply isn't terribly discriminating in what qualifies as a threat. Or, the thing is a zoo for gatecrashing species and as soon as the connection goes down completely the gate will relocate itself to a faraway island and wait for the next species to blunder through.

Lazarus wrote:

6.16451 x 1029 kg or about 1/3 of a solar mass by my calculations.

Thank you ! So this definitely makes it a Red Dwarf, and kind of a big one! Still lots of room inside though since it would have slightly more than a third of a solar radius as well, roughly 210,000 km.

GenUGenics wrote:

A lot depends upon assumptions made about the interior. If the interior is spun up to g-force at the equator, then it will indeed have significant equivalent centrifugal force on the exterior at the equator.

I ran it through SpinCalc using the given radius and rotation and got effectively microgravity. If there's an interior structure that's spinning it would have to be going remarkably quickly to counter the stars pull.

jKaiser wrote:

I'm reminded of the problems Niven ran into with Ringworld, that a rigid body on the order of size that we're talking about never exactly orbits and needs some form of position-keeping.

True, but this got me thinking about how the shell healed itself in the text. Perhaps it's not really a solid at all but more like a soap bubble. The shell is a controlled liquid that can flow to relieve structural stress on a large scale but be effectively solid on the small scale. The solid landmasses could sit on top using the surface tension like a water strider. This fits with the star model as well since the stellar wind would eventually fill the sphere and support the bubble. Add in some vents for reaction control and you could have a stable sphereoid. I wonder if the bubble rotation is tied to the rotation period of the internal star but I don't think there's enough known about that IRL to make that call. Riffing on your idea of a central mass, perhaps there could be 'shepherd' masses orbiting just inside and outside the shell much like Prometheus and Pandora at Saturn. Otherwise any eccentricity in the shell would cause it to rip apart. Man, that would make an awesome setting! Some Gatecrashers find a shattered prototype that's an Earth sized planet embedded in a tremendous piece of shell, while other aggregated pieces tumble through space around it.

Honestly, given how the crust of the Earth is semi fluid if you look at it on a long enough timescale, that makes a lot of sense. Tectonic plates on a colossal scale, essentially, if I'm understanding it correctly. Though I wonder how big the outer shepherd world would have to be and how far out. And whether it was there naturally or is an artificial world. Same for the inner shepherd.

"Solid" is really a matter of timescale geologically, but I stand guilty of oversimplifying.