Getting Day-Night Cycle and Seasons for my Dyson Outies
Setting is described here:
Handwavium-based-artifact by a Kardashev III+ civilization. We're talking about a 1-AU-radius world (except people live on the outer not inner side of the hollow sphere), so for all intents and practical purposes (at least with WWII transport tech), a humongous and near-flat world (it would take hundreds of years to drive around at 130km/h).
So to summarize, it's a big sphere 1AU (150,000,000 km) radius, maybe around a black hole just big enough to give 1g at the surface.
I can have (jet-stabilized) orbiting candles that look like the sun from the surface, and maybe fainter moon-like objects just for fun. Is there an easy way (I have no supercomputers on hand right now) to have most areas have 24/h day-night cycles and Winter/Spring/Summer/Fall seasonality?
I was initially thinking of having different suns "orbit" at various latitudes (a series of minisuns at 44 N spaced for 8-16 hour nights, another series at 45 N, etc.) and then have the next season come by altering the distance or relative angle the minisuns orbit at. It takes a certain suspension of disbelief to have a stable going "orbit" around the 45th N parallel, so I'm looking to see if there's a more physical and less handwavy way to go about it.
If the answer requires me to restrict habitable areas to the equatorial band, I could live with it, but I'd prefer to have habitable areas throughout.
This post was sourced from https://worldbuilding.stackexchange.com/q/44705. It is licensed under CC BY-SA 3.0.
1 answer
First, let's start by determining the mass of the black hole. Using Newton's law of universal gravitation - which I think we can safely use, at a distance of 1 AU - we get $$g=\frac{G(M_{\text{black hole}}+M_{\text{Dyson sphere}})}{r^2}\to M_{\text{black hole}}=\frac{gr^2}{G}-M_{\text{Dyson sphere}}\simeq\frac{gr^2}{G}$$ At the far right, I assumed that, relative to the mass of the black hole, the mass of the Dyson sphere (which is what this object essentially is) is negligible. I'm going for an order of magnitude estimate here. Anyway, plugging in the numbers, I get $$M_{\text{black hole}}\simeq\frac{9.8\times(150,000,000,000)^2}{6.673\times10^{-11}}=3.304\times10^{33}\text{ kilograms}$$ This is, for those curious, over 1,000 times the mass of the Sun. That's still orders of magnitude less than a supermassive black hole, but it would seem to be a low-mass intermediate-mass black hole (IMBH).
Let's say that we go with the idea of having a Sun-like star orbiting 1 AU beyond the surface, having a semi-major axis of 2 AU (and assuming that the orbital eccentricity is negligible). Using Kepler's third law, we find that $$P\simeq\sqrt{\frac{4\pi^2a^3}{GM_{\text{black hole}}}}=\sqrt{\frac{4\pi^2\times(300,000,000,000)^3}{6.673\times10^{-11}\times3.304\times10^{33}}}=2.199\times10^6\text{ seconds}$$ That's over 25 days to complete one orbit - which is one day/night cycle. You'd need to have the star orbiting much closer to have the cycle be 24 hours long, but that could fry the Dyson sphere! Alternatively, you could let the black hole be more massive, which would of course increase the surface gravity of the Dyson sphere.
Now, you could opt to bring the star closer to the Dyson sphere but make the star a lot less luminous, which might work. Alternatively, you could have multiple stars orbiting 1 AU away from the planet, though that setup would likely be unstable.
At any rate, here's how I envision the entire setup. Let the star(s) orbit at a larger orbital inclination, and let the Dyson sphere rotate, so different areas progress through receiving different levels of sunlight. It might look something like this:
I've drawn the star's orbit as an oval just to show perspective. The orbit is in fact circular.
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