# How would temperature variation work on the inside surface of a Dyson sphere?

Let's say I have a Dyson sphere roughly the same size of the earth with a very small "star" in the center. Continents, oceans, and people inside the sphere experience a reverse gravity in the opposite direction as the the star.

The star's output power(heat and light) is directly proportional to the equation 1 + sin(t*2pi/d)/2 + sin(t*2pi/y)/2 where t is time in seconds, d is the length of a day, and y is the length of a year in seconds.

Given all of this, how would I make it so that the inside of the sphere experiences similar temperature distribution as the real Earth? Such that, reverse-Florida is hot, and Antarctica is cool.

• Why is the "star's" luminosity periodic? Is it undergoing dramatic pulsations? I think you'll also need to specify the luminosity, radius, temperature, etc. of that body. Commented Nov 3, 2016 at 20:57
• The power is periodic because night and day. I'm not sure those other terms matter Commented Nov 3, 2016 at 21:04
• If the star's in the center, though, I don't see how there could be a night and a day. The inside should always be facing the light. Commented Nov 3, 2016 at 21:05
• Night is a trough of the second term. Day is a crest of the second term. Commented Nov 3, 2016 at 21:10
• Right, but I'm asking if there's a reason for the brightness increasing and decreasing, and I'm also asking how that scales - in other words, what unit it's in. If I plug in $t=0$, I get 1, but I don't know what that "1" means, in terms of units. Commented Nov 3, 2016 at 21:11

Energy in equals energy out. So you want different parts of the inner surface to have different temperatures? Shift one side of the equation. Energy out probably comes from black body radiation to the outside, or sending energy somewhere else like through wires or something.

To get rid of more energy near your cold places, radiate it to the outside, maybe by increasing the exterior surface area perhaps by adding fins. The sun would still be as strong in the hot places as cold places, paint your igloo black and you have a sauna.

To absorb less energy make the colder places be farther from the star, you say Dyson sphere, but what if it's kinda oblique? The farther the surface is from the star the less it energy per square meter. A flat spot might create cold places by the difference between x and sin(x). Might look kinda lumpy from the outside though.

Or you could put sunblockers between the surface and the star. This might ruin some peoples view of your star, and do remember Mr Burn got shot when he tried it.

One way is to not make it a perfect sphere. Earth is actually an oblate spheroid so it is not a stretch to make your thing a prolate (elongated) spheroid. This would cause the poles of your sphere to be further away from your mini-star, while the center ring is closer to it. This should cause the temperatures to be warmer near the center and colder near the poles.

depends how solid it is, if your dyson sphere is a near heatproof wall then you have an interesting question, because you would have a pressure cooker.

However, if its anything like the dyson sphere in Peter F Hamilton's commonwealth saga (which was a modified forcefield), that allows all light out by red-shifting it into infrared, then nothing changes to normal, beyond limitation of resources.

• Can you explain that more? If it’s only a pointer to the novel, then it ought to be a comment. Commented Nov 5, 2016 at 9:43

Heat escapes to the outside at the "poles".

This gives an effect of being cold near the poles, while hot near equatorial places.