The Dyson Sphere - Philip Mar

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Project Progress

New idea!: Since Dyson (WAS) going to come to UBC, i was thinking this would make a good project: Dyson Spheres. I would try to ideally try to model a Dyson Sphere construction that would optimize habitability in it. For example, what would be the ideal distance from the dyson Sphere (given that all the energy is boucing around inside) what benefits would come about with the huge amounts of energy? What rate would the center ring have to orbit to create the ideal gravitational fields, and, given the curve of the sphere, what are the ideal latitudes (i'd expect the gravity to drop by some factor as one goes higher up in the sphere (inside). How would we regulate atmosphere? (no gravity inside to hold it in), what would be the ideal size and distance from the star inside? How is day and night regulated (perhaps another dyson sphere within that that has small 'slits'-- to simulate day and night. This would bring up interesting geometries to make sure that when the light reaches the outer dyson sphere, the times would be ideal. Finally, it would be best to either make up a computer generated model of how it would look like (from the inside--....),and how the light and heat changes within it. (which would be non trivial). On one hand, the part about gravity shouldn't be too difficult (since it was derived in 1st year physics in a very 'hand-wavy' fashion), but it would also be interesting to work on.

Hmm, I like Dyson spheres, but I know only the general notion -- you seem to have a much more detailed model in mind. It would make a great project if you can go beyond the simple stuff and solve for optimal shapes to get uniform pseudogravity under rotation while the star pulls in, balance the thermal load on the inside with radiative cooling on the outside, solve for thermal gradients across the shell, etc. etc. Dyson isn't coming?? Dang! -- Jess 19:41, 3 October 2008 (PDT)

I know its very sci-fi, but i was thinking of something like a solid-shell Dyson sphere -- which would require probably very advanced technology to even conceive. Is this fine still? I am very excited about doing this project instead of the lightning one.

So what's wrong with sci-fi? Show us what you have in mind, and I'm sure you will get loads of suggestions and kibbitzing. -- Jess 09:42, 5 October 2008 (PDT)

So far I have only derived the (relatively simple) equations for how gravity would vary as a function of angle from the equator (latitude), it came to be quite simple for any given component- [math]\displaystyle{ g_x=gcos(\theta) }[/math]. By appropriately putting the highest possible gravity (among the range on earth), i was able to obtain an expression for which 'range' of theta would have survivable gravity. I also worked out the equations for gravity for people living on the outside. It might not be trivial to 'balance out' the gravity for those outside and inside. I thought having some people live inside would make it possible to actually have sunlight; but if this becomes completely whimsical, i'll just forget it and work out how to make the outside surface livable.

I am now working on the temperature of the Dyson Sphere. I will first assume that the Dyson Sphere is a blackbody, then work out what kinds of temperatures are achieved by the surface itself (as a function of the area of the surface). I was just wondering if anyone could comment on whether this kind of assumption is valid. I was thinking that, if all the sun's energy was being partially absorbed, then reflected then partially absorbed again within the Sphere, wouldn't that mean that, eventually, all the Sun's energy was being absorbed anyway? Would this justify approximating the Dyson Sphere as a blackbody? Once I do this, I plan to measure the equilibrium temperature of the Dyson Sphere (it absorbs and releases the same amount of energy). Then I can get the overall temperature of the Dyson sphere, assuming the Dyson civilization doesn't use any of the energy for large-scale adjustments. Regarding the thermodynamics of a dyson sphere. I dont think it should be at equilibrium. I think that the point of a dyson sphere is to keep all of the energy radiated from the sun. What you could do is see how the net energy absorption should vary at every point in the dyson sphere so as to maintain some sort of temperature. I might be wrong. Jacob 22:03, 22 October 2008 (PDT) That's not right. Without thermal equilibrium, the sphere will keep heating up! It must radiate away the same power on the outside as it absorbs on the inside, unless it "stores some up" in the form of (e.g.) antimatter using some form of heat engine between a hotter inner surface and a cooler outer one. This is sort of the ultimate Greenhouse Effect, in that short-wavelength light is absorbed on the inside and long-wavelength thermal radiation is emitted on the outside, but to a good approximation you can assume thermal equilibrium. If you treat all surfaces as blackbodies, you can write down the outside temperature as a function of the temperature at the surface of the star and the ratio of the Dyson sphere's radius to that of the star. -- Jess 10:28, 23 October 2008 (PDT)

oh ok i guess you're right--i shouldn't say thermal equilibrium, i just probably mean some way to constantly use power to keep the temperature constant somehow. thanks jake! --Philip Mar 22:35, 22 October 2008 (PDT)

I also forgot to include 2 other cases--the thickness of the dyson sphere (because the emitting surface is larger than the absorption surface) and the fact that there IS a thermal gradient between the part that is a blackbody and the part that has an albedo (earth-quality 'atmosphere'). The thickness will make the equations slightly messier, but as long as we assume that they have the same temperature throughout, it should be ok. The thermal gradient is more difficult because the shell itself for sure must conduct heat (otherwise it wouldn't be able to emit it), and so it might turn out to be a really hard calculation. We'll see. --Philip Mar 12:32, 1 November 2008 (PDT)

The second step would be to include the "area of habitation" in the inside calculation. This would mean that there would have to be an "albedo" that the earth naturally has (so we mimic it). In this case, the power absorbed is still actually on the whole going to be the same, but; let us assume that the reflected energy does not come back to these areas of habitation, then the energy would be absorbed by the other sections (still blackbody)--we'll have to split up the terms to get the different power absorbed and power emitted for different regions (assuming non-conductivity of the material).

Lastly, we include the amount of energy we want for the Dyson civilization to use. In this case, I would have the absorbed power to equal output power (for use) and emitted power (blackbody). The output power needed will be calculated based on the Third Section on how to ensure stability, such that the dyson sphere does not drift.--Philip Mar 22:04, 22 October 2008 (PDT)

I am thinking about the "effective gravity" issue: what if you made a "Dyson cylinder" instead of a Dyson sphere? If you ignore the real gravity of the star, you can either spin up the cylinder to put the outside surface in orbit about the cylinder's mass (which acts as if it were all concentrated along the axis) or you could balance it so that the apparent outward acceleration on the inside was equal to the residual gravitational acceleration on the outside. Or you could have different "bands" with different conditions. The tricky part is, of course, that you can't ignore the gravity of the star; so the question is, can you distort the cylinder to spin it so that the apparent gravity is normal to its surface everywhere? (With "bands" I think you definitely could!) Food for thought. -- Jess 10:28, 23 October 2008 (PDT) Thanks Professor Brewer! I haven't put it any real values yet to the equations for a sphere--but i will try it and see what kinds of surfaces are possible. I think the cylinder idea is really interesting and i think it would be great for a computer simulation..hm...i'll try it out! Thank you again! --Philip Mar 18:06, 25 October 2008 (PDT)

I've got the equations for Temperature a function of radius, but can't seem to get it in terms of theta. We could assume that there is no thermal gradient between the 'habitable' and 'nonhabitable' area, by saying that there is some thermal insulator between the two sections. (which would actually make sense because we could increase the amount of power taken without affecting the temperature of the habitable area--who would want to turn on their lights to suddenly find their room to be half as warm)

Just as a side issue however, I was trying to solve for how to get the thermal gradient as a function of theta, the angle from the 'equator'. Its difficult because the formulas for 'conduction' are not necessarily applicable, as the power absorbed is not over some continuous function, but over an abrupt one, because there is an albedo in the habitable section. Also, the possible energy transfer between sections are functions of temperature, and because each element of the dyson sphere is variable with respect to temperature (which in itself is also a function of energy), it makes the calculations difficult. So for now, I don't think I'm going to be including anything about temperature gradients wrt theta. If anyone has any suggestions for how I might be able to solve this (maybe i overlooked something simple gah)... thank you --Philip Mar 16:24, 1 November 2008 (PDT)

I ran into an interesting question--how many points on the dyson sphere are necessary to uniquely determine the position of the Sun using only the Sun's flux? I wasn't too sure about the answer. --Philip Mar 20:06, 1 November 2008 (PDT)