For my Science-Fantasy WIP I am using a Dyson-sphere like mega-structure as the setting. For seemingly infinite space without the headache, presented by the logistics of a space faring civilization. This particular mega-structure should perhaps be called a giga-structure since it has the diameter of the Solar System.

The surface of this giga-structure has an environment suitable for humans and other life with similar tolerances. The inaccessible interior house the eldritch mechanisms that sustain the world and drive its geological processes.

My questions are.

  1. What is the surface area in miles of this world?
  2. What is the distance from the equator to the arctic circle?
  3. What impact does the planet's size have on its climate and weather?
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    $\begingroup$ I don't think you understand what a Dyson Sphere is. It's not a giant planet-like object that you live on the outside of. It's a shell that you live on the inside of. $\endgroup$ – Nick2253 Feb 17 '15 at 15:35
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    $\begingroup$ A hollow sphere will have no gravity to stick you to the inside, so the "climate" would be vacuum just like space, but next to a wall. $\endgroup$ – JDługosz Feb 17 '15 at 16:01
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    $\begingroup$ @Trismegistus Then you need to be more specific in your question. You are not looking for a Dyson-sphere like anything. You are instead looking for a giant artificial planet. I recommend editing your question to be more clear on these points. $\endgroup$ – Nick2253 Feb 17 '15 at 16:52
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    $\begingroup$ Crazy how big this is, a "planet" at 40 AU would be worth about 1 trillion earths in terms of surface area. $\endgroup$ – Dan Smolinske Feb 17 '15 at 17:10
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    $\begingroup$ That wouldn't be a planet. It would be a star or more likely collapsed into a black hole. $\endgroup$ – bowlturner Feb 17 '15 at 19:28

What is the surface area in miles of this world?

The surface area of a sphere is $4 \pi r^2$, where $r$ is the radius. Now, you wrote

This particular mega-structure should perhaps be called a giga-structure since it is the size of the Solar System.

Besides being extraordinarily large, you have to define what you mean by "size of the Solar System." The edge of the Solar System is ill-defined. Look at this xkcd:

Voyager leaving the Solar System

There are a bunch of different definitions, all of which are incredibly different.

What is the distance from the equator to the arctic circle?

Assuming this is a perfect sphere, the distance from the equator to one of the poles is $\frac{1}{4}$ of a circumference: $$\frac{1}{4}2 \pi r = \frac{1}{2} \pi r$$

Again, you need to specify the radius. But any structure much larger than a typical Dyson Sphere would be really unstable.

How does the planet's sizes effect its weather and over all climate? Also there few lands masses relative to the size of the world's oceans.

I can't answer this. The concept of a giant Dyson Sphere is so unrealistic that this race has to have enough tricks up its sleeve to make whatever climate(s) it wants.

  • $\begingroup$ Well the sphere builders didn't make it for themselves, it's a sanctuary. Is there a site/site where one could go to enter areas/distances into the formulas and get the results? $\endgroup$ – Trismegistus Feb 17 '15 at 17:47
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    $\begingroup$ @Trismegistus Basically all you need is a calculator, but many sites will handle the unit conversions for you. (My favorite is WolframAlpha. Example, area of a 1-AU sphere using the formula $A=4\pi r^2$) $\endgroup$ – 2012rcampion Feb 17 '15 at 19:42
  • $\begingroup$ @Trismegistus WolframAlpha is definitely the way to go. $\endgroup$ – HDE 226868 Feb 17 '15 at 20:40
  • $\begingroup$ @2012rcampion Thanks for the suggestion. $\endgroup$ – HDE 226868 Feb 17 '15 at 20:41

First, the Solar system is not a set size. I'm going to use the furthest point in the orbit of Pluto as the radius of the solar system for my answer. Basically, your planet would be able to hold the Sun, all the planets, and Pluto completely within itself if it were hollow.

  1. What is the surface area in miles of this world?

$A=4πr^{ 2 }$ is the formula for the surface area of a sphere. The radius, in this case, is 7.4 billion kilometers. That means you have 688,000,000,000,000,000,000 square kilometers of surface area.

  1. What is the distance from the equator to the Arctic Circle?

The Arctic Circle exists because the Arctic exists. The Arctic exists because of the Sun and the Earth's tilt on its axis. The Wikipedia article on the Arctic Circle says that it is the line north of which the sun is visible for 6 months at a time and then not visible for the next 6 months. Therefore, the location of your arctic circle, and even whether you have one, is based on how you will provide sunlight to your megaplanet.

  1. How does the planet's size effect its weather and over all climate?

It certainly effects how you are going to get sunlight to the whole thing! Sunlight is what powers the weather. When there is wind, it is because of uneven heating of the Earth's surface. This is what causes high and low pressure zones, and air goes from high pressure to low pressure. That air moving is wind. Sunlight also causes water to evaporate. Then it forms clouds and travels with the wind to wherever it rains.

The really big question you need to answer:

How are you going to provide sunlight?

Sunlight is necessary. People need sunlight (not just light). The weather depends on having plenty of sunlight, and plants need it. No sunlight means no food chain and no weather. (No weather also results in no plants). There are several ways around this:

  1. Make it a true Dyson sphere Probably not what you want to do, but still an idea.*
  2. Make a really big sun to go with it This would be the closest to how the real world works but also not as interesting. Seems to me like a rather cheap solution.
  3. Make it an "inverted" Dyson sphere You could make it a Dyson sphere, but where people live on the outside and they get power from the star on the inside. Maybe you could put farms on the inside so they get sunlight.*
  4. Create an inverted solar system Maybe you could create a solar system where the stars orbit the giant planet. Probably the most interesting solution I have.

Warning: Do not try this at home

because it will collapse. Into a black hole. Unless you have some Unobtanium lying around to build it with, the planet will collapse under its own weight. The Sun does not collapse because of the sheer amount of energy it creates that "balances" its own weight. I'm not even going to do the calculations because it is so unrealistic for this planet to hold itself up.

I am not a physicist, but maybe you could make the planet spin fast enough for centrifugal force to keep everything where it is. Might make people dizzy though.

*Another warning: Energy supplies

You will have problems getting enough energy to plants, people, etc. if you go with option 1 or 3. This is because of the distance the Sun is away from your Dyson sphere/planet. Pluto is freezing cold because it is so far from the Sun. There is no atmosphere to get in the way of sunlight in space, but the rays of light are spreading out.

The energy output of the Sun every second is around $3.8\times { 10 }^{ 26 }$ Joules. You need to divide that between each of the $6.88\times10^{20}$ square kilometers of your Dyson sphere. That's about 552,326 Joules/sq. km/second, or 552 Joules/sq. m/second. Pretty good, right? Earth receives 1,400 Joules/sq. m/second. Not as good, although you might get by.

  • $\begingroup$ Parking the planet next to an immense White-hole would provided enough heat and light. If the artificial planet needs it's internal structure to be built from Unobtanium than so be it. The point of making the world so large is to have the vastness of space opera while still begin contained on a single world. $\endgroup$ – Trismegistus Feb 18 '15 at 19:29
  • $\begingroup$ I haven't done the research but you may have problems rotating the planet fast enough to get any kind of survivable day/night pattern. In this case you may want multiple light sources orbiting the planet. $\endgroup$ – FlyingPiMonster Feb 18 '15 at 21:53
  • $\begingroup$ Based on your comment here, I don't think you really need what you describe. The reason for the vastness of a space opera is the fact that there are relatively small (but still very large) interesting areas separated by distances that make travel take a long time. You could do this with a planet much smaller than a solar system, which would remove a lot of need for handwavium. Especially if tech levels on the planet are low enough to make travel difficult. Something 100x the surface area of Earth with sparsely placed Earth-like continents would probably get the right feel, if travel is by ship $\endgroup$ – Bryon Mar 12 '15 at 16:30
  1. Whatever you want it to be. The area is obviously dependent on the radius. Since a structure like this requires gravity manipulation and gravity manipulation currently is strictly handwavium there is no realistic value anyone can give. However, smaller would be better in both the star and the sphere. This is because even with the handwavium the matter the sphere is composed of must come from somewhere and bulk of it must be something other than hydrogen or helium, which kind of suck as building materials. Elements heavier than helium are comparatively rare and it seems unlikely anyone would use more than absolutely necessary for a wildlife preservation. Even that could still be huge, obviously.

  2. Concepts like equator and polar circle are not relevant to dyson spheres. These are defined by the angle of the Earth's axis of rotation relative to the plane of its orbit around the sun. While the sphere might rotate, no reason it would, but it could, an object surrounding the star cannot really have an orbit in any meaningful sense. And even if it did, the sunlight would always come directly from above and there would be no seasonal variation or none of the things that make the polar circles, the tropics, or the equator significant.

  3. Climate would be unusual. I think it would be dominated by the topography of the oceans and continents. The sphere would receive energy on its inner surface equally at every point and radiate an equal amount of energy as heat from its outer surface. Thus climate would depend on the differences on the ability to conduct heat from inner to outer surface. Less conductive parts would be hotter and have rising air. More conductive parts would be cooler and have descending air. These differences would create a presumably relatively stable patterns of winds and climate. Although there would probably be some repeating oscillation patterns as well as chaotic variations.

  • $\begingroup$ 1. I guess that i don't need exact figure for sizes. But an idea about the scale is useful for story planing. 2. the central region of my stories is an island chain stretching from the equator to the pole. Which is why I wanted to know the distance. 3.Occasional unstable or catastrophic is perfectly fine. $\endgroup$ – Trismegistus Feb 18 '15 at 19:15

You might ask on the Math SE how to find the surface area, quarter-circumference, etc. of any sphere. (#1 and #2)

@Nick2253, why not live on the outside? Interesting story ideas. It could be a functioning Dyson Sphere in the sense of capturing all the energy, but the "inside" is all industrial and the "outside" (where you have a "down") is houses.

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    $\begingroup$ You live on the inside for one main reason: sunlight. $\endgroup$ – Nick2253 Feb 17 '15 at 16:49
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    $\begingroup$ It's a bit chilly outside. $\endgroup$ – Serban Tanasa Feb 17 '15 at 16:51
  • $\begingroup$ If you have liquid helium for blood, the ground is still to warm without boots. The race is obsessibe about not wasting any usable energy: that's the reason for enclosing the sun and running matroshka layers of heat usage. $\endgroup$ – JDługosz Feb 17 '15 at 20:21

Based on your comments, you are not looking for a Dyson Sphere, but rather a massive artificial planet.

This will not work.

First off, the mass of such a planet would be astronomical. The gravity would be immense. All objects we know of even remotely approaching that size are gas giants or stars. This "planet" would be far more than capable of sustaining fusion, and would likely collapse into a black hole.

Even if you could somehow prevent the planet from collapsing, it would not have a habitable surface (if it even had a surface at all). Like Jupiter, the atmosphere would continuously transition from gas to liquid to solid thanks to the massive pressures.

Now, even if you got around all those issues, you still have the issue of energy. How are you going to provide sunlight to your world? Mount giant lamps in the sky? Assuming we are talking about a planet with a radius of Neptune's orbit, you would have to provide $6\times10^{28}\mbox{W}$ to provide equal energy as the sun provides to Earth. To put that in perspective, that is 200 times more energy than the total energy the sun puts out. You would have to capture 100% of 200 suns worth of energy, and then redirect that to the surface (just to provide similar ambient conditions, not to mention the extra energy to power your special machines).

  • $\begingroup$ I wanted to exhaust real solutions before turning to handwavium. Thus I posted the question here. There are massive stars and white-holes that this world could be parked in orbit around;which might solve energy issues. The core generates it's own power; attribute it to taping zero-point energy and or siphoning power from the quantum foam. $\endgroup$ – Trismegistus Feb 17 '15 at 17:40
  • $\begingroup$ @Trismegistus White holes are already handwavium. We receive 0.00000005% of the Sun's total energy on Earth. Orbiting the most luminous star known, which is $7.4\times10^6$ as luminous as the Sun, would still not be enough. You'd need to orbit something 10,000 times more luminous still. And that's not factoring in the different wavelengths and higher-energy radiation such a star would produce. $\endgroup$ – Nick2253 Feb 17 '15 at 17:53
  • $\begingroup$ If the world would need to be parked near one of brightest objects in the cosmos then that's just where I'll put it. The core could also pump heat to the surface. $\endgroup$ – Trismegistus Feb 17 '15 at 18:48
  • $\begingroup$ This iron planet 1 AU in diameter, if prevented by magic from collapsing would be so massive stars would orbit it. Ptolomaic Astronomy, anyone? $\endgroup$ – Oldcat Feb 18 '15 at 0:35
  • $\begingroup$ People, this is WB. We ask about "Impossible" Things all the time. Don't grief the guy. $\endgroup$ – Caleb Woodman Jan 6 '16 at 16:29

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