Deja Vu

That's precisely what I was thinking. To store it though you would need a solid or a liquid fuel that has a very large energy density. This is of course assuming that the collectors on such a sphere have 100% efficiency, which of course implies that a real life dyson sphere would collect less energy then is available from the sun. I should note that I just realized that I made an error when calculating that figure above, I had added an extra digit somewhere. The correct figure should be 2.236x10^27 J. Doesn't change difficulty of moving one though. Also note that the thrust generated from solar sails alone would be wholesomely inadequate to keep the sphere from crashing into the sun. Should the gravity of an object, say, a gas giant or a small star, perturb the dyson sphere too much, you would also have a tough time trying to adjust it. The best solution, IMO, would be to just simply use less mass then is available for the construction of the Dyson sphere and/or to use the gravity of other bodies to help keep it adjusted.

In your opinion, what equations, solutions, or sets are the most elegant math equations ever solved or conceived of? Personally, I like Euler's identity. That is, e^(i*pi) +1 = 0. The way it is proven is also something to marvel at too, since it comes directly out of complex analysis.

Thank you. On the subject of Jupiter's core, there are many competing theories as to what it is made out of. As for it's mass, it is not equivalent to thousands of Earth's unfortunately, the mass of it's core is at most about 15 times the Earth's mass from what I've read. Even then though, that's still a substantial amount. The composition of it's core is mostly debated, with some saying that it is rocky, and others saying that it might be made of ice or of organic material. They all agree though that the core is solid. Regardless, I think it is very unlikely we will use any of Jupiter's mass in a Dyson sphere. The pressures near the core are enormous, and in my opinion it would be easier to mine a star then to take material out of a gas giant's core. It's moons might be used though. And another thing, why bother? It would just simply add more mass and make it even more difficult to maintain.

Yes, that asteroid is called 1950 DA. It is about a kilometer wide. I would hate to be around when that thing hits us, as that would cause destruction on a scale not seen since the time of the dinosaurs. Luckily, we have 800 years to deal with it, if we decide to continue with space exploration that is.

Oooo, I love this topic, allow me to add something to this here. On constructing the dyson sphere (or swarm, which ever you prefer), one has to remember that not all of the mass in the solar system would be suitable for building. Most of the matter in the solar system is hydrogen, with Jupiter being more massive then all of the planets in the solar system combined. So, the Dyson sphere itself will not be as massive as some think. The entire mass of all the planets in the solar system is estimated to be about only .135% of that of the entire solar system, with the Sun being the bulk of that. Jupiter is about 90% hydrogen, and so as such is unusable for building. Most of the usable material would come from the 4 inner planets, whose combined mass is calculated to be about 1.11822x10^25 kg. Please correct me if I'm wrong here, I'm not using a very suitable calculator for this estimate, though it does seem about right since Earth is about 5.97x10^24 kg and Venus about 4.88 x 10^24 kg respectively (Mars and Mercury have masses of at least an order of magnitude lower). The asteroid belt has less mass then that of even a small planet, so I won't include it. Anyways, 1.11822x10^25 represents all of the usable matter in the solar system needed to construct this dyson sphere. I don't have time right now to calculate how thick such a structure would be, I'll do it later, but given it's mass it will be very difficult to move or adjust the thing, if we assume the Sayonara's figure at face value. The energy needed to change it's velocity by, say 20 m/s, would be about 1.47775x10^28 Joules, using the formula E=1/2mv^2. Solar sails simply wouldn't be enough. Keep in mind though that this is a very simplistic calculation, I'm sure there are other things we would have to worry about or take into account. Given this, it would be much more practical to build a swarm. SkepticLance's idea isn't too bad compared to building a sphere.

Something seems familiar about this thread

I'm not sure if you already solved this problem, given the date you posted this, but I will help you out anyway. Given the info above, you are probably much better off using stratified sampling because there is a lot of variation (I may be wrong on this, I will need to see the data to be certain) on the students permanent addresses, their degrees, economic status, loan status, sex, race, etc. Stratifying the samples will allow you to make comparisons much more easily between them. The problem I see with clustering is that you might end up with sampling biases.

I'm kinda lost on you here, can you please elaborate some more on this? I don't think the logarithmic spiral would look like a cone when you add a 3rd dimension.

Hey there! New member from Pennsylvania. I'm a college student majoring in mathematics, going into my sophomore year. I don't know much of anything about the universe I live in, so that's why I'm here. My interests include Fishing, Anime and Manga, and MMORPG's, and history, the history of science and math in particular. Hope to have fun on this site.