[Tycho?]

As the topic starter is probably starting to realize, there is no quick or easy answer to this question. It depends on a wide variety of variables and other bits of information not easily attained. I dont see how your teacher expected you to solve this without much more information.

A square root is the same as an exponent to one half. Square root of 4 = 4^(1/2) Its just a different way of writing it, makes derivatives easier.

"...recycling more and more energy, everywhere, except the outer perimeter. This matter will have an open side." This part doesn't seem to make sense. How is radiating energy the same as recycling it? Matter will have an open side? What does that even mean?

Pretty much yeah, but its not very useful to think of an orbit as a straight line in this context, its more just confusing.

You sorta have a point. Look up redshift effect on wikipedia, one of its causes is the expansion of the universe.

Oh yeah, actually I've read something like that. Use a laser to ionize a path of air to the target, then throw a big current down there. Thats actually a viable way to make a lightning gun.

You could probably find this out by looking up static electricity, spark, voltage or potential difference. You'll also need to know a bit about current (amperage), resistance, conductivity, electical ground and electric insulators. Seriously, you need to know about this stuff to talk about lightning guns, look it up on wikipedia. Anyway, electricity moves when there is a potential difference, which is when there is an excess of positive or negative charge. Since like charges repel and opposite charges attract, a large amount of say negative charge in one place will try to move where there are fewer negative charges and more positive charges. An example: You have two conducting rods, with the tips of the rods being a small distance away from each other. To get a spark, you would want an excess of one type of charge on one of the rods, and a difficiency of that type of charge on the other rod. When you add more (lets say negative charges) to one side, and take negative charges away from the other side, you create a potential difference. If this difference is large enough, the negative charges will travel through the air to the other rod, in order to equalize. (the air "breaks down" when it allows current to flow across it. You should look that up as well). Now on to the actual device. In order to make a spark (lightning is basically a VERY large spark) you need an excess of charge. The trouble is, that when you put your excess of charge somewhere it will discharge along the path of least resistance. For a lightning gun to work, the electricity will have to move from your gun, through the air, into your target, an into the ground. You have to make that particular path the one easiest for the electricity to travel through. Other wise your gun will just shoot straight towards the ground, or to a piece of metal sticking out of the ground. And I dont know a good way to make that happen, particularly over any kind of distance.

I highly doubt this is going to happen in that time frame. I doubt the US will be able to afford it, and its not like the Russians are swimming in money or technology at the moment. Besides the amount of helium 3 that is actually on the moon is little more than a guess. You need to go through very throurough surveying before you build a base on the moon to mine the stuff. And jesus, we can't even use helium 3 yet! We dont have even the most simple of fusion reactions down pat, there still in the experimental phase. Wait until ITER is up and running before you even think about helium 3.

Well it would certainly lead to bigger and better things, but that doesn't mean that things would change over night. If we have all the fundamental workings, we still have to figure out how these fundamental workings affect the universe and world we live in. So really it would be a lot like other breakthroughs in physics, where the technological breakthroughs come years or decades after the physics has been worked out.

Well B does have a lower mass than A, but why woud they pick the outermost star?

Thats a good question. Any star orbiting either Centauri Alpha or Beta would be recieving lots of light from both of them, so its not like you could have one star over another. I really dont know why they phrased it that way, quite strange.

Does anybody actually read sunspots posts? Because I know I stopped long ago.

I'd be quite skeptical of that, but true or not its would be neat to get the guy into a lab to see why his brain is totally different from not only humans, but most other living beings.

If the train you were on was going a very high percentage of c, like 99.99% c, you would see everything normally within the train. However people stationary relative to the train would look in the train and see things moving extremely slowly, while you in the train would also see people on the outside moving extremely slowly. There would also be lenght contractions, and disagreement between obververs about the mass of objects.

Well the way to solve it would be pattern anaylsis, going through and looking for things that repeat themselves, and see how they compare to letters or words showing up in regular english. But since we dont have any clues on what the cipher is I doubt any one here will want to take the time to decode it.

Mass can be created or (more easily) destroyed by converting it to energy, like in nuclear reactions.

Yup, that could work. I kinda doubt that would be more efficient than other ion drives though.

I dont think I've ever heard anybody with any credintials say the universe has any kind of edge. While it might be finite in extent, you wouldn't ever come come to a wall where the universe ends, you'd just be looping back around. But when talking about the entire universe and these sort of things, its best to take any opinion with a grain of salt. The best scientists in the world dont have anything but educated guesses on these sort of questions.

You dont need to "push against" anything. In the case of the space shuttle for example, it fires its rockets, and propells burning gass out at high speed. Since every action has an equal and opposite reaction (Newtons 3rd law) this pushes the shuttle forward. Another example is a gun. You are holding a rifle, and you shoot it, bang. Bullet flies out the barrell at high velocity. The gun flies backwards with an equal force, which is why you feel kickback. Rockets dont need to "push" against the air, the ground or anything else to function. As for how many particles are in space it depends on how close to a planet you are. 100km up is generally considered "space" but there would be far more particles there than in the space between stars.

http://www.google.com Seriously. At least look up what a black hole is before asking a question like this.

I got a valentine. From my friends girlfriend. Oh well, I can't say I actually care.