If we could design something that could get up to 1/2 the SOL. what is the chance it would make it from earth orbit to the edge of the solar system without hitting something that would cause it to break apart? Also what about a trip of 4.5 lightyears in intersteller space?
Also don’t worry about accereration time just assume 1/2 SOL as soon as it leaves earth orbit.
The speed at which you travel (presumably in a straight line) through the system is going to make very little difference to the number of objects (if any) that you encounter (not quite true, as you are slightly more likely to have a moving object collide with you if you occupy each point along the route for longer); the problem, I would think, would be that encountering a speck of dust or possibly even a hydrogen atom (of which there are a few scattered about; something like 1 per cubic metre I think) at that speed is a far more serious event than it would be at lower speeds.
Travelling that fast is pretty dangerous. Just about anything you run into is going to cause damage and even interstellar space isn’t completely empty. In a solar system, planetary and asteroid bodies aside, I think you are even more likely to encounter the odd dust speck. At that speed (334,800,000 mph) even a piece of dust would likely put a hole in your ship. You had better have the equivalent of Star Trek’s deflector dish or some other means of protecting your ship or you aren’t likely to survive your 4.5 light year trip.
Space isn’t empty. There is dust etc. One of the Gemini (I think it was Gemini) had a window cracked or chipped by what is thought to have been something like a speck of paint. And Gemini was traveling at a speed far, far below half the speed of light.
The hydrogen atoms would become, effectively, a sleet of very hard radiation at .5C. Even if you missed every other physical object, you’d get cooked pretty thoroughly, unless you can find away to avoid interstellar hydrogen, or put it to use. Bussard Ramjet, anyone…?
At half the speed of light, your [symbol]g[/symbol factor will be about 1.15 . This means that any object “at rest” you encounter will have, as measured aboard the ship, a kinetic energy of about 15% of its mass. A one micron particle of reasonable density (which is probably something you could expect to encounter) would have a kinetic energy of about 47 Joules, comparable to what you might see in a thrown baseball. This is for each such particle you encounter, and there’s a lot of them. Whether your ship can handle this, of course, depends on the construction of your ship.
A Bussard ramjet probably wouldn’t be very useful, by the way, unless you have some means of getting energy out of the hydrogen more efficient than fusion. Even then, magnetic fields won’t have any effect on most of the matter you’ll encounter.
You mean in Star Trek? If so, Earth is most definitely NOT in the Neutral Zone - the Neutral Zone is analogous to the Korean DMZ (and that may have even been what the writers had in mind when they came up with the Neutral Zone and the Romulans). We, the Federation (including Earth) are on one side, the Romulans are on the other, and the Neutral Zone is in-between, approximately 1 light-year in diameter.
This picture should give you a better idea of the layout of the galaxy as it appears in Trek.
There is one extra (and I think important) item to consider with this. A one micron dust particle with the energy of a thrown baseball is far more dangerous than the baseball itself. I’ve been hit by thrown baseballs and it hurts but except for a nice bruise I walked away from it. Now consider the effort a nurse uses to stick you with a syringe…WAY below the energy of a baseball but she just poked a hole in me (and the syringe is bigger than one micron).
In short it’s about energy vs. the area the energy is spread across. Just like wearing snow shoes keeps you on top of the snow whereas just your shoes would let you sink into it. I’m not sure what damage a one micron particle with the energy of a baseball can do to metal and glass but I’d wager it’s worse than a baseball hitting the same spot. At the very least it will start abrading the outside of your spaceship. Again I don’t know how often you’re likely to run into these things at 0.5c but if it’s anything like a sandblaster I’ve seen working you’re going to be in trouble sooner or later.
Hmm… I worked out the energy for a 1-milligram speck of dust encountered at 0.5c, using the formulas someone presented in a previous discussion of impacts-in-space… And the figure came out to the kinetic equivelant of 2.5 TONS of TNT! Or 11.25 million Joules. Now, I know that striking even a tiny object like that at half the speed of light would be a pretty powerfull impact, and I was using a formula that doesn’t count for objects traveling close to light speed (Though that should make it -more- powerfull, right?), but that seems like it might be a bit off. Seems like it might be QUITE a bit off…
But, it looks like it holds up to the formulas… KE = 1/2mV[sup]2[/sup] for non-relativistic speeds, and 4.18x10[sup]15[/sup] Joules = 1.0 megatons TNT … Assuming I got those right, anyway. Obviously, it’s not going to be like a huge nuclear blast, but nuke-yield seems like a good way of visualizing extremely high energy states like that.
I tried looking over the formulas for relativistic kinetic energy, but… My head started hurting. Mainly because everyone puts down the formulas, but nobody explains them, or even what those variables stand for…
As for micron-wide object hitting with 47 joules of energy, I’m pretty sure it should be capable of blowing in one side of a ship and out the other, assuming it weren’t completely vaporized on impact (In which case you’ve got a 1-micron-wide object likely turned to plasma and fanning out at a velocity of a little less than 0.5c, carrying a small ammount of material from your hull with it). Probably wouldn’t be pretty. Extreme-velocity impacts generally aren’t
taps at the calculator and if I got this right, that micron-wide object at 47 joules would have about 60 million times the energy-per-area of a 9mm pistol bullet. Hell of a sandblaster…
(All of the above presented with the fact that I could be 100% wrong. Please feel free to correct me if I am)
OK, the total energy of an object is E = [symbol]g[/symbol]mc[sup]2[/sup]. m is the mass, and c is the speed of light. Watch your units here; the units you use for m and c will determine the units of your energy. For example, if you put your mass in kilograms and c in meters/second, then energy will be in kg m[sup]2[/sup]/s[sup]2[/sup] (also known as Joules).
[symbol]g[/symbol] is the relativistic dilation factor, given by [symbol]g[/symbol] = 1/sqrt(1 - v[sup]2[/sup]/c[sup]2[/sup]). It’s a dimensionless (i.e., unitless) number, and I unfortunately don’t know of any simple way to remember the formula. We’ll leave the derivation of this aside for this thread.
Now, this gives you the total energy, but that includes the “rest energy” which comes from the mass (E = mc[sup]2[/sup]), and we just want the kinetic energy, so KE = (symbol]g[/symbol] - 1)mc[sup]2[/sup]. In this example, we have v = .5c, so [symbol]g[/symbol] = 1/sqrt(.75) = 1.15 , so [symbol]g[/symbol] - 1 = .15 .
Note that this method is accurate for all speeds, but for speeds considerably less than the speed of light, KE = 1/2 mv[sup]2[/sup] is a good approximation. The energy given by the relativistic formula will always be higher than that given by the Newtonian formula.
A one milligram particle will be over a billion times more massive than the particle I calculated, and have an energy greater by the same amount, so yes, you should be seeing something that looks like a very large bomb. Fortunately, though, once you get away from low earth orbit, particles that big are pretty rare.
Cool! Thank you very much, that will be incredibly helpfull
I know, I was just curious how much damage a tiny fleck like that could cause. Maybe a speck of dust, or a grain of sand, or something like that. Not something you’d be too likely to encounter, but I imagine you wouldn’t be too likely to see it before hand, either. I can just imagine a bunch of ships traveling through a system and one of them spontaneously exploding…