athelas, 0-.25c in 30 minutes would require an acceleration of over four thousand G’s. Man, that will certainly take the wrinkles out of your spacesuit.
Mangetout, I’m not sure how to calculate the force due to each particle (F=ma) since we do not know how quickly the particle would be accelerated to the speed of the ship. (Also, F=ma breaks down at larger fractions of c. Gamma comes in somewhere: F = m^2c^2 - Gamma(m^2a^2)? )
Using E=mc^2 to find the amount of energy a hydrogen molecule could possibly release gives 10^-30 x 10^16 = 10^-15 J.
Using your 30 million particles per second estimate still only bring us to 10^-9 J per second, ie. still negligible. However, you are absolutely correct in postulating a Hiroshima should anything like a small rock hove into view.
Indeed, JR, that’s one heckuva rollercoaster. I believe Start Trek uses “inertial dampers” to compensate for this problem. When the writers were asked how they worked, they replied “fine, thanks”.
I’d love to see the 10 scientific revolutions required to make the journey possible. But I think you’ll still be discussing this in 50 years. Star Trek was not a documentary.
My turn to screw up some numbers.
We will travel at .1c for example
Lets assume that there are 10^6 nucleaons/m^3 ( 1 atom /cm^3) in the interstellar medium. Now the trip is 4.5 lyrs (4.15x10^16m) and our ship is 10m across and circular for an area of about 75 m^2. So we will burrow out 3.26x10^18 m^3 hitting 3.26x10^24 nucleons in total.
Now now lets assume that 90% of the particles are at rest relative to the ship. So they need to decelerate releasing their energy. 1x10^-11 J. Now assume that 10% will hit with an opposite velocity of .5c (relatively .6c in total) for an energy release of 4x10-11J.
So total released energy if 3.26x10^24*(.9x10^-11+.4x10^-11) = 4.2x10^13 J. Now over 40 years this work out to having the front bathed in 33.4 kW.
Now ice has a heat of fusion of 6x10^3 J/mole so we would need 1.05x10^10 moles of ice. Now water has 18g/mole so we need 18.9x10^7 kg of water. This works out to 18.9x10^4 m^3 or water. With our ship being 75m^2 the ice needs to be 2.5 km long.
Now I’ll sit back and await the obvious math mistakes.
** Scott Dickerson **
If I did the math right, according to your estimates, there are exactly 0.0004 civilizations transmitting right now. In that case, SETI really IS a waste of time and money.
My figures:
N* -> 100 000 000 000
fp -> 1/3
ne -> 1 ? (I’ll asume there’s 1 earth like planet in each planetary system)
fl -> 0.8 (I’m optimistic about life in that earth like planet)
fi -> 1/3 (I’m being waaaay more optimistic than you about the evolutionary advantage of intelligence)
fc -> 1/2 (i’m counting that if you are intelligent, you’ll someday send a message to space. Although I cut it in half just to be safe)
fL -> 1/10,000,000 (I’m guessing we’ll be transmitting at least 10 times as long a we’ve been. And take that as a standard)
This results in 444 currently transmitting civilizations in the milky way. (if I did the math right). That is certainly not to many. What a bummer.
You are assuming that the ice retains all the heat forever. But a spaceship shield would lose heat by radiation, and if that isn’t enough it could be connected to a cooling device, so this isn’t a valid assumption. I think the way to calculate the shield loss rate is to calculate the power input from interstellar gas/dust, make assumptions about the radiation environment, and find the equilibrium temperature of the ice surface. Then you can calculate the sublimation rate. I’m afraid I don’t have the numbers handy to do the calculation.
I was assuming the incident energy vapourized the ice. 445 J/s will vapourize .07 moles/s. It’s a back of the envelope calculation kind a thing.
If anyone has a fluid dynamics book, it would be interesting to see how the interstellar environment mimics an atmosphere at velocities nearing c. Sleek ships that are aero(interstellar?)dynamic might minimize the problem.
What about a sweeper ship? Have an immense magnetic field to sweep all those hydrogen atoms into the accelerator then accelerate those out the back? Add some extreemly high power lasers to the front, a way to harvest the hydrogen and store it. The ship can then get in a comet like orbit through the Ort cloud and it can vaporise and harvest any comets it finds. It would also need a VERY good tracking system to find any pebbles or bigger in its path so it can vaporise them. The front and back of the ship would be mirror images ie the engines can run forward or backward.
The trip would be like this. The ship would be created in Earth or Sol orbit, perhaps even by finding a handy asteroid such as Eros, mining it out hollow (there SHOULD be some profit by mining it out…). The hydrogen and oxygen would be mined on the moon and launched via railguns to the ship. When the ship is built and fueled (both will be underway at the same time) it will use a large chunk of its fuel to get in a comet like orbit around the Sun. When it gets to the Ort cloud it will harvest any comets it comes accross by altering its orbit slightly or by towing them with other smaller ships. This part of it will be unmanned, controlled by AI. When the ship comes back closer to the sun a manned ship is sent to bring over the colonists, already in suspended animation (which has been perfected during the ships long Ort orbit). The manned ship hooks up with the Ship, brings over the frozen colonists, a small unfrozen crew, supplies, and (if neccesary) tops of the fuel tanks. At the right time the Ship accelerates in a Sol slingshot orbit. Once again, as it passes through the Ort Cloud it can harvest any comets it comes accross, once again possibly by using tug ships. Once its free of the Ort cloud and nearer to intersteller space it can turn its engines to max and really acclerate. Sometime during this time the crew would go into suspended animation, and perhaps have a 2 month (S-time) rotation of someone to keep an eye on things. It would then use all or say 2/3 of its fuel for accl (this depends on how much hydrogen it can harvest and how much it needs for deccl) which I’d say would be around 1/4 of its journey. The sweeper would still be functioning at this time to prevent it from damage. After the engines shut off, it would accl by the sweeper only. When it came time to begin deccl (at the 1/2 mark?) the sweeper would switch to harvest mode and store all the hydrogen it comes accross. The hydrogen would be deccelerated by the Particle Accelerator which should have some deccl effects on the ship, and like I said the hydrogen would be captured and stored. At the proper time the ship would then reverse its engines and using the stored hydrogen as accelrent decl as much as it needs. At this time anything in the ships path should not be a problem. It once again uses a slingshot like orbit to deccl, and if all the math was right it would be in a proper Alpha Centauri orbit.
As for what powers the Ship, either a Plutonium Fission reactor, a Hydrogen Fusion reactor, or a combination of both.
Another thing to consider is if Alpha Centauri is moving toward or away from The Sun. If its moving away, the Ship would not need to deccl as much.
I’m sorry this post is so hinked I’m typing as fast as it comes to my brain and I’ve had WAY too much coffee.
CHAOSGOD:
Thanks for doing the math!
I hope everyone keeps in mind that this equation is about the existence, at a given time, of EM-transmitting cultures; not an estimate of how many “intelligent” cultures exist. My obscure point is to say that EM-type communication is likely only a minor waystation as intelligence develops.
BIOHAZARD:
You might find my post, above, interesting. It discusses the sort of craft you have in mind.
Is that the correct figure? (Had I been labouring under a wrongful assumption of 1 particle per cubic metre?) - if so, that’s worse, ten million times worse than I thought.
Or maybe a light or microwave powered craft.
Light-powered craft of that particular design won’t work in space; they don’t actually get their thrust from photons, but from air that is rapidly heated by a laser and used as a propellant; in some ways, it would be more honest to describe them as ‘air-powered’.
The number I found was 1 nucleon/cm^3 which scales up to 10^6/m^3, and its only a million (10^6) times worse, how bad can that be?
Since we’re in GD…cite :The Interstellar Medium
Darn it, when I went to school, the interstellar medium only had an average density of 1 atom of hydrogen for every ten cubic centimeters. Now it’s up to 1 atom per cumit centimeter? Who’s been dumping all the hydrogen into the galaxy when I wasn’t looking?!
I know but that article mentions carrying hydrogen for outerspace propellant.
You’re right, only a million times worse, not ten million.
Well even then its not that bad, at least it didn’t work out to needing 2500km of ice.
If we’re lucky scr4 might be able to get better numbers than my roughed out ones.
It’s a big empty galaxy, we have plenty of time.
Alien’s ideas about warping space to increase speed seem speculative to me, but there is nothing speculative about warping space to allow for greater acceleration. If we could get an extremely massive (or extremely dense) body to move at an extremely high acceleration, it would create a “wake” for a spaceship to follow. That spaceship could, in Earth’s reference frame, match the extreme acceleration without experiencing any acceleration in its own reference frame. If we could get our hands on 10^27 kg of neutron star material (and keep it from flying apart), we could send our ship at several thousand g’s without harming the passengers. However, the size of the ship would be limited due to tidal considerations. This would have the bonus of having those pesky hydrogen atoms slam into the lead body rather the spaceship proper. Of course, while this has no theoretical problems, the practical aspects of getting 10^27 to accelerate at several thousand g’s are rather daunting.
A more realistic plan would to build a giant laser that would be aimed at the spaceship (was this suggested before?). This would eliminate the need to carry along fuel, which completely changes the energy calculations (although the redshift would make it look to the spaceship like the amount of power the laser is putting out is continually decreasing; it might make sense to ramp up the power to compensate) . In fact, there’s no theoretical reason why the energy from one trip couldn’t be reused in another, although the practical problems in storing that much energy in a reusable form may very well be insurmountable.
Here’s a riddle: if we had two ships, each with a mirror, the first could send a laser beam at the second. The recoil from the laser would push the first away from the second. When the laser beam hit the second one, it bounces off the mirror. The recoil from this bounce will push the second away from the first. The beam will bounce back and forth, each time pushing the spaceships away from each other. The two spaceships will accelerate forever. Why is this not a feasible method of propulsion? (Hint: nothing I have said is untrue, but some of it is misleading).
One last thought on which to ponder: there really isn’t any (current) sane reason to go to another solar system. Therefore, any group that goes probably won’t be sane (eg religious cult). If humanity colonizes other stars, Earth may end up the only place where humanity isn’t ruled by religious fanatics.
This page says that the density of the interstellar medium in the “local cloud” is 0.1 particles per cubic centimeter. The Handbook of Space Astronomy and Astrophysics (my favorite reference, mostly because it was written by my former advisor) says the particle density is 0.1 cm[sup]-3[/sup] between clouds, but I think by this definition the area around us is “between clouds.”
By the way, The Ryan, what do you mean there is no reason to go to another solar system?? Besides all the valuable scientific knowledge, there’s one important and perfectly sane reason: Because we want to.
The Devil Raccoons of Luna, of course! (Though I can no longer find the link to Opal’s hilarious picture! :()