Friday, November 18, 2005

The Real Prospects for Interstellar Travel (Part I)

I’ll talk a bit about the prospects for interstellar travel: While science fiction is filled with tales of predominantly interstellar exploits, and ships that zip from one star system to another like it was a piece of cake, realistically, based on the physics that we know right now, interstellar travel is a difficult proposition, even theoretically.

For one thing, unless some savant finds a way around the speed of light limit, and overthrows the limitations of mass, energy, and momentum allowing us to take such shortcuts around that limit, we are confined to travel at or below the speed of light. The nearest star, Alpha Centauri is 4.3 LY away. Other nearby stars are Barnard’s Star at 5.94 LY away, Lalande 21185 is 8.315 LY away. Sirius at 8.6 LY away. Procyon at 11LY, ect. If all it meant was to accelerate up to light speed, then journey for 5-20 years to reach the new star system, such a voyage would hardly be an insurmountable task. Difficult, yes, time consuming, yes, but quite doable. Foreseeable advances in technology, such as the possibilities of inducing hibernation, or of indefinitely lengthening lifespan through some genetic or medical technology (in which case we might not care as much about the duration of such a trip) could help ease the voyage. Or we could suck it up and deal with the isolation.

However, the critical assumption here is that we will be able to easily accelerate our spacecraft up to near light speed. This is a task of extraordinary magnitude, when viewed as a problem involving conventional rocketry.

The mass that a rocket has in fuel is related to the total amount of change in it’s own velocity (or delta v) that it can make, and to the exhaust velocity of the propellant. In idealized cases, such as gravity free, drag free flight, this is a good measure of how far and fast a given spacecraft can go.

Tsiolkovsky’s equation.
Mpayload/mrocket = exp(-delta v/exhaust velocity)

Our everyday chemical rockets have exhaust velocities on the order of 4000 m/sec. They can achieve delta vs of about 9000 m/sec – 11000 m/sec (with the use of staging). If we were to look at the mass ratio required to get from 0 up to the speed of light, delta v would be 3E8 m/sec.

Ln(Mrocket/Mpayload) = 3E8/4000 = 75000. In other words the mass of the rocket would be 10^32572 greater than the mass of the payload. In other words – no starship for you, smack! It’s clearly a ridiculous number. Chemical propulsion won’t cut it.

Nuclear fission propulsion, such as nuclear thermal propulsion can improve this number a bit. Exhaust velocities of 12,000 m/sec (for solid-core nuclear thermal with oxygen augmentation), 40,000 m/sec (for nuclear electric propulsion), 100,000 m/sec (for more exotic and theoretical forms) are possible. These would yield mass ratios of 10^10000, 10^3257, and 10^1302 respectively. Still, not anywhere near good enough.

Fusion propulsion, through reaction and expansion through a magnetic nozzle, promises very high Isps (Isp is effective exhaust velocity/9.8m/sec^2, and is a common measure of rocket fuel efficiency). Estimates vary wildly because we don’t have the technology yet to produce energy from a fusion reaction. Isps of 300,000 sec are given for IEC fusion at Mass ratio: 10^43. 10^43 is still problematic, due to the fact that you would have to have a tank for all that hydrogen. The tank must be less than 43 orders of magnitude lighter than the hydrogen fuel.

Anti-matter propulsion is the ultimate fuel source for a rocket. It packs the maximum possible energy (hence impulse) per unit of fuel. When anti-electrons react with electrons, only gamma rays and neutrinos are left over. But realistic anti-matter propulsion needs a way to direct the product particles out the back of the spacecraft, hence they need to be charged. Anti-proton-nucleus reactions do this much better. However, to do this, you need a large mass of anti-matter. Anti-matter is currently produced at great expense in particle accelerators, or trickles in very slowly in the form of some cosmic ray types. Anti-matter would get you mass ratios as small as 20. This is quite manageable, but for a payload of 1000 tons, you would need 19000 tons of an even matter/anti-matter mix!

Basically, conventional rockets won’t be able to get us up to light speed. There are other ways to work the problem, however:


Anonymous Anonymous said...

Is that the end? What are the other ways to work the problem?

Thursday, July 16, 2009 8:04:00 PM  

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