Interstellar travel question

[RulerOfNothing]

This is something that has been bothering me for a while, and I am hoping that someone more knowledgeable than me about astrodynamics can help. It regards the problem of propelling a spacecraft from Earth's orbit to Alpha Centauri, and I want to know how to work out some facts about this hypothetical voyage (such as the required delta-v and the best position to launch from)

[ijuin]

Required delta-v depends pretty much on how soon you want to get there. Alpha Centauri is 4.36 light years from Sol, so at a cruising speed of 10% of the speed of light you will get there in 44-45 years. For a one-way mission, total delta-v is just over twice your cruising speed. For a round-trip mission, total delta-v is just over four times your cruising speed.

As for where to launch from, the delta-v involved in the flight is so much more than the velocity needed to orbit/escape from Earth that it pretty much doesn't matter where you launch from--though if your engines can not lift your entire starship from the ground into orbit, then you might want to assemble the whole thing in low Earth orbit.

Propulsion-wise, unless new discoveries in physics give us additional options, we have three viable choices for our engines:

1: Antimatter rocket. Antimatter is the most energy-dense fuel that can be carried, and with the use of drop-off fuel tanks, your starship can reasonably travel at 90% of the speed of light both ways on its voyage (especially if you refuel the 'matter' half of the reactant at Alpha Centauri instead of carrying all of your return fuel). Such speed can let you take advantage of relativistic time dilation to make the voyage shorter from the astronauts' frame of reference (only about two years each way instead of five).

2: Lightsails. Have about a terawatt of solar-powered lasers in our solar system focusing their beams onto the sail to drive it, and you can get up to 40-80% of the speed of light. By separating part of your sail at the opposite end to act as a mirror to reflect the laser back onto your spacecraft, you can slow down at the other end, and then you can do the same again (assuming that the people back on Earth keep the laser turned on) to accelerate back towards Sol.

3: Fusion. Being a hundred and fifty times less energetic than antimatter, you probably won't be going faster than 20% of the speed of light with this--unless you can build a workable Bussard Ram-Rocket, that uses a huge magnetic field to scoop up hydrogen from the interstellar medium, thus giving you an inexhaustible fuel supply. On the other hand, fusion reactors are much less likely to go kaboom if their fuel leaks, unlike antimatter.

[Sordid]

Needless to say, with all three of these options the 'viable' bit really means more of a 'slightly less sci-fi than warp drive, in that a century or two in the future it might, if we're lucky, become a useable propulsion method'. If you're talking about current technology, forget about it. A generation ship is pretty much the only way to go if you want to set out right away, but of course it won't be you arriving at the destination.

[cjameshuff]

Some sanity checks: the kinetic energy of a 1 kg at 0.9c is would take annihilating 1.3 kg of matter and antimatter to release. Relativistic delta-v:

dv = c*tanh(Isp/c*ln(m0/m1))

Assuming proton-antiproton annihilation for the bulk of the energy, Isp/c is 0.6:

0.9 = tanh(0.6*ln(m0/m1))

e^(atanh(0.9)/0.6) = m0/m1

e^(atanh(0.9)/0.6)*1 kg = 11.6 kg initial spacecraft mass. 5.3 kg of antimatter for each kg of spacecraft accelerated to 0.9c. Then you have to stop, delivering 1 kg to the destination for every 11.6 kg that you accelerate to 0.9c. This clearly requires unreasonable amounts of antimatter. Some form of matter annihilation that doesn't require antimatter would work...if we ever discover it.

Fusion has similar problems, it's only going to get you a few percent of c at best. Bussard ramjets do solve the problem of carrying mass+energy source, but in our region of space, they produce more drag than thrust once they get above a few percent of c. They might be useful for decelerating if you use something else to accelerate, though.

Given how difficult antimatter is to make, beam propulsion really seems like the only thing that is likely to get a payload to another system in a human lifetime. It completely sidesteps the big issue of having to carry a power plant and reaction mass on the accelerating craft. It's also not limited to lasers, though the particle beam options are probably better suited to lower power, higher thrust, shorter range applications within the solar system.

[cray]

1: Antimatter rocket. Antimatter is the most energy-dense fuel that can be carried

Antimatter by itself has a high energy density (about 100x better than fusion or 1000x better than fission), but that's a misleading idea unless you wave in magical forcefields.

When you start factoring in the mass of its storage units - particularly with current technology - the energy density goes to crap. I mean, right now you get a few thousand free-floating positrons or anti-protons stuck in electromagnetic traps, and it's even harder hard to trap neutral anti-hydrogen atoms at all. Using 100kg of magnetic trap for 1000 positrons is a very poor energy-to-weight ratio. Something on the order of multi-Avogadro's numbers. And there's leakage: the particles don't stay trapped, but rather it's only minutes or hours until they're gone.

On the other hand, fusion (which gets about 1% of the energy out of matter) or fission (at 0.1%) need much less in the way of tankage. Hydrogen (deuterium or tritium) doesn't store densely in terms of mass-of-hydrogen to mass of tankage, not by liquid fuel standards, but having 1 ton of tankage per 3 to 10 tons of hydrogen is much better than having kilograms per picogram (or nanojoule).

Now, if you figure out some way to carry big blocks of anti-iron in a simple magnetic field, then you can think about your 90% light-speed.

--unless you can build a workable Bussard Ram-Rocket,

Well, more to the point, 'unless you can build a workable protium fusion reactor.' It does no good to scoop up hydrogen that will only be inert reaction mass (and a drag, since you're accelerating it from 0 to your cruising speed - conservation of momentum).

A highly recommended book on the subject of realistic space flight is 'The Starflight Handbook: A Pioneer's Guide to Interstellar Travel,' by Mallove and Matloff. It's a collection of engineering studies on the difficulties, challenges, and solutions to realistic interstellar travel.

[ijuin]

Assuming proton-antiproton annihilation for the bulk of the energy, Isp/c is 0.6:

Alternatively, electron-positron annihilation gives ISP/c above 0.9, but then you have to figure out how to confine teracoulombs worth of them without protons and antiprotons to balance them.

Anyway, the rocket equation tells us that a mission propulsive delta-v exceeding four times the effective exhaust velocity (assuming no refueling) is outright implausible even with staging, and without staging the limit is around 2.5 times the effective exhaust velocity.

Needless to say, with all three of these options the 'viable' bit really means more of a 'slightly less sci-fi than warp drive, in that a century or two in the future it might, if we're lucky, become a useable propulsion method'.

By 'viable', I meant 'does not require anything that we believe to be outright impossible according to our current concepts of physics and engineering'.

For anything that we could build 'right now' (with current technology and a budget the size of the entire US Department of Defense), a few megawatt-class VASIMR engines powered by a fission reactor is the upper limit. http://en.wikipedia.org/wiki/VASIMR One of these could get us to Neptune in a single year, but interstellar travel within a human lifespan is still out of the question.

[cjameshuff]

For anything that we could build 'right now' (with current technology and a budget the size of the entire US Department of Defense), a few megawatt-class VASIMR engines powered by a fission reactor is the upper limit. http://en.wikipedia.org/wiki/VASIMR One of these could get us to Neptune in a single year, but interstellar travel within a human lifespan is still out of the question.

In terms of setting velocity records, I suspect we could do better right now with laser propulsion, actually. You can scale up lasers and optical apertures more easily than you can scale up reactor power and energy density. Double the reactors for a beam launch means double the acceleration, double the aperture means double the effective range of the beam. Double the reactors for a VASIMR launch means a considerably larger dry mass and a relatively small boost in acceleration and delta-v.

It's a bit early for missions to other stars, though. I'm thinking more along the lines of heliosphere probes consisting of a bare minimum of instrumentation, a few kilograms of sail and electronics, powered by the same beam used for propulsion.

[ijuin]

In terms of setting velocity records, I suspect we could do better right now with laser propulsion, actually. You can scale up lasers and optical apertures more easily than you can scale up reactor power and energy density. Double the reactors for a beam launch means double the acceleration, double the aperture means double the effective range of the beam. Double the reactors for a VASIMR launch means a considerably larger dry mass and a relatively small boost in acceleration and delta-v.

Maybe, but lasers-in-space for a photon-driven sail of a given acceleration will require orders of magnitude more electricity than a VASIMR system. Lasers require on the order of one hundred megawatts per newton of thrust, while VASIMR has been demonstrated at a power consumption of 50-80 kilowatts per newton of thrust for an exhaust velocity of 50 km/s, with power requirements increasing with the square of exhaust velocity (hypothetically 2,000 to 3,000 km/s if the power density could be raised to match the laser example above).

As such, laser propulsion for interplanetary manned flight will have to wait until gigawatt-class solar power satellites become available, while VASIMR can run on an array not much larger than that of the International Space Station (for within Jupiter's orbit at least). We could build a VASIMR manned mission to Jupiter by 2030 that could get there in less than a year if we cared to spend the kind of money that we spent on Apollo.

[Kosmos929]

Why not consider pulsed fission, as in Project Orion (the real one, not the one that we just killed)?

[cjameshuff]

Maybe, but lasers-in-space for a photon-driven sail of a given acceleration will require orders of magnitude more electricity than a VASIMR system. Lasers require on the order of one hundred megawatts per newton of thrust, while VASIMR has been demonstrated at a power consumption of 50-80 kilowatts per newton of thrust for an exhaust velocity of 50 km/s, with power requirements increasing with the square of exhaust velocity (hypothetically 2,000 to 3,000 km/s if the power density could be raised to match the laser example above).

All of the above assumes a lightsail craft of the same mass as the VASIMR craft. What you miss is that the thrust can be applied to a much lighter payload. The laser craft doesn't have to carry any reactors, and requires a tiny fraction of the thrust to achieve the same acceleration. Rather than massing a few hundred tons, it can be a few kilograms. It might take more power to exert a newton of thrust, but the same result will be achieved with on the order of a hundred thousand times less thrust.

The laser craft has no power density requirements...you could run it off hamster wheels if you stacked enough together, because the power source stays stationary. VASIMR carries its power source, and current power sources are really just not good enough to let it reach its potential (though they're plenty good enough to put it to work as an orbital tug or bulk transport craft).

As such, laser propulsion for interplanetary manned flight will have to wait until gigawatt-class solar power satellites become available, while VASIMR can run on an array not much larger than that of the International Space Station (for within Jupiter's orbit at least). We could build a VASIMR manned mission to Jupiter by 2030 that could get there in less than a year if we cared to spend the kind of money that we spent on Apollo.

No, VASIMR can't (usefully) run on such a small solar array. We're putting a small, low power one (200 kW) on the ISS soon, complete with battery pack to charge it up so we can actually run it, in pulses for a few minutes at a time. VASIMR scales up well to high powers, but realistically requires nuclear reactors (or beamed power) as a power source. If you're just throwing a few kilowatts at it, you may as well just use some form of ion drive, it'll be lighter and perform better.

A 10 MW beam could push a 1 kg sailprobe at 0.067 m/s^2. After a month, that adds up to 175 km/s, while still within 1.5 AU distance, without playing any fancy tricks like doing the boost during a solar flyby (like a beam-assisted H-reversal trajectory). All you need is a bigger aperture to increase effective range so you can keep accelerating. All you need to increase acceleration is total power...power density and energy density are irrelevant.

A 10 MW 50 metric ton VASIMR craft with 50 kW/N will get 10.5 km/s in that same time period. Improving overall delta-v significantly without making it far slower means squeezing more power and more energy out of a given mass of reactors, radiators, and other power systems. It'll take a lot more where it's going, but it isn't winning a speed race.

[ijuin]

The laser craft has no power density requirements...you could run it off hamster wheels if you stacked enough together, because the power source stays stationary. VASIMR carries its power source, and current power sources are really just not good enough to let it reach its potential (though they're plenty good enough to put it to work as an orbital tug or bulk transport craft).

Using solar panels of a similar power/mass ratio as those on the International Space Station would imply that any solar power system masses on the order of a hundred tons per megawatt. For your ten megawatt beam below, you would need to deploy over a thousand tons of solar panels--a daunting task if you have to use chemical rockets to lift that stuff up from Earth. Until we find a cheaper way of getting stuff into orbit (or start building them out of raw materials from the Moon or asteroids), economic considerations favor fission power over solar when you are at the multi-megawatt scale. You might do better using said fission reactor to power your laser instead of the VASIMR engine though . . .

A 10 MW beam could push a 1 kg sailprobe at 0.067 m/s^2. After a month, that adds up to 175 km/s, while still within 1.5 AU distance, without playing any fancy tricks like doing the boost during a solar flyby (like a beam-assisted H-reversal trajectory). All you need is a bigger aperture to increase effective range so you can keep accelerating. All you need to increase acceleration is total power...power density and energy density are irrelevant.

A 10 MW 50 metric ton VASIMR craft with 50 kW/N will get 10.5 km/s in that same time period. Improving overall delta-v significantly without making it far slower means squeezing more power and more energy out of a given mass of reactors, radiators, and other power systems. It'll take a lot more where it's going, but it isn't winning a speed race.

The 1 kg sailprobe is comparing apples to oranges--I thought we were speaking of manned spacecraft, which by definition would require dozens of tons of payload as a minimum? Sure, if your payload is small enough that the one ton of engine mass and dozen tons of reactor/structural mass dwarf it, the VASIMR looks like dead weight, but not so much when 50% of your non-propellant mass is payload. I think I specified a manned mission to an outer planet as an example of where VASIMR is optimal for a near-future (i.e. within our lifetimes) mission. Missions where the delta-v exceed three times VASIMR's plausible exhaust velocity will run into the same 'can't carry enough fuel' limitation as any other carry-your-reaction-mass craft.

[cjameshuff]

The 1 kg sailprobe is comparing apples to oranges--I thought we were speaking of manned spacecraft, which by definition would require dozens of tons of payload as a minimum? Sure, if your payload is small enough that the one ton of engine mass and dozen tons of reactor/structural mass dwarf it, the VASIMR looks like dead weight, but not so much when 50% of your non-propellant mass is payload. I think I specified a manned mission to an outer planet as an example of where VASIMR is optimal for a near-future (i.e. within our lifetimes) mission. Missions where the delta-v exceed three times VASIMR's plausible exhaust velocity will run into the same 'can't carry enough fuel' limitation as any other carry-your-reaction-mass craft.

Well, I was talking interstellar missions on human timescales in general, and...

It's a bit early for missions to other stars, though. I'm thinking more along the lines of heliosphere probes consisting of a bare minimum of instrumentation, a few kilograms of sail and electronics, powered by the same beam used for propulsion.

[cray]

Why not consider pulsed fission, as in Project Orion (the real one, not the one that we just killed)?

Basically, semantics: the 'exhaust velocity' (or 'specific impulse') is relatively limited on the scale of 'fast' interstellar flight. Believe it or not, raging plutonium or uranium explosions are not the hottest, fastest things in the universe, and to maximize the amount of velocity you get for a given mass of fuel, you want high specific impulses.

The solution is to shift to fusion. Peak speeds of 3-10% of light-speed are considered possible.

http://en.wikipedia.org/wiki/Project_Orion_(nuclear_propulsion)#Interstellar_missions

It's not speedy on human timescales, but fusion Orion ships do have some advantages over other fairly viable propulsion methods: acceleration and thrust are awesome, and the ships scale up great. You don't need to maintain mega-scale boost/brake lasers at Earth, but can instead just scale up nuclear bombs. After the first few kilograms of plutonium, you can just pile in the lithium deuteride and scale up arbitrarily. Reliable and simple.