>I was imagining a sort of staged rocket, where you ejected the casing of the previous rockets as you slow, so that the mass of the rocket was always a small fraction of the mass of the fuel.
Of course, but your very last stage is still a rocket with a reactor. And if you cannot build a rocket with 30g motor+reactor weight, then you cannot go to such small stages and your final mass on arrival includes the smallest efficient rocket motor / reactor you can build, zero fuel, and a velocity that is below escape velocity of your target solar system (once you are below escape velocity I’ll grant you maneuvers with zero mass cost, using solar sails; regardless, tiny solar-powered ion-drives appear reasonable, but generate not enough thrust to slow down from relativistic to below-escape in the time-frame before you have passed though your target system).
>But Eric Drexler is making some strong arguments that if you eject the payload and then decelerate the payload with a laser fired from the rest of the “ship”, then this doesn’t obey the rocket equation. The argument seems very plausible (the deceleration of the payload is *not* akin to ejecting a continuous stream of small particles—though the (tiny) acceleration of the laser/ship is). I’ll have to crunch the number on it.
That does solve the “cannot build a small motor” argument, potentially at the cost of some inefficiency.
It still obeys the rocket equation. The rocket equation is like the 2nd law of thermodynamics: It is not something you can trick by clever calculations. It applies for all propulsion systems that work in a vacuum.
You can only evade the rocket equation by finding (non-vacuum) stuff to push against; whether it be the air in the atmosphere (airplane or ramjet is more efficient than rocket!), the solar system (gigantic launch contraption), various planets (gravitational slingshot), the cosmic microwave background, the solar wind, or the interstellar medium. Once you have found something, you have three choices: Either you want to increase relative velocity and expend energy (airplane, ramjet), or you want to decrease relative velocities (air-braking, use of drag/friction, solar sails when trying to go with the solar wind, braking against the interstellar medium, etc), or you want an elastic collision, e.g. keep absolute relative velocity the same but reverse direction (gravitational slingshot).
Slingshots are cool because you extract energy from the fact that the planets have different velocities: Having multiple planets is not thermodynamic ground state, so you steal from the potential energy / negative entropy left over from the formation of the solar system. Alas, slingshots can’t bring you too much above escape velocity, nor slow you down to below escape if you are significantly faster.
Edit: probably stupid idea, wasn’t thinking straight <strike> Someone should tell me whether you can reach relativistic speeds by slingshotting in a binary or trinary of black holes. That would be quite elegant (unbounded escape velocity, yay! But you have time dilation when close to the horizon, so unclear whether this takes too long from the viewpoint of outside observers; also, too large shear will pull you apart).</strike>
edit2: You can afaik also push against a curved background space-time, if you have one. Gravity waves technically count as vacuum, but not for the purpose of the rocket equation. Doesn’t help, though, because space-time is pretty flat out there, not just Ricci-flat (=vacuum).
That’s what I used to believe. But now, on closer analysis, it seems that it doesn’t. The rocket equation holds when you are continuously ejecting a thin stream of mass; it doesn’t hold when you are ejecting a large amount of mass all at once, or transferring energy to a large amount of mass.
The thought experiment that convinced me of this: assume you have a gun with two barrels; you start at rest, and use the gun to propel yourself (ignore issues of torque and tumble). If you shoot both barrels at once, that’s two bullets, each of mass m, and each of velocity v. But now assume that you shoot one bullet, then the other. The first is of mass m and velocity v, as before. But now the gun is moving at some velocity v’. The second bullet will have mass m, but will be shot with velocity v-v’. Thus the momentum of the two bullets is lower in the second case; thus the forward momentum of the gun is also lower in that case.
(The more bullets you shoot, and the smaller they are, the more the gun equations start to resemble the rocket equation).
But when you eject the payload and blast it with a laser beam, you’re essentially just doing one shot (though one extended over a long time, so that the payload doesn’t have huge acceleration). It’s not *exactly* the same as a one shot, because the laser itself will accelerate a bit, because of the beam. But it you assume that, say, the laser is a 100 times more massive than the payload, then the gain in velocity of the laser will be insignificant compared with the deceleration of the payload—it’s essentially a single shot, extended over a period of time. And a laser/payload ratio of 100 is way below what the rocket equation would imply.
>I was imagining a sort of staged rocket, where you ejected the casing of the previous rockets as you slow, so that the mass of the rocket was always a small fraction of the mass of the fuel.
Of course, but your very last stage is still a rocket with a reactor. And if you cannot build a rocket with 30g motor+reactor weight, then you cannot go to such small stages and your final mass on arrival includes the smallest efficient rocket motor / reactor you can build, zero fuel, and a velocity that is below escape velocity of your target solar system (once you are below escape velocity I’ll grant you maneuvers with zero mass cost, using solar sails; regardless, tiny solar-powered ion-drives appear reasonable, but generate not enough thrust to slow down from relativistic to below-escape in the time-frame before you have passed though your target system).
>But Eric Drexler is making some strong arguments that if you eject the payload and then decelerate the payload with a laser fired from the rest of the “ship”, then this doesn’t obey the rocket equation. The argument seems very plausible (the deceleration of the payload is *not* akin to ejecting a continuous stream of small particles—though the (tiny) acceleration of the laser/ship is). I’ll have to crunch the number on it.
That does solve the “cannot build a small motor” argument, potentially at the cost of some inefficiency.
It still obeys the rocket equation. The rocket equation is like the 2nd law of thermodynamics: It is not something you can trick by clever calculations. It applies for all propulsion systems that work in a vacuum.
You can only evade the rocket equation by finding (non-vacuum) stuff to push against; whether it be the air in the atmosphere (airplane or ramjet is more efficient than rocket!), the solar system (gigantic launch contraption), various planets (gravitational slingshot), the cosmic microwave background, the solar wind, or the interstellar medium. Once you have found something, you have three choices: Either you want to increase relative velocity and expend energy (airplane, ramjet), or you want to decrease relative velocities (air-braking, use of drag/friction, solar sails when trying to go with the solar wind, braking against the interstellar medium, etc), or you want an elastic collision, e.g. keep absolute relative velocity the same but reverse direction (gravitational slingshot).
Slingshots are cool because you extract energy from the fact that the planets have different velocities: Having multiple planets is not thermodynamic ground state, so you steal from the potential energy / negative entropy left over from the formation of the solar system. Alas, slingshots can’t bring you too much above escape velocity, nor slow you down to below escape if you are significantly faster.
Edit: probably stupid idea, wasn’t thinking straight <strike> Someone should tell me whether you can reach relativistic speeds by slingshotting in a binary or trinary of black holes. That would be quite elegant (unbounded escape velocity, yay! But you have time dilation when close to the horizon, so unclear whether this takes too long from the viewpoint of outside observers; also, too large shear will pull you apart).</strike>
edit2: You can afaik also push against a curved background space-time, if you have one. Gravity waves technically count as vacuum, but not for the purpose of the rocket equation. Doesn’t help, though, because space-time is pretty flat out there, not just Ricci-flat (=vacuum).
>It still obeys the rocket equation.
That’s what I used to believe. But now, on closer analysis, it seems that it doesn’t. The rocket equation holds when you are continuously ejecting a thin stream of mass; it doesn’t hold when you are ejecting a large amount of mass all at once, or transferring energy to a large amount of mass.
The thought experiment that convinced me of this: assume you have a gun with two barrels; you start at rest, and use the gun to propel yourself (ignore issues of torque and tumble). If you shoot both barrels at once, that’s two bullets, each of mass m, and each of velocity v. But now assume that you shoot one bullet, then the other. The first is of mass m and velocity v, as before. But now the gun is moving at some velocity v’. The second bullet will have mass m, but will be shot with velocity v-v’. Thus the momentum of the two bullets is lower in the second case; thus the forward momentum of the gun is also lower in that case.
(The more bullets you shoot, and the smaller they are, the more the gun equations start to resemble the rocket equation).
But when you eject the payload and blast it with a laser beam, you’re essentially just doing one shot (though one extended over a long time, so that the payload doesn’t have huge acceleration). It’s not *exactly* the same as a one shot, because the laser itself will accelerate a bit, because of the beam. But it you assume that, say, the laser is a 100 times more massive than the payload, then the gain in velocity of the laser will be insignificant compared with the deceleration of the payload—it’s essentially a single shot, extended over a period of time. And a laser/payload ratio of 100 is way below what the rocket equation would imply.