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.
>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.