Bomb#20
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To expand on what Loren wrote, a rocket, unlike an aircraft, has to do everything itself. So it has to be hyper-efficient. The trouble is, there are two different measures of efficiency -- energy efficiency and reaction-mass efficiency -- and they conflict with each other. To get a given amount of thrust, i.e. a given push, you have to throw some reaction mass out the back, at some speed. The strength of the push is just the amount of mass you jettison multiplied by how fast you shove it away. So to be reaction-mass efficient you want to throw it out as fast as possible: make it fly away from you twice as fast and you only need to throw away half as much stuff to get the same push. But kinetic energy is E=1/2mv2, and that square term means that to be energy efficient you want to throw it out as slow as possible. Throwing away twice as much stuff at half the speed takes only half as much energy to give you the same push. Since the rocket is carrying with it both the energy and the reaction mass, there's always this balancing act going on, where the rocket scientists had to figure out how fast to throw the reaction mass in order to not run out of either mass or energy too soon. "Specific impulse" is basically the same thing as the speed of the rocket exhaust, just expressed in funny units. The idea is, if you're throwing your reaction mass out so fast that you accelerate in the opposite direction at 1 g, "specific impulse" is however long can you keep doing that before you run out of reaction mass. (And a bigger fuel tank doesn't help, because that just means you'll have to throw out more fuel per second, just to accelerate your bigger fuel tank at 1 g.)What's the thrust impulse distinction?
There are basically two kinds of space rockets we've built: high-thrust low-specific-impulse rockets like the Space Shuttle, and low-thrust high-specific-impulse rockets like the Dawn space probe. We don't make the high-thrust high-specific-impulse rockets you need for your proposal, because the energy requirements are severe -- you shoot out a lot of reaction mass very fast, and pay the v2 penalty. The only things we know how to build that deliver that much energy per kilogram are nuclear reactors and atomic bombs.