Dear Straight Dope:
I've always been puzzled by escape velocity. It always seemed to me that what one really needed was escape acceleration, which seems to me to be anything greater than 9.81 meters per second squared. If an object (rocket, meditating yogi, etc.) could maintain a constant acceleration of 10 meters per second squared for an indefinite period of time, wouldn't that result in something like an escape from the Earth's atmosphere? (I'm assuming of course that I don't need to worry about fuel for thrust or air density for lift.) Is a slow ascent into space just impossible on some level?
You’re correct that you could, in principle, leave the Earth at any speed. In fact, you don’t even need any particular acceleration, relative to the Earth: You do need to exert a force to counter gravity equal to 9.8 m/s2 times your mass, but then, you need to do that anyway to keep from falling through your chair. If you had a ladder into space (hey, don’t laugh–it’s seriously being considered, if we can make the materials strong enough), you could climb up it at whatever leisurely pace you’d like.
So what is escape speed all about, then? In order to escape the Earth slowly, you need to continually exert a force to counter gravity. But suppose that instead of a ladder, you have a cannon. You can give your spacecraft-to-be an initial speed, but after that, it’s on its own. If you take a typical cannon, point it straight up, and fire, the cannonball is going to go up for a while, then slow, stop, and fall back to the Earth. Put more powder in your cannon, and the ball will get higher before this happens.
But suppose you put enough powder in your cannon that the cannonball leaves the muzzle at 11.1 kilometers per second. Now something interesting happens: The cannonball doesn’t just get very high before turning around; it never never turns around. Gravity still acts on it, so it’ll slow down relative to the earth, but it won’t stop. It’ll continue forever into the Great Unknown, without your ever having to do more than give it that initial speed.
You’ll notice I’m saying “escape speed" rather than “escape velocity." The two terms aren’t interchangeable. Velocity is a vector, which means it has both magnitude and direction. But escape speed doesn’t depend on direction. If I have a high-powered cannon, I can point it wherever I want, up or at any angle, and my cannonball still won’t fall back to the Earth. I could even point it down, if there were a tunnel conveniently carved through the Earth so it wouldn’t just smack into the surface. Since the direction doesn’t matter, just the magnitude, what we have is escape speed.
You may also have noticed that escape speed isn’t needed for a rocket. A rocket isn’t like a cannon: It’s always producing thrust, even after liftoff. So why aren’t there any slow rockets? It’s largely a matter of cost. Burning rocket fuel is an expensive way to generate force, so you want to get it over with quickly, in order to waste as little fuel as possible supporting the rocket against gravity. But if you had enough fuel, and weren’t in a hurry, you could ascend as slowly as you liked.
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