segundus wrote:I don't understand this. Geostationary satellites orbit at the same speed the earth revolves. So if you launch one of them, why would you need to gain any speed in addition to the speed you already have from being on the surface of the earth?
Well. Basically, rotating the same number of rotations in a given time at a greater distance - such as in orbit, which we can all agree is farther from the center of the earth than the surface is from the center of the earth - requires more energy. This is because you're going faster and covering more distance.
A similiar example/experiment... do you have an office chair? Good. Clear some space. Now, start spinning, but keep your legs in. Once you're going as fast as you can, kick your legs out. You'll be going much slower... but if you pull your legs back in, you'll start going the same speed you were before you kicked them out, ignoring (ch)air resistance.
rmsgrey wrote:I think it's a Heinlein novel where a character observes that the idea of reaching escape velocity in order to get into deep space only applies if you're making essentially a ballistic launch (and then using your engines to compensate for atmospheric resistance) - if you can sustain the thrust, you could get into deep space at walking speed - it would just take longer and far more energy.
Actually, if you did it right, it wouldn't take any more energy. Get your periapsis sufficiently above the atmosphere, then burn prograde once in a while there. If you sent up an astronaut who could conjure up an infinite amount of food and water, you could just throw a loaf of bread backwards once in a while, singlehandedly propelling your spacecraft into the depths of space while dying of old age and bringing on Kessler syndrome years early.
The amount of energy to reach terminal velocity (and get past any further resistance you may face on the way out from atmosphere or solid objects) is the same amount of energy it would take to escape the sphere of influence and pass into the area where the sun's pull matters more than the earth's - though the earth's would still be exerting some force, it'd be negligible in comparison. And when you're on an escape trajectory, your speed at periapsis will, I believe, be escape velocity - though I could be wrong, it could just be your speed at periapsis if your periapsis were at the center of gravity of the body being escaped.
Regarding the what-if itself, he simply states it's impossible and doesn't discuss what would happen if it were possible, which is double irritating because it's theoretically possible. It's much more concievable than throwing a baseball at .9c - simply state that your fuel never runs out and detail the forces on the craft or any other problems it may run into from a light, 4m/s descent.