You'd have your radiators in the shade, where it's at least a hundred degrees cooler and you have the thermal mass of the asteroid where you can dump heat temporarily. Sourcing Helium might be difficult, but maybe you can get it from one of the gas giants?
That'd be even less efficient; the gas giants have much deeper gravity wells than Earth, and it's correspondingly much harder to bring material up from them. Jupiter's exhaust velocity is 60 km/s, Saturn's is 35 - compared to a measly 11 km/s for Earth. And as the rocket equation tells us, the fuel required goes up exponentially the greater the change in velocity you need.
This is easy to google (I should have done so before) but still hard to believe. If that's peak speed for only a short time because of fuel limits, it's less hard to believe.
...what do you mean by "peak speed for only a short time because of fuel limits?" It's space. You don't need fuel to maintain speed. What's going to slow you down?
Oh: To clarify, "Escape velocity" is the speed you need to escape Earth's gravity well entirely, so that you are no longer orbiting the Earth at all; it's about the amount of velocity you need to go on interplanetary missions. If you just want to go to, say, the Moon, then you don't need to go that fast. If you just want to go to low Earth orbit (LEO), then orbital velocity's only around 7 km/s.
But that isn't "peak speed" or anything, that's just ... how fast you have to go to be in low Earth orbit. The International Space Station is traveling at 7.67 km/s right now.
