Q:

I know that a rocket has to have enough thrust to accelerate itself to about 25,000 mph to escape the Earth, but why that speed? Let’s say that in some futuristic vessel, it had 100 times more power than the fuel-propelled rocket and had an almost unlimited source of fuel. Couldn’t this vessel just push it’s way up gradually out of the Earth’s atmosphere at , let’s say, 1000 mph?

- Rex (age 41)

Myrtle Beach,SC

- Rex (age 41)

Myrtle Beach,SC

A:

Hi Rex,

Sure, you can build rockets that will escape the Earth's gravity more slowly. The futuristic rocket you describe would have to have a much higher exhaust velocity than current rockets have so that it can get more thrust while burning its fuel more slowly.

It turns out that this is a waste of fuel, though. Lifting a rocket up slowly in a gravitational field requires overcoming an extra constant downwards thrust. If the lifting is done slowly, the force of gravity times the time it acts is the change in momentum of the rocket due to gravity, which must be offset by throwing burnt fuel (exhaust) in the opposite direction. In the limit of a very very slow rocket which just hovers over the ground, it burns fuel but does not go anywhere.

It turns out the most economical use of fuel for a rocket is to burn it all as quickly as possible and let the rocket fly away ballistically when the fuel is gone.

It is also not possible to include an unlimited source of fuel because the unburnt fuel must be lifted along with the rest of the rocket. This is inescapable, because in order to get a Newton's 3rd law reaction push, some mass has to be tossed out the back side of a rocket, and that mass must have been carried along (of course if your rocket acquires mass from its surroundings, like air, and throws it out the back, you've made a jet engine which isn't a bad idea).

As for the escape velocity, that's just the the speed such that the kinetic energy of the rocket is big enough so that as it pulls out of the Earth's gravitational field and exchanges kinetic for potential energy, it has enough to make it "all the way out".

Tom

Sure, you can build rockets that will escape the Earth's gravity more slowly. The futuristic rocket you describe would have to have a much higher exhaust velocity than current rockets have so that it can get more thrust while burning its fuel more slowly.

It turns out that this is a waste of fuel, though. Lifting a rocket up slowly in a gravitational field requires overcoming an extra constant downwards thrust. If the lifting is done slowly, the force of gravity times the time it acts is the change in momentum of the rocket due to gravity, which must be offset by throwing burnt fuel (exhaust) in the opposite direction. In the limit of a very very slow rocket which just hovers over the ground, it burns fuel but does not go anywhere.

It turns out the most economical use of fuel for a rocket is to burn it all as quickly as possible and let the rocket fly away ballistically when the fuel is gone.

It is also not possible to include an unlimited source of fuel because the unburnt fuel must be lifted along with the rest of the rocket. This is inescapable, because in order to get a Newton's 3rd law reaction push, some mass has to be tossed out the back side of a rocket, and that mass must have been carried along (of course if your rocket acquires mass from its surroundings, like air, and throws it out the back, you've made a jet engine which isn't a bad idea).

As for the escape velocity, that's just the the speed such that the kinetic energy of the rocket is big enough so that as it pulls out of the Earth's gravitational field and exchanges kinetic for potential energy, it has enough to make it "all the way out".

Tom

*(published on 10/22/2007)*