h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

I have read that a rocket must travel at 25,000 mph (escapce velocity) to leave earth orbit. However, if something like a Harrier Jump Jet left the ground at say 1 metre per second (ignoring fule restrictions and lack of air etc) and kept on going, up and up, why couldn't it eventually get into space - I would have thought the effect of gravity and air resitance would get progessively less the higher it went?

Firstly, that speed you've quoted is nothing to do with rockets. The escape velocity is the speed at which a projectile will not arc back to Earth but will break free of the Earth's gravitational field. Rockets, because they directly oppose the Earth's gravity, are generally discussed in terms of acceleration. The acceleration due to gravity is only 10m/s^2, but a rocket needs to accelerate at (significantly) more than that for the 30 seconds or so it takes to clear the atmosphere, resulting a speed upwards of 1,000m/s.

Secondly, if you were going to attempt something like this with a Harrier, you will find that, yes, as you get higher, there will be less gravity, but there will be more air resistance (because particles in the ionosphere move much, much faster) and - more importantly - all the principles that dictate how jet engines and wings work will just cease to function if there's not enough density of air to push against.

B

Gasoline (petrol/aircraft fuel and various other things) does not have enough energy density in its combustion to lift itself into orbit, let alone anything even heavier attached to the combustion tank.

Hence why rockets use much more energetic fuel.

>However, if something like a Harrier Jump Jet left the ground at say 1 metre per second (ignoring fule restrictions and lack of air etc) and kept on going, up and up, why couldn't it eventually get into space - I would have thought the effect of gravity and air resitance would get progessively less the higher it went?<

In principle you are right but sadly you'd need such a big fuel tank that this could not be achieved realistically (see my previous post too). Also the gravity from the earth never ends and so you'd never break free from its gravity like this.

If, however, you use a fuel that can provide *more* energy than earth's gravity can ever exert over an infinite range of distance then you will break free from its gravitational pull.

(actually most rockets don't do this - they just give their attached projectile enough energy to achieve an orbit of the required height)

"if something like a Harrier Jump Jet left the ground at say 1 metre per second (ignoring fule restrictions and lack of air etc) and kept on going, up and up, why couldn't it eventually get into space"

It could.

A rocket does, in fact, have to travel at 25,000mph to *leave* earth orbit. But if it's IN orbit, it's already doing more than 17,000mph.

"Escape velocity" as a concept is something that applies only to ballistic paths, i.e. unpowered bodies. In other words, "25,000mph" is the answer to the following question: "If I wanted to throw ball so hard that it never came down, how fast would it have to be going when it left my hand, neglecting air resistance?"

Note that the ball in that questions gets ALL its energy from the initial push to 25,000mph, and coasts the rest of the way. A rocket, on the other hand, climbs to orbit just as you say, much slower, although not as slow as your hypothetical Harrier, pushing all the way. And since it's pushing all the way, escape velocity is irrelevant.

There are asteroids which are small enough that you could, conceivably, stand on them and throw a ball up so hard it would never come down... indeed, there are no doubt millions of rocks so small that their escape velocity is low enough that if you timed it *just* right you could jump into orbit...

>>... as you get higher, there will be less gravity, but there will
be more air resistance (because particles in the ionosphere move
much, much faster)<<

The air resistance DECREASES with increasing altitude. This is
because there is less air with increasing altitude - the air
density and pressure falls off exponentially. The decrease of
gravity falls off much more slowly with altitude and is considered
to be relatively unchanged across the thickness of the atmosphere.

If we take 300 km altitude as the thickest part of the Ionisphere (in
terms of charges per cubic metre), then the air density is
effectively zero compared to the surface.