Escape velocity; or Why is that rocket going so fast?

Why do rockets have to go so fast to escape the Earth’s gravity well? Two thoughts in particular bother me:

  1. Shouldn’t it be easier the farther rockets travel from the surface, as gravity lessens?

  2. We all can beat gravity temporarily. Go on, jump. That wasn’t too hard, was it? All a rocket has to do is keep jumping.

I know that this post displays amazing ignorance, but that’s what y’all are here to fight. Get cracking!! :wink:

Sua

Problem is, a rocket can’t ‘keep jumping’ indefinitely. When it runs out of fuel that’s it.

Think of it as how fast you’d have to throw something (let’s say a ball) for it to leave earth’s gravity well. Once the ball leaves your hand there is no more acceleration acting on that ball (unless you count negative acceleration pulling it back to earth). If it isn’t going fast enough the ball comes back.

If you had a rocket that could burn it’s engines indefinitely then it could escape earth moving at any speed your care to name…say 1 mph. Unfortunately fuel burns fast and is heavy…there is a trade off between adding more fuel and conserving weight. Current rockets give it all they have quickly to build speed and hope that’s enough.

Not only should it be, it is. But the change in gravity is rather gradual, and you have to consider that you are already four thousand miles from the center of the Earth. You build a tower seven miles high, and you can launch your rocket from a point four thousand and seven miles from the center of the earth. You gain the advantage of the proportional increase in square of those two numbers. That turns out to be 99.56 percent of the gravity at the surface. That’s not a big advantage.

The actual launch problem is more often solved by accelerating the object so that it reaches an orbital velocity first. From above the atmosphere, you then boost additional fuel to the vehicle. From that altitude and from an orbital elevation the velocity is not lost while doing all this. Then you can launch from orbit to pass by the moon in such a way that you steal bits of velocity from it as you pass. Then you fire your rockets again from very far away, and the escape velocity is much less than it would be at the surface.

Escape velocity is the velocity at which something does not need any additional force to escape earth’s gravity. Basically, if something is travelling away from earth, there is a constantly diminishing force resisting it’s motion. Perhaps the easiest way to think of this is to put it in terms of energy.

When the rocket launches, it has a kinetic energy of ½mv[sup]2[/sup]. As it travels, gravity uses up some of that energy, by doing work on the rocket in the opposite direction. The work done (and therefore, the energy lost) is equivalent to the integral of the force over the distance travelled. Escape velocity means that the distance travelled is from the earth’s surface to the edge of the universe.

So, you find the integral of the gravitational force over the distance from the earth’s surface to infinity. This gives you the total kinetic energy needed at the start of the voyage. It is simple to derive the velocity from this. Luckily, you can also cancel out the mass in the equation. I’d go further in detail, but I can’t remember integration at the moment.

Can anyone tell me the Delta V necessary to go from the surface of Earth to low earth orbit? (In km/s if at all possible)

>> Why do rockets have to go so fast to escape the Earth’s gravity well?

I am not sure the question is clear and that is why the responses are all over the place.

First off, I would take the “well” out. (I mean as opposed to escaping the Earth’s gravity badly?)

Secondly, they don’t have to go at any speed, it is just more efficient to do so. The faster you go and the sooner you do it, the less fuel you need.

Here are the two extremes: A projectile that is shot at sea level with escape velocity, would have enough energy to escape the Earth’s gravitational force without further help. This is the most efficient fuel use as all the energy is communicated to the payload.

The practical problems are obvious: you cannot shoot anything useful (much less people) without destroying it. Also the atmosphere kind of gets in the way.

So you take a more gradual approach. You accelerate as fast as your rockets and payloads can take it. because the slower you do it, the more energy you need… part of the fuel is used to lift more fuel, not useful payload.

the other extreme is a rocket that barely has enough lift off force so it just burns fuel hovering over the ground and gets nowhere. That just wastes fuel and gets you nowhere. So you see the middle is where you want to be but there’s no theoretical reason that makes it impossible to escape the Earth’s gravity at a leisurely pace. Just practical reasons.

FTR, I meant “gravity well” as in the space-time distortion caused by Earth’s gravity, not a qualitative assessment of attempts to reach orbit.

Okies, so let me see if I am getting this right. The massive energy used by rockets to lift off, etc. is actually for efficiency’s sake. You have to use X amount of energy to get a certain mass into orbit, and it is more efficient to try to build your delta vee up quickly. That makes sense, thanks!

V.

Delta V? Heck, Boeing hasn’t even launched a Delta IV yet! :wink:

>> I meant “gravity well”

Ah Ok, ha ha, now I get what you meant.

Yes, the slower you go out, the more fuel you need, using a rocket that is; if you could use an elevator to take an Apollo capsule to the moon you could probably pay for the needed electrical energy with a few dollars :slight_smile:

IIRC, the value of escape velocity for our gravity well is about 7 mi/s or 11 km/s. If you had a gun that could fire vertically that fast from sea level, you’d never get your bullet back. And waterj2, is right, mass is not an issue. Your “bullet” could be just that, or a rocket, or even a single atom.

In fact, that explains why we don’t have free hydrogen in our atmosphere. At normal earth temps, the random molecular motion of hydrogen results in frequent excursions above 11 km/s. Hence, as the molcules drift upwards, at the edge of our atmosphere they stop running into other things and simply “escape”! However, planets with higher gravity (like Jupiter) have a higher escape v and, hence, are able to hold on to their hydrogen.

Interesting to note, there are a few ideas on how to make an actual space elevator. It wouldn’t be able to get you to the Moon, but it could get you to twice as far out as geosynchronous. The cable would need to be made from carbon nanotubes, and the cars would probably need to be beamed power, rather than carrying their own supply, but it could be done, in principle, and given enough capital, we theoretically have adequate technology to do it.

By the way, castle_bravo, orbital speed for a given height is equal to escape speed divided by the square root of two, so for low Earth orbit, it’s a bit less than 8 km/s. May I ask, BTW, what exactly you’re building in your backyard, there?

>> FTR, I meant “gravity well” as in the space-time distortion caused by Earth’s gravity, not a qualitative assessment of attempts to reach orbit.

I misunderstood “well”. I should have remembered: when I was a kid, every time someone said “well, well, well…” my father would say “three holes!” and still expected his kids to think he was so witty :slight_smile: