escape velocity??

Question

what is escape velocity ? It seems to me that any speed would eventually get you beyond a gravity well if you traveled long enough .Can someone help me out here?

Answer 1

Escape velocity is the velocity one would have to give an object on the surface so that it would eventually leave the gravity well just by its own inertia and without any further force acting on it. It is also the velocity of an object on impact that started to fall at zero velocity from an infinite distance.

And yes, any initial velocity will get you out there if you can keep it up long enough. The engineering limits on rockets ensure that for all practical purposes we end up bringing things up to speed very close to escape velocity, anyway.

Answer 2

No not any velocity can get you out of earth's gravity well.

Consider the velocity you impart to a baseball thrown hard, straight up in the air -- how far does it go up before it slows down, and starts to come back down.
Consider the muzzle velocity of a powerful rifle. The bullet goes up much higher than the baseball, but it still comes back down.

Keep thinking of devices that can impart greater and greater velocities (larger guns, electromagnetic rail guns, etc.) It takes more and more initial velocity to attain greater height.
Some gun can actually be made large enough to impart enough initial velocity such that the object fired can escape. But some small velocity cannot cause an object to escape.

It you maintain a velocity over time within a gravity well, that becomes acceleration. Even a rocket with a (lot of fuel) that has a thrust to produce 1.001g will eventually escape, but it's not the velocity, it's the acceleration that counts.

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Answer 3

Aman is correct - and I must admit that I am confused by tlbs statement about maintained velocity in a gravity well being acceleration. I mean, in a relativistic sense, just sitting on the ground is equivalent to acceleration, but I don't think that's what you are talking about.

If you accelerate to 5 miles per hour relative to the earth's surface and maintain that relative velocity without accelerating by means of thrust control, then you will eventually escape the gravity well. You will also use a lot of fuel doing it. The more economical way is to accelerate to escape velocity - 7 miles / second or so - and then coast.