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Name: Carl W.
Status: N/A
Age: 40s
Location: N/A
Country: N/A
Date: 2001-2002

I am a parent and was discussing escape velocity with my sons. The discussion turned to the fact that you would in theory never get out of a planets gravitational field (assuming it diminishes with distance but does not vanish). This being the case, if an object was launched from the surface at a velocity, it would immediately begin to slow down and given enough time would reach zero velocity and at that point begin to fall back to the object and would not in fact escape. Is there something wrong with this argument? or is escape velocity more complicated than simply looking at one (actually both) objects gravity?

The premise is correct, but the result is wrong. It is correct that a gravitational field weakens with distance, but never completely vanishes. So indeed, every single object with mass in the universe pulls on us with is gravitational field (and we on them).

The error in the argument is the idea that, just because the force is felt over an infinite distance for an unending time, it will have an infinite effect. On the contrary, the energy of gravitational attraction between two objects is finite. Basically, it is easy enough to calculate the gravitational potential energy between the earth and, say, a spaceship in two situations: with the spaceship at the surface of the earth, and with the spaceship an infinite distance from the earth. The difference between these two potential energies is the energy required to move an object on the earth to a state of complete separation.

So, what would happen if you were to make the spaceship move so fast that its kinetic energy exactly equaled this separation energy? It would move away from the earth quickly at first, and then slower and slower, but it would still move away forever and never fall back. It would not stop completely until it reached an infinite distance from the earth, and there it wouldn't feel any gravitational attraction to the earth any more. The initial velocity needed to make this happen is the escape velocity.

What if the spaceship were moving FASTER than the escape velocity? It would move away from the earth forever, because it has more than enough energy to keep going. Even at infinite distance, it would have kinetic energy left over.

Richard E. Barrans Jr., Ph.D.
Assistant Director
PG Research Foundation, Darien, Illinois

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