Name: Carl W.
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
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
Richard E. Barrans Jr., Ph.D.
PG Research Foundation, Darien, Illinois
Click here to return to the Physics Archives
Update: June 2012