A closely related idea to that of orbital velocity id escape velocity.
As long as you don't give an object any more kinetic energy than potential
energy it will remain bound in a closed orbit around its parent body.
If you increase the kinetic energy too much, however, the object will be
able to escape "to infinity" and still have some left-over motional (kinetic)
energy. Another way of saying this is that if an object moves fast
enough it will have enough energy to escape from the gravitational pull
of its parent body. It is very easy to determine the escape velocity
needed to escape from a gravitation object. The following is an Astro 210
derivation:
The maximum work done on a satellite of mass 'm' falling from infinity
to the surface of a planet or star of radius 'r' and mass 'M' is just the
gravitational potential energy = -GMm/r. If we "reverse" out thinking
we can see that if we give an object enough kinetic energy (1/2mv2)
then it can "go back up" to infinity and still be moving. This means
it has escaped and will never return. So...
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