Message-Id: <v01540b03b16833ea0828@[192.174.2.173]>
Date: Sat, 25 Apr 1998 17:24:57 -0800
To: pinhole@exploratorium.edu
From: pauld@exploratorium.edu (Paul Doherty)
Subject: escape velocity
Consider a funnel, a classical cone, point down in a uniform gravity field.
The funnel has sides that are extremely high.
Place a marble at rest at any point except the vertex and it will
accelerate toward the vertex. This is a model for a force toward the center
of the funnel.
Such a funnel has no escape velocity. no matter what velocity you give to
the marble it will always roll back to the center.
Now change the shape of the funnel.
Make it shaped like the bell of a tuba. A hyperbola of revolution with the
point down and the curve of the mouth approaching a horizontal plane at
infinite distance as -1/r does.
Release a marble at rest at any point of this bell and it will experience a
force toward the center. (An inverse square force actually!)
Yet, launch a marble outward from any point within the funnel,
there will be a velocity which will give the marble enough energy to coast
to infinity.
This is escape velocity.
The potential energy is simply the height in this model.
Sometimes it takes me a while to think up useful models.
Paul Doherty