Equatorial Tangential Velocity and Escape Velocity
What would happen if a planets rotation speed at the
equator was equal to the escape velocity?
Did you know a person has less weight at the equator than at the poles?
The short answer is that something "very bad" would happen. Think
of it this way. Suppose you had a ball a meter off the ground at
the equator. And suppose that in fact the rotation of the earth was
fast enough that an object near (1 meter high) the surface of the
earth was moving at the escape velocity. In this case the object
would float in mid-air. From the point of view of a person stuck to
the planet it would appear to float stationary. To a person
observing from space it would appear to make one revolution around
the earth per day.
If the object was closer than that critical height, then it would
slowly curve in towards the earth picking up a little velocity in
the direction of the earth's rotation and hitting the surface (were
the earth completely smooth or the critical height sufficiently
large, then the object could orbit as an ellipse like many of our
satellites). If the object was a little further away then it would
be ejected, never to return.
Now what would that mean for the planet itself? Well, I would not
want to be standing on it. Atmosphere and things with sufficient
velocity would be ejected from the planet. However, it would
probably be much worse than that. Much of what keeps the earth
together as a solid mass is the gravitational attraction. If the
orbital velocity was high enough, then much of that force would be
missing (canceled to a large extent). Suddenly the high pressures
in the earth's interior would be unbalanced and I would expect the
planet to more or less fly apart from its current form.
You can apply this line of reasoning to look at other planets and
how planets (or stars) form as well.
Now, back to a person's weight at the equator. It is less by a
small percentage due to the rotation of the earth. However, it is
also a bit less because there is a small bulge in the earth near the
equator. Why might there be a bulge near the equator? And why
would standing on a bulge at the equator further reduce a person's
weight? The total effect is around a 0.3% to 0.4% reduction. Next,
ask if there is a market for someone to buy precious metals like
gold at the equator and then sell them at the poles.
Michael S. Pierce
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Update: June 2012