How atrocious is "center of gravity"?

[THOMAS SANDIN <sandint@NCAT.EDU>]

        "Center of mass" is a mass-weighted average position. "Center of
gravity" is a gravitational force-weighted average position (I could have
said "weight-weighted"). If  g  is essentially constant over the system,
the center of gravity is essentially at the center of mass. Then we can do
without the term "center of gravity".
        However, here's an example where both terms are useful. Suppose a
meter stick is in orbit about the earth. If the stick is NOT horizontal,
particles of the stick closer to the earth have a bit more gravitational
force than equal-mass particles farther from the earth. As a result, the
center of gravity is below the center of mass. Since we can treat the
entire weight of the stick as acting at its center of gravity, the weight
of the stick exerts a torque about the stick's center of mass, tending to
align the stick's long axis with the earth's gravitational field.
        This torque can be used to orient satellites (my memory is that
the jargon is something like gravitational-gradient orientation). Allowed
to swing freely, the stick will oscillate back and forth about its
alignment position. It's not hard to get a good approximation for its
period using centers of gravity--I did so many years back when the AAPT
was looking for experiments to be done in orbit.
                                                        Tom Sandin


On Thu, 13 Apr 2000, Leigh Palmer wrote:

> Of greatest importance is that one should *never* allow the use of
> "center of gravity"! There is no case where this atrocious construct
> is more appropriate than "center of mass".
>
> Leigh