Re: curvature of buckets of water

[Leigh Palmer <palmer@SFU.CA>]

> I have a question about "absolute rotation."  If one placed the bucket of
> water in the center of the rotating platform, one gets a curved surface.
> If one places the bucket of water off-center of the rotating platform, one
> also gets a curved surface but the orientation of the surface will be
> different.  Will the shape still be the same?  That is, if one is in the
> bucket's frame of reference, is there any way one can tell that the bucket
> is off-center rather than just "tipped over" (away from what appears to be
> the center of rotation)?

Yes. The figure of the surface of an off-center bucket is simply an
off-axis paraboloid of revolution, a somewhat uncommonly employed
optical element. The segments of the Keck telescopes ao Mauna Kea
are all off-axis paraboloids.

> In a related matter, suppose one is trapped inside a box on a foreign
> planet. Is there an experiment that person can do to determine whether
> they are located coincident with the axis of rotation (i.e., north or
> south pole) rather than at some other latitude?

Given one more piece of information (the period of rotation of the
planet) one could use a Foucault pendulum and a stopwatch to
determine one's exact latitude. In principle the curvature of the
water surface in a bucket held relatively stationary on the surface
of the planet will take the (convex) form of the planet's constant
potential surface in the rotating frame*. This can be seen through
a telescope by observing Jupiter or (more dramatically) Saturn. The
detailed nature of the surface could depend strongly on local
gravitational anomalies, of course, but the effect will be too
small to detect in a bucket. (See my earlier physics question.)

Leigh

*This is a religious issue. There are some in this group who do not
acknowledge the existence of the centrifugal potential term which
must be included here. They would object to the term "potential" as
it is used in this explanation.