ATM Optical Flat

[Richard Schwartz <richas@idt.net>]

The emperor Zong of the asteroid Weird has ordered and optical flat.   I
thought I might be able to fill the order with a mercury dish.   The
asteroid is perfectly spherical and does not rotate, so a fixed mercury
dish would have a spherical shape.    What if I spin the dish
slightly?    What will be the shape of the mercury surface?  What will
the error curve look like?

Yes, you predicted the next question:   what if the asteroid is
rotating and you know lattitude of the flat?

Assume that the asteroid had a spherical shape and a constant known
density that is the same as the earth.   Assume that the asteroid is the
same diameter as earth.

. . . Richard