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Re: Accuracy / precision / resolution / etc.



Of course, knowing a little physics doesn't hurt either. It's a good bet
that the product GM is known precisely because of the way it appears in
Kepler's 1-2-3 law: (1 over 4 pi^2) GM Period^2 = Radius^3. Then a
laboratory measurement of G lets us infer M.

That's correct in spirit. Celestial mechanical measurements can be
made with astronomical precision in the solar system (and, we presume,
astronomical accuracy). Kepler's laws hold only for two body systems,
of course, and the third law holds only in the limit of a massless
planet. The solar system is not a two body system, of course, and
astronomical measurements are well known to differ quite appreciably
from two body approximation results (that's how Neptune was
discovered). When all perturbations are taken into account, however,
the value of GM can be inferred very precisely.

The universal gravitational constant G, however, is very difficult to
measure in the laboratory. Of course we do measure it in the
undergraduate laboratory, but getting each successive order of
magnitude improvement beyond that determination is heroically
difficult. One clear reason is the long range froces generated by
everything which can't be shielded or even accounted for
satisfactorily. A measurement conducted in space is called for, but
that is difficult, too.

When Cavendish first measured G he published his result in a paper
entitled "Weighing the Earth". It is clear that he already had a very
accurate value for GM.

Leigh