Re: Accuracy, etc.--astronomical measurements

[David Roberts <droberts@BOWDOIN.EDU>]

John Denker, in replying to Leigh Palmer on the question of the
uncertainties in the values of the Mass of the Sun etc. ends his comment
with what it seems to me is the most important point:
> ==============
>
> 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 is, only the product GM appears in _any_ celestial mechanics formula
(check, e.g. JMA Danby's _Fund. of Cel. Mech.)  Thus _astronomical_
observations  of orbital radius and orbital period lead to a value of the
product, say GM(sun).  Because of radar distances and atomic clocks, the
product is very well known.  By the same token,  the ratios of planet/Sun
mass can be found with great precision and accuracy.  At this point, the
astronomers can go no farther---  a value of G is required to convert
from, say, solar masses to kg.  But this value of G has had to be
determined by Earth-based experiment, e.g. that of Cavindish.  Thus the
ratio of GM(observed) / G(Cavindish) is limited by the uncertainty in G,
and thus astronomical masses expressed in kg are relatively poorly
determined.

A further remark:  a highly accurate value of GM is just what you want for
sending rockets to Mars, etc.

We sometimes say the physicists can do experiments, but astronomers must
wait for them to happen.  An important distinction, I think.

David Roberts
Physics, Bowdoin College