Re: [Phys-l] How did Newton estimate the Gravitational constant?

[John Denker <jsd@av8n.com>]

On 10/28/2010 03:00 AM, Brian Blais wrote:

> A student asked me this question in class yesterday, and I wasn't
> sure (haven't looked at the Principia in a long time, but always
> found the arguments a bit hard to follow).  I imagine he could do it
> from a rough estimate of the mass of the Earth, mass of the Moon, and
> distance to the Moon.  With the Moon's period you could get a value
> for G.  Is this how he did it?  I know that the direct measurement
> wasn't done until later, by Cavendish.

This is a "teachable moment" concerning how science is done.
One of the rules is to consider all the plausible hypotheses.
These include:
  a) Newton estimated G by some means.
  b) Newton did *not* estimate G.

I don't know for sure that hypothesis (b) is correct, but it
is a hypothesis that must be considered ... and indeed the
overwhelming preponderance of evidence favors (b).  Evidence 
in support of (b) includes the contemporaneous reaction to
and interpretation of the work of Cavendish.

The non-evidence for (a) includes the fact that the results
for which Newton is famous do not depend on the numerical
value of G, but only on the fact that G is a constant over
a huge (possibly infinite) range of times and distances.

Further non-evidence for (a) includes the fact that if Newton
had estimated G, his value for G and its accuracy or lack
thereof would be objects of curiosity.  I would expect this
to be mentioned in encyclopedia articles on gravitation, 
but it is conspicuously absent.