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

[John Denker <jsd@av8n.com>]

On 10/28/2010 06:41 AM, Brian Blais wrote:
> it is interesting to imagine how one *might* estimate it, given only
> materials available in Newton's time.  clearly, if he felt no need
> (his methods produced useful results without needing it), it is
> likely he never estimated the quantity.

Well, you can always conjecture that the earth is a solid
ball of rock, which leads immediately to a conjecture for
the mass, since the size is known and the density of rock
is more-or-less known.

Newton implicitly used this idea in the Principia (1687)
[in book III, aka "treatise of the system of the world"]
  http://books.google.com/books?id=KaAIAAAAIAAJ&pg=PA528

Specifically, in this brief passage Newton implicitly assumed 
a mountain would have the same density as the earth as a whole.  
With 20/20 hindsight we know that for typical mountains this 
will be wrong by a factor of 2 or so.

On 10/28/2010 06:37 AM, Daryl Taylor wrote:
> > Cavendish's GOAL was to determine the
> > density of the earth in 1798, but he was the first to experimentally
> > determine the actual force between two masses in a laboratory

Maybe, maybe not, depending on what you mean by "laboratory".
Certainly Cavendish was not the first to report a reasonably
accurate number for the average density of the earth.  He
cited the earlier work of Maskelyne:

  A Proposal for Measuring the Attraction of Some Hill in This Kingdom by Astronomical Observations
  http://rstl.royalsocietypublishing.org/content/65/495.full.pdf+html

  An Account of Observations Made on the Mountain Schehallien for Finding Its Attraction
  http://rstl.royalsocietypublishing.org/content/65/500.full.pdf+html

  Summarized at:
  http://en.wikipedia.org/wiki/Schiehallion_experiment

See also
  Martin C. Gutzwiller. 
  Moon-Earth-Sun: The oldest three-body problem. 
  http://www.apam.columbia.edu/courses/ap1601y/Moon-Earth-Sin%20RMP.70.589.pdf