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

The Mechanical Universe text and videos describe the Cavemdish experiment,
moer picturesquely, as "weighing the earth."

"Trust me. I have a lot of experience at this."
General Custer's unremembered message to his men,
just before leading them into the Little Big Horn Valley

On Thu, 28 Oct 2010, Daryl Taylor wrote:

Ahh, I stand corrected... Sorta... 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 and thereby
actually calculated 'G' implicitly without stating it as a number. (Even
though my AP textbook says he did... sigh...) He used ratios of two forces
which allowed for calculations without 'G'. His experiment did indeed lead
others to accurately calculate 'G'. According to the wonderful world of
Wiki, the first mention of 'G' as an accepted numerical value was in 1873 by
Baille & Cornu, roughly 75 yrs after Cavendish did his work.

See? I lied to my own students... Now, will I be big enough to correct this
next class? Of course...

On Thu, Oct 28, 2010 at 8:21 AM, Karshner, Gary <>wrote:

The French revolution hadn't happened. This gave us the metric
system, plus Newton's calculus, Fluxion Theory, was based more on geometry
then algebra we use today. In geometry the usual approach to calculations
was to do it by ratio and proportion. The Gravitational constant doesn't
appear until Boys measurements in the late 19th century. Cavendish
experiment determined the density of the earth and not big G.
Hope this helps. Our twenty twenty hindsight often distorts the way we
perceive history.

-----Original Message-----
From: [mailto:] On Behalf Of brian whatcott
Sent: Thursday, October 28, 2010 7:00 AM
Subject: Re: [Phys-l] How did Newton estimate the Gravitational constant?

On 10/28/2010 5:00 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

Further, did he have any way of estimating the distance to the Sun? I
couldn't think of one that was available at his time, but he was more
clever than I. :)



I quickly reviewed Book 1 Section 12 and saw propositions given in the
usual geometric way of that time, that an inverse square law for force
operates between bodies in elliptical orbit depending on their joint masses
and inversely as the distance squared. I did not see an estimate
for the scaling constant, but I had no time to spare. Is it
established that Newton gave this estimate?

Brian W
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Daryl L Taylor
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