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

• From: Jack Uretsky <jlu@hep.anl.gov>
• Date: Thu, 28 Oct 2010 21:59:58 -0500 (CDT)

So Newton had a value for M_{E}G. He could estimate M_{E} from knowing g at the earth's surface.
Regards,
Jack

"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, Karshner, Gary wrote:

Brain,
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.
Gary

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of brian whatcott
Sent: Thursday, October 28, 2010 7:00 AM
To: phys-l@carnot.physics.buffalo.edu
Subject: Re: [Phys-l] How did Newton estimate the Gravitational constant?

On 10/28/2010 5:00 AM, Brian Blais wrote:
Hello,

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.

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. :)

thanks,

bb

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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_______________________________________________
Forum for Physics Educators
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