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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 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. :)



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