Newton's Estimates of Object Masses & Distances

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Newton did not know the exact masses of celestial bodies like the Earth, Moon, and Sun, as these values were not determined until the Cavendish Experiment in 1797. Prior to this, only the product of mass and gravitational constant (GM) was known. However, approximate distances to the Moon and Sun were established by ancient Greeks, providing a foundation for Newton's work. The mass of the orbiting body is largely irrelevant in determining the size and shape of its orbit, as long as it is significantly less massive than the central body. This understanding allowed Newton to formulate his equations without precise mass measurements.
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How did Newton estimate or know the masses of various objects, like the earth, moon, sun, etc., in order to check his equations? And how about the distances, say to the moon, and sun?

Thanks.
 
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Niklas Koppernigk 1473 - 1543
Johannes Kepler 1571 - 1630
Issac Newton 1643 -1727
Bernard of Chartres (around 1100) used to say that "we [the Moderns] are like dwarfs perched on the shoulders of giants [the Ancients], and thus we are able to see more and farther than the latter."

Science never takes place in a vacuum. There have been scientists before and there will be after. In this special case, e.g. Kepler's laws have already been know.
 
exmarine said:
How did Newton estimate or know the masses of various objects, like the earth, moon, sun, etc., in order to check his equations? And how about the distances, say to the moon, and sun?
Thanks.

He didn't know the masses. Nobody knew these values until Henry Cavendish performed the Cavendish Experiment and measured the value of G in about 1797, more than 50 years after Newton died. Before that, only the product GM was known. This is why the Cavendish Experiment is sometimes referred to as "weighing the Earth". The distances were known, at least approximately. Even the ancient Greeks had a decent estimate of the size of the Earth and the distances to the Sun and Moon.
 
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How did Newton estimate or know the masses of various objects, like the earth, moon, sun, etc., in order to check his equations? And how about the distances, say to the moon, and sun?

As long as the orbiting body is much less massive than the central body (e.g. the Moon about the Earth to a fair approximation; any planet about the sun) the size and shape of the orbit don't depend on how massive the lighter body is.
 
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...

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