This might be a bit of a historical question in nature.

Obviously given that we know the constant G, the mass of the sun, and the distance between a solar body and the sun we can calculate it's mass. Ditto if one of the other variables are missing.

What I don't understand however is how we managed to find the initial variables that we used to calculate all other variables? E.g. how did we find the distance between the Earth and sun and the sun's mass?

Sorry if the question is more historical than physical, but I couldn't find a place that describes how we arrived at our current knowledge.

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    $\begingroup$ This question is probably best for History of Science and Mathematics stack exchange, but because it has enough physics I will leave it to the community to decide $\endgroup$ – Cicero May 17 '15 at 20:33
  • $\begingroup$ Thanks, I wasn't aware that there is a history of science stack exchange. If the community decides it does not belong here I'll gladly remove this post and post it over there. $\endgroup$ – Afiefh May 17 '15 at 20:37
  • $\begingroup$ Any ways, here is my answer, for your reference @Afiefh $\endgroup$ – Cicero May 17 '15 at 20:42
  • $\begingroup$ If you found this answer useful, you can check the answer to make it official, @Afiefh. Otherwise, please let me know how I can improve my answers, for I always am looking for ways to improve! $\endgroup$ – Cicero May 19 '15 at 0:44

$G$ was historically calculated from the Cavendish experiment, involving balls and a torsion balance. The earth's mass was actually calculated before the sun's mass. Using the assumption that the earth was a sphere, its circumference and thus its radius could be determined through geodesy, as was done historically even before Newton. The acceleration of an object, and thus the average force exerted on the object, is easy to compute and was done so by Galileo and others. With these facts, the earth's mass could be calculated. We can use Kepler's laws and geometry to determine the earth-sun distance, or parallax. Since we obviously know the period, from this, we can easily determine the sun's mass. Finally, as for determing the distances to other space bodies, for planets we use Kepler's laws and geometry or parallax and for other bodies in modern times we use more sophisticated apparatus.


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