Derivation of earth orbit

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Could someone explain the idea, method of how earth orbit was derived, in non-mathematical terms (well, some math is fine too)? I am more interested in the (ingenious) engineering/experimental approach behind it. I guess it's related to or requires the determination of earth mass, and from the thread by that name I got the picture of how earth mass was first estimated and then refined. Now, what about earth's orbit? It's distance to Sun, Sun's mass, etc.? Was Sun's mass first estimated using its size estimate (from eclipse data) and gas density?

Thanks in advance.
 

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Could someone explain the idea, method of how earth orbit was derived, in non-mathematical terms (well, some math is fine too)? I am more interested in the (ingenious) engineering/experimental approach behind it.
The orbit of Earth around Sun is described by Newton's law of gravity and by Newton's laws of motion, no way to avoid mathematics. From Newton's laws you can derive Kepler's laws, which were historically discovered as the first. Kepler's laws seem to involve less math at the first glance, but if you want to really understand them, you cannot avoid the calculus (as for Newton's laws). If you are more interested in the observational data and the way they were gathered, try to google for "history of astronomy".

I guess it's related to or requires the determination of earth mass
As the mass of Earth is negligible in comparison to the mass of Sun, the Earth's mass is not required in order to determine the approximate orbital data, as we can pretend that Earth is orbiting around the center of Sun.

Was Sun's mass first estimated using its size estimate (from eclipse data) and gas density?
No, the first estimates were performed by Newton using his derivation of the Third law of Kepler.
 

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