# Historically, how do we know that Earth moves around Sun? And it does so in an elliptical orbit?

I know the basics of solar system like how Earth moves around Sun, and that we have so many planets, elliptical orbit of earth, and how far is sun from earth etc etc. I want to take a step back and understand how mankind has been able to construct this knowledge of solar system piece by piece. Questions:

-- Sun is something we see on daily basis, so it would not be strange if humankind got curious to know about it, and made theories,observations,maths to prove it. How did Copernicus and others came up with the theory that earth moves around sun in elliptical orbit. How did they prove it? Has there been any actual way by which we have actually observed sun being in center and earth moving around in elliptical orbit. or we made such theory and result of this theory have been proved by other observations like day,night,change in weather at a point and at different points on earth.

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In his lecture The Cosmic Distance Ladder (video), mathematician Terence Tao describes the history of how mankind has successfully mapped the solar system and beyond. In particular, he describes why Copernicus put the sun in the center (reason: he discovered that the sun is dozens of times bigger than the earth) and how Kepler found his laws of planetary motion (He needed a reference point that was fixed in place, but all planets move. His brilliant idea was too choose Mars as the reference point, but only looking at it after a full orbit, when its position returns to the original one).

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The direction in which the celestial bodies are located is seen directly in the telescopes (two angular coordinates); the distance from the Earth is the hard part. For planets, we may measure the distance by waiting for a radar echo.

Aristarchus has invented a useful method to get a third piece of information: when the Moon is exactly half-full, Sun-Moon-Earth form a right angle with the Moon angle being 90 degrees.

The distance from the Earth to the Sun has also been measured by the transit-of-Venus method - to measure the time it takes to cross the Sun. Another method is parallax - measuring and comparing the apparent locations of the celestial objects at the same time, as seen from two places on the Earth.

Tycho Brahe

Still, the angular information - 2/3 of the coordinates - is the most accurate one. Tycho Brahe, a royal astronomer in Prague, measured the positions of planets extraordinarily accurately. The fact that he believed the geocentric system couldn't affect his precision. After all, you may describe everything from the Earth's reference frame.

His young assistant Johannes Kepler - who realized that Copernicus' heliocentric model was right - used those accurate data by Brahe to derive his Kepler's laws. Note that even if you don't know how the distance from the Earth is changing as a function of time, Kepler's laws make many very constraining predictions for each moment of time - where the planets and the Sun should be seen. Kepler has simply made the right guess and verified the predictions of this guess.

In Prague, Brahe was afraid that Kepler could try to get rid of him, so that Kepler would become the main royal astronomer himself. At the end, Brahe died because of not-quite-understood problems with the bladder. I don't claim that Kepler poisoned him. ;-)

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Thanks. You have also address my question physics.stackexchange.com/questions/5192/… . On a related note, how is the size of sun calculated? – xyz Feb 15 '11 at 8:17
One looks into the telescope, what is the apparent radius - the angle in which the Sun is seen - and multiplies this angle by the distance of the Sun to get the diameter. – Luboš Motl Feb 15 '11 at 8:31
Scientific American had an interesting article that suggested that IIRC Tycho Brahe believed that the planets revolved around the Sun, but the Sun, Moon, and stars revolved around the earth. The Sun, Moon, and stars could have had something pushing them around the heavens, but people had explored enough of the Earth to determine that it didn't have anything pushing it. Further, the lack of celestial parallax during the year implied that in order for the Earth to be orbiting around the sun, stars would have to be both impossibly big and impossibly far away. – supercat Nov 29 '14 at 17:48
Of course, nowadays astronomers have determined that some stars are in fact mind-bogglingly big and many stars are mind-bogglingly far away, it's not hard to imagine that a theory that planets orbit the sun, but the sun, moon, and stars all orbit the earth, would have required less acceptance of unproven phenomena than a heliocentric view (e.g. to accept the latter, one must accept that really big stars exist because if the Earth is orbiting the sun they must exist, when there is was no proof of their existence that wouldn't rely upon the Earth's orbiting the Sun). – supercat Nov 29 '14 at 17:53

This is a very general question best answered by reading up on material found in wikipedia

The short answer is that forces like the gravitational force have orbits for circling masses that are elliptical in nature, where the sun sits at one focus of the ellipse. Circles are an ellipse where the two foci overlap.

If you read the wiki article, you will see that a lot of data were gathered over the centuries on the motion of the planets on the celestial sphere, the geocentric system. Copernicus realized that a heliocentric system would fit the data simply and beautifully instead of the epicycle system that had dominated astronomy till then. The orbits were ellipses.

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I think this conflates the point somewhat. Copernicus did not know the orbits were ellipses, and his model, as I understand it, did not fit the data much better than epicycles. Actually, epicycles can fit the data brilliantly, if you try hard enough. youtube.com/watch?v=QVuU2YCwHjw – Mark Eichenlaub Feb 15 '11 at 7:56
well, circles were good enough at the time I guess. Of course the epicycles given good accuracy describe the motions very well and with the same number of parameters. It is just a coordinate transformation after all. The point is that the heliocentric is much more compact and can predict orbits. – anna v Feb 15 '11 at 8:33
The epicycles "are good enough" recently. At least in the 70ties epicycles were used to calculate space flight on computers. Whether this is done today, I don't know, but I think yes. – Georg Feb 15 '11 at 10:15

I really liked Ethan Siegel's explanation of this over at ScienceBlogs: http://scienceblogs.com/startswithabang/2010/09/geocentrism_was_galileo_wrong.php

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## protected by Qmechanic♦Jul 2 '14 at 11:37

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