How was it first determined that Earth orbits the Sun?

I remember the disussion on abuzz. At that time I could draw a 2D figure (in this case 2D is sufficient as planets are on the same ecliptic plane) of the locus of the solar system barycenter during the interval of 1990-2005 (prospect). I had noticed that the motion of the barycenter was mainly determined by the positons of Jupiter and Saturn. Jupiter, you know, has the 11 year cycle of revolving around the Sun. And motion of the barycenter appears to have nearly 11 year cycle. I do not know whether it affects the solar activity. If solar activity were affected by the positon of the barycenter, then the effects would be said to be caused by the positon of Jupiter among others.

satt_focusable : i did some searching, and for scales:

Jupiter and Saturn are by far the most massive planets. Effect of the Earth on barycenter of SOL is only 450 km, whereas Jupiter's influence is about 750.000 kilometers which is just outside the Sun.
Saturn's influence is about 400.000 km.

Never mind. You can always correct your typos here.

As for Ptolemy, you know, he was a astronomer/mathematician who maintained the geocentric theory of planetary motion. However he was also a traveller, and he believed that Earth was round; one of the basis of it was the observation of the mast of a ship coming to the shore from below the horizon.

I'm glad because I loved that discussion. I learned something in that thread, and I treasure that.

So, for all those who are interested in this "historic" thread, here it is: http://boston.abuzz.com/interaction/s.209484/discussion

It's a good observation I haven't heard before. But the dynamics of the solar system are such that there is an equilibrium of forces between gravity and acceleration. So the chemical and nuclear reactions that are going on in the sun can't "know" where the solar system's center of gravity lies.

Of course, planets could impose tidal waves upon the sun, just like the moon imposes them on the earth. These tidal waves might affect the Sun's nuclear chemistry indirectly. And as you say, they would have the periodicity of a Jupiter "year" because Jupiter's mass dominates that of all other planets. But this tidal effect doesn't depend on whether the barycenter is inside or outside the sun. And the planets' mass is so tiny compared to that of the sun that I don't really think the sun spots "feel" them either. But you never know.

Thomas.
I know that a mere correlation does not prove the causality. But anybody wonders what causes the solar cycle, and tries some correlated phenomena.
From the calculation done for my programming exercise in July 2001 (a peaceful July!), I noticed that the speed of the motion of the barycenter was that of a motorcycle.

Sure! I didn't mean to brush you off in my post, and if I came across that way, I'm sorry.

Thomas..
Discussions are for deepening knowledge, and you do not need to say sorry.
Anyhow, tidal forces by Moon make the interior of the Earth heated, and those of Jupitor on its satellites let volcanos errupt. I do not think one can immediately shy away from roles of tidal forces on solar cycles.

bookmark sorry folks

Not immediately. But I shied away anyway, for two reasons.

1) the relation of the masses. Earth and Jupiter are much smaller compared to the sun than Earth's moon compared to Earth and Jupiter's larger moons compared to Jupiter.

2) The distances involved. Tidal forces are proportional to the gradient of the gravity force, so scale with 1/r^3. The distance between Earth and Sun, measured in Sun radiuses, is dramatically larger than the distance between Earth and Moon, measured in Earth radiuses. I never performed the calculation for the distance between Jupiter and Europa, measured in Europa radiuses, but I'd be surprised if the same logic didn't apply.

That's why I'm instinctively skeptical of the influence of the planets on Sun spots. Of course I have no proof that my instinct is right.

It also got him imprisoned by the Catholic church. A mistake that they still haven't admitted to after 400 years.

I hear that the Roman Catholic church was prepared to make concessions then if an evidence was shown of the theory.

How about them making concessions now that they were wrong then? Funny how if a married man see's a another woman on Saturday night, and has a sexual thought about her, he's supposed to confess on Sunday morning. So why should the church not have to admit it's mistake after centuries?

I cannot quite understand the statement above.
In 1992, the Roman Catholic Church formally admitted that Galileo's view was correct.

I believe that they only formally admitted that they MAY have been mistaken!

Galileo was "not guilty."

http://www.dslnorthwest.net/~danwilcox/galileo.html

I'm just noticing that I've replied to every question in this thread except the one that started it: "How was it first determined that Earth orbits the Sun?"

I don't think it was really determined. The step from the geocentric to the heliocentric model reflects a change in the way people thought about astronomy rather than a change in what people know about astronomy. It is still possible today to describe the motion of the solar system in terms of a geocentric model. This model would predict the future constellation of stars correctly. It makes perfectly good theoretical physics -- except for the minor detail that equations which wouldn't even fill lines in the heliocentric model would fill pages in that geocentric model.

Even in Ptolemy's model, planets and stars didn't circle the Earth in nice circles, but in complicated, wobbly trajectories called 'epicycles'. Every time a new astronomical observation was made, theorists had to add new epicycles to account for it, making the Ptolemaic model more and more of a mess.

The heliocentric model invented by Copernicus avoided this mess, so more and more astronomers switched over to it. This happened at increasing frequency after the telescope was invented and Galilei discovered that our moon and the planets had mountains on it like the Earth, and that they weren't perfect spheres as predicted by Aristotle. Aristotele was an adherent to the Ptolemaic model and the ultimate philosophical authority figure from the Middle Ages until the early 17th century. It took some serious undermining of his authority until astronomers overcame their hesitance to trust Copernicus.

Theoretically the heliocentric theory might be said to be well established after Kepler-Galileo-Newton's theorizing of motion of bodies, and the tidal theory was a triumph of the theory. However one may safely say that the (approximate) heliocentric theory was "determined" when the actual flight experiments of spacecrafts were successful into the outer space in the Solar system, as the experiment is vital for empirical science.

Part of the challenge was to show Earth rotated around the heavens and not the opposite as Aristarchus of Samos predicted in 600BC (the Earth rotates) and as Copernicus agreed 2000 years later 1543 (Earth rotates about its own axis and about the Sun) but no one could prove it until Paris 3rd February 1851 ago using Foucault's pendulum.

http://www.calacademy.org/products/pendulum/page3.htm

Suspend a 200 lbs ball on a 220 ft steel wire and let it swing in a 10 foot arch for 24 hours and it does a 225 degree rotation (the wire is attached is a fixed point in space so it can not imbude rotation to the path of the pendulum - only the Earth moving can do that, so the rotation in one day will equal 360 degrees * sin (lattitude) ) - showing the Earth is rotating around the Sun and not vice-versa.

Those who played and important part from Anaxagorus through Aristarchus, Ptolemaus, Kopernik, Bruno, Galilei, Kepler, Hyugens, Newton and Bessels are document nicley here: http://solar-center.stanford.edu/FAQ/Qsunasstar.html

g__day..
Foucault's pendulum only proves that the Earth rotates around its axis.