Talk:Tychonic system

"Brahe"

I was puzzled by the references to the scientist as "Tycho" rather than "Brahe," so it seems worth noting the reason for this (according to the Tycho_Brahe page, anyway). Supposedly this was the convention of the time in his native Scandia, and has become convention. --Stellmach 01:14, 16 July 2006 (UTC)

Stellar parallax

I removed the comment about how the Tychonic system has the "advantage" of not predicting stellar parallax. The distances to the stars were not known when Copernicus and Brahe were alive, so I don't understand how parallax could be a scientific issue at the time. If I'm mistaken about this and people did consider parallax to be an issue, please supply a citation for this and I'll shut up. --Shastra 18:43, 2 August 2006 (UTC)

"The distances to the stars were not known when Copernicus and Brahe were alive, so I don't understand how parallax could be a scientific issue at the time." The question is, why did Tycho expect them to be close enough to show parallax? The reason was that he estimated the distance based on the apparent angular size. A star appears to be about a minute of arc in diameter, the Sun 30 minutes of arc, so the stars must be 30 times as far away---close enough to show a naked-eye parallax. Tycho's "mistake" was that he didn't know wave optics: the apparent diameter of a star is not the "real" apparent diameter, but appears larger due to various effects. Considering that he never married his girlfriend, my guess is that this scientific argument was the motivation for his system, not fear of contradicting the Bible. — Preceding unsigned comment added by 193.29.76.37 (talk) 11:07, 10 August 2011 (UTC)

They didn't know the distance to the stars, no, but they did consider it to be a lot smaller than it actually is. They certainly knew that you got a null result from measuring stellar parallax—this is how Tycho decided that his "new star" in 1572 was not just a comet (he got a null result for the parallax measurement, and claimed that this was typical of something at the distance of stars—i.e. in the eighth sphere—and he had confirmed that stars show no parallax).

Here is a quote from Thoren's book on Tycho:

By the 1570s however, there was a growing interest among younger men in the implications of the Copernican cosmology. The problem was that if the earth moved, there should be an annual parallax or shift in the apparent positions of the stars. If this annual parallax could not be detected, it would imply that the universe and the individual stars were so immense as to stagger the imagination. The same line of thought led to a reconsideration of the order and distances of the planets and even to speculation about the infinite size of the universe and a plurality of worlds. The appearance in 1572 of the new star also raised the possibility of a dynamic rather than static universe. ... The only empirical test [of the Copernican theory] lay in seeking astronomical parallax. Fortunately for the development of science, this test was single edged. It could prove the motion of the earth but not disprove it, as the failure to find the earth's motion reflected in an annual displacement of the stars could be explained away (and had to be, for three hundred years) by postulating stellar distances too remote to allow detection of the displacement. But the fact remained that the one astronomical check available provided negative evidence.

I don't know if it has to be labeled as an advantage (I understand it sound awkward since it is now known that this theory is incorrect, but in its time that was an advantage and the reason it could stick around as long as it did), of course. In any case I respect your desire for a citation. --Fastfission 19:28, 2 August 2006 (UTC)

OK, I stand corrected. Thanks for the reference. I still think this needs to be formulated in a way that makes the circumstances more clear (regarding the advantage part). If you want to revert again in the meanwhile, I won't interfere. --Shastra 19:49, 2 August 2006 (UTC)

I'll write it up in a more clear way in a little bit, to make it clear what aspects were and weren't as much of an issue in their time. --Fastfission 21:04, 2 August 2006 (UTC)

I rewrote the section again, to address whether or not it should be labeled as an advantage. The goal was to show where he was right, and where and why he was wrong. - Shaheenjim (talk) 07:37, 10 February 2009 (UTC)

Blunder on Bessell and Henderson

The current following last para obviously a blunder on Bessell and Henderson who discovered stellar parallax in the 1830s, not stellar aberration in early 18th.

"The discovery of stellar aberration in the early 18th century by Bessel, Henderson and James Bradley established that the Earth did in fact move around the Sun, after which Tycho's system fell out of use among scientists. In the modern era, the few who still subscribe to geocentrism use a Tychonic system with elliptical orbits."

Will correct --Logicus (talk) 19:07, 10 January 2008 (UTC)

Stars

Based on the theory of a Tychonic system, the sun and moon orbit the earth, and the other planets in the solar system orbit the sun. But what about stars (other than the sun)? I assume that they orbit the earth in this theory, but the article should probably state that explicitly. And what about the comets in the solar system? Or moons of other planets in the solar system? There's also the issue of planets in other planetary systems, but I suspect that they weren't known at the time. - Shaheenjim (talk) 07:39, 10 February 2009 (UTC)

When Tycho published there were no other moons known in the solar system (not until Galileo's discovery of the moons of Jupiter in 1610). But those can be accounted for quite easily in this model (vs. the Ptolemaic) as the idea of multiple sources of rotation is accepted. As with the Ptolemaic system, the sphere of stars itself rotates around the Earth (I doubt the difference of them rotating around the sun would be detectable?). And "other planetary systems" were totally out of the question (they've barely really entered the question today!). --98.217.14.211 (talk) 01:14, 11 March 2009 (UTC)

One of Brahe's primary objections to the Copernican model was the immense distance and size of the stars required. He contended that the stars were much closer and of a comparable size to our Sun. JoshuaLibrarian (talk) 20:57, 11 April 2022 (UTC)

Rotating reference frames and the principle of relativity

The principle of relativity can't be used for a rotating reference frame, special or general relativity. In such a non-inertial reference frame there will be complex effects due to additional terms, measurable by local experiments such as a Foucault pendulum. In an inertial frame of reference the laws of motion will be simplest. This does not mean that non-inertial reference frames can't be used to describe a physical system. --Dgroseth (talk) 05:09, 2 September 2009 (UTC)

No, you are wrong about this. A rotating frame can be used under the General principle of relativity. The rotating frame will not be an inertial frame. Roger (talk) 06:27, 2 September 2009 (UTC)

First I suppose I owe an apology, I assumed by "theory of relativity", you meant special relativity, and the "Special principle of relativity". The "General principle of relativity" can technically be used here, and in more than one way. There are issues with how it is used and what the reader's background understanding is, given the way it is written. For example, given Modern Geocentric theory and the general principle, is it easy to understand the motion of Neptune, or why it looks blue unlike Saturn?

I can think of 2 possibilities: Either you're using the "General principle of relativity", and a mild form of the concept of Generalized coordinates such as in classical Lagrangian mechanics and Hamiltonian mechanics, or, you're using the General principle of relativity and General Relativity itself, including all the gory details and handing it over to the public as a great way to understand the universe, or at least the solar system.

If it is used with classical mechanics, it can be very useful in the region near the earth, with the pseudo-forces and tidal effects relatively small and easy to correct for, since the Earth is essentially in free fall.

As distances get as large as the lunar distance (~0.00257 au, ~389 times closer than the sun) odd things start to happen. First the lunar orbit does not prefer the equatorial plane, but instead precesses about the ecliptic, inclined by 5.145 +/- 0.16 degrees. Then there are other solar effects even the ancient Greek astronomers tried to correct for.

Now consider the planet Neptune at a distance of ~30 au from the Sun or 29-31 au from Earth. Light travels at 173.145 au / day or 172.672 au / sidereal day which seems like a long distance, until you realize that number must be used as a circumference. Thus any object farther than 27.482 au in equatorial distance appears to travel sideways faster than the speed of light in the rotating reference frame. For an object in the ecliptic, it can be as far as 29.953 au only if is at 90 or 270 degrees on the ecliptic.

Since Neptune is always near or above the speed of light in that rotating and accelerating frame, it is hard to justify classical mechanics and classical approximations without a lot of hand waving. Thus, I am forced to use General Relativity and an ugly metric tensor. Does the average reader understand that?

Also, I will still have problems understanding why Neptune is blue because there is no practical way to mix General Relativity and Quantum Mechanics today. Even string theory is impractical. Any ideas? --Dgroseth (talk) 05:31, 14 September 2009 (UTC)

I am not suggesting that this article attempt to explain modern physics. Roger (talk) 07:00, 14 September 2009 (UTC)

Epicycles

This page says it is essentially equivalent to the Copernican system, which seems fair enough: you just have to shift your fixed point from the sun to the earth.

However, that clearly means that the Tychonic system uses epicycles (hence I removed "and eliminated all need for epicycles"). That also means the lede picture is flawed/simplifed, since it shows things going round in circles William M. Connolley (talk) 21:15, 21 October 2011 (UTC)

I changed it to being equivalent to a heliocentric system, but you changed it back, saying that it was not equivalent to all heliocentric system. That's right, but I did not say that it was equivalent to "all" heliocentric system. Saying that it was equivalent to the Copernican system can be misleading because of the epicycle issue you noted. Roger (talk) 21:03, 22 October 2011 (UTC)

I'm trying to find a good source for this, but I think that the T system really is *exactly* equivalent to the C system, but shifted of course. It can, obviously, only be equivalent to one sun-centered system. I *think* T just took C's system (epicycles and all) and shifted the earth to the center. One of the other pages about geocentrism - but I can't find it now - asserts that the two systems are exactly equivalent William M. Connolley (talk) 21:10, 22 October 2011 (UTC)

So you changed a correct statement into a dubious one that you are unable to substantiate. I suggest that you change it back, and leave it that way until you find a source that backs up your claim. Roger (talk) 22:37, 22 October 2011 (UTC)

No. The correct statement is that it is Copernican (assuming it really is - I still don't have a good source for this, I admit. [1] is a source, [2] another, but may not be good). Your version is wrong - it must be. There are many heliocentric systems: Keplers, Copernicus's, ours. They cannot all be equivalent to the Tychonic system, obviously William M. Connolley (talk) 21:00, 23 October 2011 (UTC)

This was, of course, alse

Don't like this [3]. Tycho died in 1601 William M. Connolley (talk) 08:15, 23 November 2011 (UTC)

Possible error in the relation of the Tychonic and heliocentric systems

Apparently this point may have been previously discussed. Also, this is not my area of expertise. Still, I am troubled by a statement in the article: "It can be shown that the motions of the planets and the Sun relative to the Earth in the Tychonic system are equivalent to the motions in a heliocentric system."

Is this statement completely accurate? I do not think so. Perhaps the term "heliocentric system" must be qualified in some way, e.g., so as to eliminate Keplerian elliptical orbits with varying orbital speeds. Absent an infinite number of, e.g., epicycles, can a circular orbit constant velocity Tychonic system be rendered completely mathematically equivalent to an elliptical orbit variable velocity heliocentric system? I do not think so. Also, as noted in the previous discussion, at the very least the terms "Tychonic system" and "heliocentric system" need further specification. Otherwise it is unclear what is even being asserted.

So, in short, the cited problematic statement needs more work. — Wsjacobs (talk) 03:05, 18 August 2013 (UTC) Wsjacobs (talk • contribs) 02:14, 18 August 2013 (UTC)

This issue was resolved by changing the problematic sentence to specify that the intended referent was Copernicus' heliocentric model (as opposed to heliocentric models in general) and by quoting in support two sentences from Thomas Kuhn's The Copernican Revolution.Wsjacobs (talk) 22:47, 30 August 2013 (UTC)

Shirley the key point is the (mathemeatical, not physical) equivalence of the Tychoian and Heliocentric systems. It doesn't matter exactly *which* heliocentric system, you get an entire family of Tychoian ones, each corresponding to a heliocentric one. The pix we show here in the article clearly don't correspond to a Copernican one, since the Tychoian orbits are shown as circles, but Copernicus throws in epicycles and all that antique hangover crap William M. Connolley (talk) 07:19, 31 August 2013 (UTC)

Thank you for your post. In order to clarify the matter further I re-edited the problematic sentence to read: "It can be shown that the motions of the planets and the Sun relative to the Earth in Brahe's system are mathematically equivalent to the motions in Copernicus' heliocentric system." In this way, both intended referents are adequately specified, as well as making explicit the asserted equivalence.Wsjacobs (talk) 00:51, 1 September 2013 (UTC)

Fit "better" than the Copernican system.

It is not possible for a Tychonic system to "fit" better than a Copernican system. The two are clearly fully dual in that they are transformable to each other, with the except of the observation of the stars. Longomontanus et al, (the Tychonics) may have fit a better system to Tycho's more accurate data (they were within a factor of 2 of Tycho's margin of observational error), but that just meant that there was corresponding heliocentric system that was just as well fit.

In support of Tycho's system it just be limited to saying that, unlike the Copernican system, it removed the parallax problem and retained a non-moving earth, which most people favored at the time (even at this time, this was already widely debated.) One should not give the reader a false impression that Tycho's system was in any way better than the Copernican system, on data fitting or otherwise.

Remember, that in parallel to the Tychonic's work, Kepler was working on his own Copernican system and at pretty much the same time produced a system whose fit with Tycho's data was less or equal to the margin of error of his observations. My only point of this being that Tycho's system would not have been correctly and widely considered "more accurate" since it was not. So we should probably not say that in the article. Removing the parallax and maintaining geocentrism were its primary and only trumps at this time.

Qed (talk) 23:22, 4 December 2014 (UTC)

"Room for improvement" in the caption of the first picture

The first picture in this article is

((see below for a discussion about the caption))

(the one shown here.) The caption [the one in the article -- (not here on the "Talk:" page)] for that first picture says:

In this depiction of the Tychonic system, the objects on blue orbits (the moon and the sun) rotate around the earth. The objects on orange orbits (Mercury, Venus, Mars, Jupiter, and Saturn) rotate around the sun. Around all is a sphere of stars, which rotates.

IMHO that use of the verb [the word] "rotate" is incorrect (it should say "revolve" instead).

I did check wikt:rotate, the Wiktionary entry ("s.v.") for the word "rotate", and wikt:revolve, the Wiktionary s.v. for the word "revolve".

Yes, I am aware that it does say that "rotate" can mean "revolve", and "revolve" can mean "rotate". However, IMHO that does not mean that using one to mean the other, is a good idea, or is advisable in an encyclopedia like this (where, IMHO, it is preferable [advisable] to use language carefully, and to set a good example for readers, of the correct [or, "the more correct"] way to use such verbs).

Even though Wiktionary does say that "rotate" can mean "revolve", and "revolve" can mean "rotate", this can be explained by the fact that Wiktionary (or any similar dictionary) sometimes backslides from being prescriptive) and instead lapses into a tendency to describe (or reflect) current usage. (...along with the fact that, "current usage" might be full of mistakes made, by those who are ignorant of the "best practices" for using these verbs.)

So, even if we like to be nice and kind and forgiving here, IMHO it is not advisable to completely forget about setting a good example! I suggest that, -- (without offending anyone) -- this article^{[well, the caption of the first picture, in this article]} could improve its use of the verbs "rotate" and/or "revolve".

Notice: The Wiktionary entry for the word "revolve", (see wikt:revolve#Verb) does show, as an example sentence -- the first example sentence! -- this sentence:

The Earth revolves around the sun.

while the Wiktionary entry for the word "rotate", (see wikt:rotate#Verb) shows, as its first example sentence -- this sentence:

He rotated in his chair to face me.

These examples can serve as a hint as to what the "best practices" are, here. That is, [set a good example by doing this:] use "revolve" for sentences like "The Earth revolves around the sun.", and use "rotate" for sentences like "He rotated in his chair to face me.".

I intend to edit that caption, in accordance with this philosophy. The proposed edit would probably consist of:

• changing "rotate" to "revolve" 3 places; and
• adding "around the earth" at the end of the last sentence

If anyone has any objections (or advice, or other comments), then please [feel free to] chime in.

If there are no responses -- after some reasonable time, to wait for comments, "if any" -- then I intend to go ahead with this edit.

Sorry this was so long. Thanks for listening. --Mike Schwartz (talk) 07:21, 19 February 2015 (UTC)

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