Coincidence in Tycho's Model of the Solar System

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jewish_scientist
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Coincidence in Tycho's Model of the Solar System

Postby jewish_scientist » Thu Feb 02, 2017 2:52 pm UTC

I found this animation of Tycho's System and noticed something odd. The radius of Saturn's orbit appears to be equal to the diameter of the Sun's orbit. Is there a reason for this, or is it just a coincidence?
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jaap
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Re: Coincidence in Tycho's Model of the Solar System

Postby jaap » Thu Feb 02, 2017 3:26 pm UTC

The model in that video is not to scale. The gaps between the orbits of neighbouring planets in that video are all the same, whereas in actuality the distances increase further out. Because the video uses equal distances, you will get such apparent coincidences as it makes sixth planet exactly twice as far from the sun as the third planet.
See here for example for the actual distances:
https://en.wikipedia.org/wiki/Solar_System#Distances_and_scales

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Re: Coincidence in Tycho's Model of the Solar System

Postby Copper Bezel » Thu Feb 02, 2017 7:46 pm UTC

So Tycho Brahe would have known some of the relative distances at the time? Would being such a different geometry change anything? I see his system was specifically designed to match the observations of a heliocentric model, so it's more the geometry I couldn't guess at than the precision of the measurements. But he drew it that way, too.

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thoughtfully
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Re: Coincidence in Tycho's Model of the Solar System

Postby thoughtfully » Thu Feb 16, 2017 3:06 am UTC

Tycho's system is actually consistent with observations, IIRC. It is just a matter of where you put the origin. A fully geocentric model gets objective stuff wrong, like the phases of Venus.
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Re: Coincidence in Tycho's Model of the Solar System

Postby Eebster the Great » Thu Feb 16, 2017 9:09 pm UTC

Well the Tychonic model certainly doesn't match observations of, for instance, the parallax of stars or the aberration of light, but these had not yet been observed in Galileo's time. In fact, the lack of observed parallax was taken as evidence favoring Tycho's model over Copernicus's. The reason the were not able to detect parallax was the great distance of stars (requiring a sensitivity of better than one second of arc for all but the very closest stars). But at the time, astronomers were generally unwilling to believe stars were so far away. Stars appear to the unaided eye to have an angular diameter of several minutes of arc. If they were indeed so large and so distant, their absolute diameter would need to be gigantic, on the order of the size of the entire solar system. Of course, we better understand vision now, and with the development of improved telescopes, we soon realized that stars do not have such a large angular diameter, but in fact one typically less than a thousandth of a second of arc. And when we did finally observe stellar parallax in the early nineteenth century, it was the final nail in the Geocentric model's coffin (a century earlier, James Bradley had already given a description of the aberration of light, itself observed decades before that, so there were already extremely few Geocentrists by that time).

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Re: Coincidence in Tycho's Model of the Solar System

Postby Copper Bezel » Fri Feb 17, 2017 12:33 am UTC

That's really fascinating. It didn't occur to me that (within the bounds of the solar system) this would be a simple coordinate swap, but that makes sense now. Thanks, both of you. = D
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Re: Coincidence in Tycho's Model of the Solar System

Postby jewish_scientist » Fri Feb 17, 2017 2:38 pm UTC

I just came across this videothat shows how ancient astronomers explain the retrograde motion of the planets.
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commodorejohn wrote:
I wish that someone would tell them that it is not a good idea to mock the giants you are standing on.

But man, that's the entire cultural foundation of the 21st century!


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