<p>I'll say yes here, but only if the epicycles are used as approximations. Here's how they would be useful:</p>

<ul>
<li><strong>The eccentricity of the celestial body's orbit is low, i.e. $e&lt;&lt;0$.</strong> This means that it would be nearly circular, and epicycles could therefore be reasonably accurate. For example, it would not be a good idea to use epicycles to model Mercury's motion, because it has a high <a href="https://en.wikipedia.org/wiki/Orbital_eccentricity" rel="nofollow">eccentricity</a>. Comets would also be poor choices. Triton, on the other hand, has low eccentricity.</li>
<li><strong>Only a vague approximation is needed.</strong> If you aren't looking for calculations with a high degree of accuracy, you could use epicycles. It would be a bad idea to use epicycles to put a spacecraft into a precision orbit, but a better idea to use them in a toy simulator. NASA, however, has higher standards.</li>
<li><strong>You don't need to use general relativity.</strong> One of general relativity's most important predictions was the <a href="https://en.wikipedia.org/wiki/Tests_of_general_relativity#Perihelion_precession_of_Mercury" rel="nofollow">precession of Mercury's orbit</a>. Over long periods of time, general relativity triumphs over classical theories when it comes to this accuracy. It would be hard to use epicycles to model this - although potentially possible.</li>
</ul>

CC BY-SA 3.0
2014-10-18T15:58:35.680Z
Surely the point about epicycles is that they are not meant to be approximations. If it's approximations you want, use a circle!
adrianmcmenamin
CC BY-SA 3.0
2014-10-18T16:03:57.377Z
@adrianmcmenamin Didn't you write in your answer that epicycles *are* perfect circles? Besides, adding more epicycles could possibly increase the accuracy of the model. Right?
HDE 226868
CC BY-SA 3.0
2014-10-15T01:04:37.353Z
2014-10-15T01:04:37.353Z
HDE 226868
<p>None of these things are epicycles. Epicycles are perfect circles. These orbits are ellipses: it's a fundamental difference and so the answer is a very firm 'no'.</p>

CC BY-SA 3.0
2014-10-14T16:40:10.727Z
An ellipse can be constructed using epicycles, which were their raison d'etre. My point though is that the ancient forcing of perfect circles, caused "artifacts" such as eccentricities and mean positions. I suppose they could've chosen some other geometrical twists. Such as pretzel shaped orbits. But as epicycles conceptually-apparently correspond to the physical Lunar orbit in a heliocentric system, and the "mean Sun" corresponds to the Sun's barycenter, does this say anything about the geometry of space? Did the ancients somehow by pure geometry, unknowingly prevision some basic physics?
LocalFluff
CC BY-SA 3.0
2014-10-14T16:45:02.073Z
The Lunar orbit around Earth in a Copernican system, can be turned into perfect circles by using epi-epicycles. Maybe that's why he generalized that concept to all planets, because it makes it work the better as a prediction.
LocalFluff
CC BY-SA 3.0
2014-10-13T21:53:15.893Z
2014-10-13T21:53:15.893Z
adrianmcmenamin
<p>Copernicus put the Sun in the center of the Solar system. This turns the Moon's orbit into an epicycle around Earth orbit. And the Jovian moons (later discovered) have orbits which are epicycles around Jupiter. Since Copernicus created a physical epicycle in the Moon, it maybe wasn't so strange to think about "epicycles of epicycles" as he did to improve the model's fit to calendar data.</p>

<p>Actually, Ptolemy and Brahe did not put Earth in the center of their Solar system models. They used a fixed point in empty space near the Earth which they called "mean Earth". And Copernicus used a corresponding "mean Sun". And as a matter of fact, planets do turn around a barycenter which is not in the center of the Sun, but nearby.</p>

<p><strong>Do epicycles and "mean Earth/Sun" actually have physical correspondents in the orbits of moons and the barycenter respectively?</strong> That'd be a bit funny since they are purely geometric constructions with the purpose to make data fit better, created even without a thought about gravity or anything physical at all.</p>

<johannes-kepler>
Are epicycles and mean Earth/Sun actually useful astrophysical concepts?
LocalFluff
# Are epicycles and mean Earth/Sun actually useful astrophysical concepts?

(Asked by: username_0 on 2014-10-13)

Copernicus put the Sun in the center of the Solar system. This turns the Moon's orbit into an epicycle around Earth orbit. And the Jovian moons (later discovered) have orbits which are epicycles around Jupiter. Since Copernicus created a physical epicycle in the Moon, it maybe wasn't so strange to think about "epicycles of epicycles" as he did to improve the model's fit to calendar data.

Actually, Ptolemy and Brahe did not put Earth in the center of their Solar system models. They used a fixed point in empty space near the Earth which they called "mean Earth". And Copernicus used a corresponding "mean Sun". And as a matter of fact, planets do turn around a barycenter which is not in the center of the Sun, but nearby.

**Do epicycles and "mean Earth/Sun" actually have physical correspondents in the orbits of moons and the barycenter respectively?** That'd be a bit funny since they are purely geometric constructions with the purpose to make data fit better, created even without a thought about gravity or anything physical at all.

**Tags:** johannes-kepler

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## 2 answers

### Answer by username_1 on 2014-10-15. Score: 2

I'll say yes here, but only if the epicycles are used as approximations. Here's how they would be useful:

* **The eccentricity of the celestial body's orbit is low, i.e. $e<<0$.** This means that it would be nearly circular, and epicycles could therefore be reasonably accurate. For example, it would not be a good idea to use epicycles to model Mercury's motion, because it has a high [eccentricity](https://en.wikipedia.org/wiki/Orbital_eccentricity). Comets would also be poor choices. Triton, on the other hand, has low eccentricity.
* **Only a vague approximation is needed.** If you aren't looking for calculations with a high degree of accuracy, you could use epicycles. It would be a bad idea to use epicycles to put a spacecraft into a precision orbit, but a better idea to use them in a toy simulator. NASA, however, has higher standards.
* **You don't need to use general relativity.** One of general relativity's most important predictions was the [precession of Mercury's orbit](https://en.wikipedia.org/wiki/Tests_of_general_relativity#Perihelion_precession_of_Mercury). Over long periods of time, general relativity triumphs over classical theories when it comes to this accuracy. It would be hard to use epicycles to model this - although potentially possible.

> **Comments:**
> **username_2**: Surely the point about epicycles is that they are not meant to be approximations. If it's approximations you want, use a circle!  
> **username_1**: @adrianmcmenamin Didn't you write in your answer that epicycles *are* perfect circles? Besides, adding more epicycles could possibly increase the accuracy of the model. Right?  

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### Answer by username_2 on 2014-10-13. Score: 1

None of these things are epicycles. Epicycles are perfect circles. These orbits are ellipses: it's a fundamental difference and so the answer is a very firm 'no'.

> **Comments:**
> **username_0**: An ellipse can be constructed using epicycles, which were their raison d'etre. My point though is that the ancient forcing of perfect circles, caused "artifacts" such as eccentricities and mean positions. I suppose they could've chosen some other geometrical twists. Such as pretzel shaped orbits. But as epicycles conceptually-apparently correspond to the physical Lunar orbit in a heliocentric system, and the "mean Sun" corresponds to the Sun's barycenter, does this say anything about the geometry of space? Did the ancients somehow by pure geometry, unknowingly prevision some basic physics?  
> **username_0**: The Lunar orbit around Earth in a Copernican system, can be turned into perfect circles by using epi-epicycles. Maybe that's why he generalized that concept to all planets, because it makes it work the better as a prediction.  

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