<p>Saying why gets tricky beyond "because of Jupiter", but to clarify on the quote, the statement "Earth's eccentricity follows a 100,000 year cycle" is loosely true but it's also an oversimplification.    <a href="https://en.wikipedia.org/wiki/Milankovitch_cycles#Orbital_shape_(eccentricity)" rel="noreferrer">From Wikipedia</a>.</p>

<blockquote>
  <p>The Earth's orbit approximates an ellipse. Eccentricity measures the
  departure of this ellipse from circularity. The shape of the Earth's
  orbit varies between nearly circular (with the lowest eccentricity of
  0.000055) and mildly elliptical (highest eccentricity of 0.0679)<a href="http://climatica.org.uk/climate-science-information/long-term-climate-change-milankovitch-cycles" rel="noreferrer">2</a> Its geometric or logarithmic mean is 0.0019. The major component of
  these variations occurs with a period of 413,000 years (eccentricity
  variation of ±0.012). Other components have 95,000-year and
  125,000-year cycles (with a beat period of 400,000 years). They
  <strong>loosely combine into a 100,000-year cycle</strong> (variation of −0.03 to +0.02).</p>
</blockquote>

<p>If the highest is 0.0679 and the variations are 0.012 and up to 0.03, that's over 50% variation peak to peak.  That's amplitude, not period, but if we look at the chart it's clearly not a neat and tidy cycle though it's somewhat close to a 100,000 year period (top line on the chart below).</p>

<p><a href="https://i.sstatic.net/yFuAh.png" rel="noreferrer"><img src="https://i.sstatic.net/yFuAh.png" alt="enter image description here"></a></p>

<p><a href="http://climatica.org.uk/climate-science-information/long-term-climate-change-milankovitch-cycles" rel="noreferrer">Source of image</a>.</p>

<p>The cause of Earth's eccentricity variation is the other planets, primarily Jupiter, with Venus and perhaps Mars (small but close) and Saturn also having effects.  Whether a particular planet is responsible for a particular period is a good question.   I'm not sure.</p>

<p>Ultimately this is a version of the 3 body problem or, more specifically, <a href="https://en.wikipedia.org/wiki/Orbital_perturbation_analysis" rel="noreferrer">orbital perturbation</a>, which is complicated mathematics.   Unfortunately, I can't give a good explanation of precisely why the gravitational perturbations work out to roughly 100,000 years or, more specifically, 413,000, 95,000 and 125,000.   Maybe someone else can. </p>

<blockquote>
  <p>What would be the simplest set of conditions and/or fewest body system
  that would lead to this particular type of periodic variation in
  eccentricity?</p>
</blockquote>

<p>The fewest bodies would be 3.   Sun-Earth-Moon is one example.  The Moon undergoes eccentricity variation on a much faster cycle than any of the planets.   Sun, Earth, Jupiter or any set of Sun and two planets would work too provided the planets were sufficiently large and/or sufficiently close to affect each other's orbits and (I think) you'd want the two planets to not be in orbital resonance.  That might create a different kind of pattern.  </p>

CC BY-SA 3.0
2018-04-07T16:20:38.767Z
I've been trying to think of an additional comment to make or question to ask, but your answer is really complete, thanks!
uhoh
CC BY-SA 3.0
2018-04-07T20:02:39.803Z
@uhoh as a sidebar, Mars eccentricity variation is more interesting.   Mercury's seems more stable due to it's 3:2 resonance short term, but may undergo much larger variations long term.   Venus's variation seems similar to Earth, pushing up to .06 eccentricity at peak.   Mars is more wild, perhaps cause it's closer to Jupiter, current eccentricity of 0.093 and perhaps flirting with 0.2 at it's extreme and certainly over 0.1 (at 0.2, at closest pass, Mars might approach Jupiter brightness).    http://www.scholarpedia.org/article/Stability_of_the_solar_system#Evolution_of_planetary_orbits.
userLTK
CC BY-SA 3.0
2018-04-08T00:23:23.133Z
Wow, that darn Jupiter, what a rascal!
uhoh
CC BY-SA 3.0
2018-04-08T02:44:22.373Z
The vertical axis tick labels on the Precession graph are a little odd...
Eric Towers
CC BY-SA 3.0
2018-04-08T10:05:38.003Z
@EricTowers as is the axis for eccentricity. There are other typos in the article, it seems to me incompletely prepared for publication.
uhoh
CC BY-SA 3.0
2018-04-08T17:04:36.497Z
Sorry for the poor source.   It was the best image for variation of eccentricity that I found.   Wikipedia has one, but it's not as visual and didn't post.   Despite the typos, the line matches the other eccentricity graphs I've seen.
userLTK
CC BY-SA 3.0
2018-04-07T10:22:39.947Z
2018-04-07T10:31:04.863Z
2018-04-07T10:31:04.863Z
userLTK
<p>This <a href="https://astronomy.stackexchange.com/a/11555/7982">answer</a> says:</p>

<blockquote>
  <p>Earth's orbital eccentricity varies over time from being nearly circular (low eccentricity of 0.0034) and mildly elliptical (high eccentricity of 0.058). It takes roughly 100,000 years for Earth to undergo a full cycle.</p>
</blockquote>

<p>Why does the Earth's orbital eccentricity oscillate with a period of about 100,000 years? What would be the simplest set of conditions and/or fewest body system that would lead to <em>this particular type</em> of periodic variation in eccentricity?</p>

<orbital-mechanics><mathematics>
Why does the Earth's orbital eccentricity oscillate with a period of about 100,000 years?
uhoh
# Why does the Earth's orbital eccentricity oscillate with a period of about 100,000 years?

(Asked by: username_0 on 2018-04-07)

This [answer](https://astronomy.stackexchange.com/a/11555/7982) says:

> Earth's orbital eccentricity varies over time from being nearly circular (low eccentricity of 0.0034) and mildly elliptical (high eccentricity of 0.058). It takes roughly 100,000 years for Earth to undergo a full cycle.

Why does the Earth's orbital eccentricity oscillate with a period of about 100,000 years? What would be the simplest set of conditions and/or fewest body system that would lead to *this particular type* of periodic variation in eccentricity?

**Tags:** orbital-mechanics, mathematics

---

## 1 answers

### Answer by username_1 on 2018-04-07. Score: 14 | Accepted answer

Saying why gets tricky beyond "because of Jupiter", but to clarify on the quote, the statement "Earth's eccentricity follows a 100,000 year cycle" is loosely true but it's also an oversimplification. [From Wikipedia](https://en.wikipedia.org/wiki/Milankovitch_cycles#Orbital_shape_(eccentricity)).

> The Earth's orbit approximates an ellipse. Eccentricity measures the
> departure of this ellipse from circularity. The shape of the Earth's
> orbit varies between nearly circular (with the lowest eccentricity of
> 0.000055) and mildly elliptical (highest eccentricity of 0.0679)[2](http://climatica.org.uk/climate-science-information/long-term-climate-change-milankovitch-cycles) Its geometric or logarithmic mean is 0.0019. The major component of
> these variations occurs with a period of 413,000 years (eccentricity
> variation of ±0.012). Other components have 95,000-year and
> 125,000-year cycles (with a beat period of 400,000 years). They
> **loosely combine into a 100,000-year cycle** (variation of −0.03 to +0.02).

If the highest is 0.0679 and the variations are 0.012 and up to 0.03, that's over 50% variation peak to peak. That's amplitude, not period, but if we look at the chart it's clearly not a neat and tidy cycle though it's somewhat close to a 100,000 year period (top line on the chart below).

[![enter image description here](https://i.sstatic.net/yFuAh.png)](https://i.sstatic.net/yFuAh.png)

[Source of image](http://climatica.org.uk/climate-science-information/long-term-climate-change-milankovitch-cycles).

The cause of Earth's eccentricity variation is the other planets, primarily Jupiter, with Venus and perhaps Mars (small but close) and Saturn also having effects. Whether a particular planet is responsible for a particular period is a good question. I'm not sure.

Ultimately this is a version of the 3 body problem or, more specifically, [orbital perturbation](https://en.wikipedia.org/wiki/Orbital_perturbation_analysis), which is complicated mathematics. Unfortunately, I can't give a good explanation of precisely why the gravitational perturbations work out to roughly 100,000 years or, more specifically, 413,000, 95,000 and 125,000. Maybe someone else can.

> What would be the simplest set of conditions and/or fewest body system
> that would lead to this particular type of periodic variation in
> eccentricity?

The fewest bodies would be 3. Sun-Earth-Moon is one example. The Moon undergoes eccentricity variation on a much faster cycle than any of the planets. Sun, Earth, Jupiter or any set of Sun and two planets would work too provided the planets were sufficiently large and/or sufficiently close to affect each other's orbits and (I think) you'd want the two planets to not be in orbital resonance. That might create a different kind of pattern.

> **Comments:**
> **username_0**: I've been trying to think of an additional comment to make or question to ask, but your answer is really complete, thanks!  
> **username_1**: @uhoh as a sidebar, Mars eccentricity variation is more interesting.   Mercury's seems more stable due to it's 3:2 resonance short term, but may undergo much larger variations long term.   Venus's variation seems similar to Earth, pushing up to .06 eccentricity at peak.   Mars is more wild, perhaps cause it's closer to Jupiter, current eccentricity of 0.093 and perhaps flirting with 0.2 at it's extreme and certainly over 0.1 (at 0.2, at closest pass, Mars might approach Jupiter brightness).    http://www.scholarpedia.org/article/Stability_of_the_solar_system#Evolution_of_planetary_orbits.  
> **username_0**: Wow, that darn Jupiter, what a rascal!  
> **username_2**: The vertical axis tick labels on the Precession graph are a little odd...  
> **username_0**: @EricTowers as is the axis for eccentricity. There are other typos in the article, it seems to me incompletely prepared for publication.  
> **username_1**: Sorry for the poor source.   It was the best image for variation of eccentricity that I found.   Wikipedia has one, but it's not as visual and didn't post.   Despite the typos, the line matches the other eccentricity graphs I've seen.  

---

