<p>What is usually shown in cyclic plots showing precession is the <em>precession index</em> ($e \cdot \sin\varpi$ where $e$ is the eccentricity and $\varpi$ is the moving <a href="https://en.wikipedia.org/wiki/Longitude_of_the_periapsis" rel="nofollow noreferrer">longitude of the perihelion</a>). It is dimensionless ($e$ and $\sin \varpi$ being ratios).</p>

<p>Here is the precession index for the last 2 Myrs that I plotted using <a href="http://vo.imcce.fr/insola/earth/online/earth/La2004/INSOLN.LA2004.BTL.100.ASC" rel="nofollow noreferrer">data</a> from <a href="http://dx.doi.org/10.1051/0004-6361:20041335" rel="nofollow noreferrer">Laskar et al. (2004)</a> (in the data file, first column is the age, second the eccentricty, third the obliquity and fourth the longitude of perihelion from moving equinox):
<a href="https://i.sstatic.net/ZyOYS.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ZyOYS.png" alt="Precession cycles"></a></p>

<p>As for the range of values, by definition a $\sin$ can only take values on the range [-1,1], while the eccentricity (at least during the last 100Myrs) has values ranging from 0 to 0.067; hence a resulting precession index ranging in theory from -0.067 to 0.067.</p>

<hr>

<p><strong>References</strong></p>

<p>Laskar, J., Robutel, P., Joutel, F., Gastineau, M., Correia, A. C. M., &amp; Levrard, B. (2004). A long-term numerical solution for the insolation quantities of the Earth. <em>Astronomy &amp; Astrophysics</em>, <em>428</em>(1), 261–285.</p>

CC BY-SA 3.0
2016-04-07T07:15:18.577Z
2016-04-08T08:20:27.403Z
2016-04-08T08:20:27.403Z
plannapus
<p>I am wondering what is measured in the plots of change of precession, e.g. when describing Milankovitch Cycles. The values typically vary between .06 and −.06. I am also wondering about what the different values for extreme points mean, but that will probably be answered with the first question.</p>

<climate><paleoclimatology><milankovitch-cycles><orbit>
What does the precessional parameter measure?
Max
# What does the precessional parameter measure?

(Asked by: username_0 on 2016-01-17)

I am wondering what is measured in the plots of change of precession, e.g. when describing Milankovitch Cycles. The values typically vary between .06 and −.06. I am also wondering about what the different values for extreme points mean, but that will probably be answered with the first question.

**Tags:** climate, paleoclimatology, milankovitch-cycles, orbit


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## 1 answers

### Answer by username_1 on 2016-04-07. Score: 3

What is usually shown in cyclic plots showing precession is the *precession index* ($e \cdot \sin\varpi$ where $e$ is the eccentricity and $\varpi$ is the moving [longitude of the perihelion](https://en.wikipedia.org/wiki/Longitude_of_the_periapsis)). It is dimensionless ($e$ and $\sin \varpi$ being ratios).

Here is the precession index for the last 2 Myrs that I plotted using [data](http://vo.imcce.fr/insola/earth/online/earth/La2004/INSOLN.LA2004.BTL.100.ASC) from [Laskar et al. (2004)](http://dx.doi.org/10.1051/0004-6361:20041335) (in the data file, first column is the age, second the eccentricty, third the obliquity and fourth the longitude of perihelion from moving equinox):
[![Precession cycles](https://i.sstatic.net/ZyOYS.png)](https://i.sstatic.net/ZyOYS.png)

As for the range of values, by definition a $\sin$ can only take values on the range [-1,1], while the eccentricity (at least during the last 100Myrs) has values ranging from 0 to 0.067; hence a resulting precession index ranging in theory from -0.067 to 0.067.

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**References**

Laskar, J., Robutel, P., Joutel, F., Gastineau, M., Correia, A. C. M., & Levrard, B. (2004). A long-term numerical solution for the insolation quantities of the Earth. *Astronomy & Astrophysics*, *428*(1), 261–285.


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