<p>The values </p>

<p>$$\alpha_0 = 0.00 - 0.641 T$$
$$\delta_0 = 90.00 - 0.557 T$$</p>

<p>provide a <em>first-order estimate</em> of the movement of the right ascension ($\alpha_0$) and declination ($\delta_0$) of the direction of the Earth's north pole for short periods of time after the epoch, expressed to three digits of precision only. $T$ represents the time after epoch expressed in units of Julian centuries (36525 days). The centuries unit was chosen to make the values of order unity, <em>not because</em> the values are meant to be used to extrapolate for centuries. You should be thinking of using this for a period of years, <em>until the next update is published</em>.</p>

<p>This is because the motion sets off in that direction, but will move in approximately a circle about the pole of the ecliptic, and in about 26,000 years return to roughly the same direction. Watch <a href="https://www.youtube.com/watch?v=qlVgEoZDjok" rel="nofollow noreferrer">Steven Senders' snappy video</a>. </p>

<blockquote>
  <p>This movie was created with Blender and is used in the Spitz Fulldome Curriculum for the SciDome planetariums around the world. </p>
  
  <p>Precession is the wobble of the Earth which makes the poles shift position over ~26,000 years as well as the position of the Vernal and Autumnal equinoxes in the sky. This movie illustrates the movement. </p>
  
  <p>Hopefully this movie gives a little more meaning to the Dawning of the Age of Aquarius. </p>
  
  <p><a href="https://www.spitzinc.com/" rel="nofollow noreferrer">https://www.spitzinc.com/</a></p>
</blockquote>

<p>The Earth's axis <a href="https://en.wikipedia.org/wiki/Nutation" rel="nofollow noreferrer">precesses</a> around the ecliptic pole due to gravitational interaction between the Earth's tilted equatorial bulge and (mostly) the Sun. There is also a faster and much smaller amplitude <a href="https://en.wikipedia.org/wiki/Precession" rel="nofollow noreferrer">nutation</a>.</p>

<hr>

<p><strong>below:</strong> Earth's Rotation, Precession and Nutation. From <a href="https://en.wikipedia.org/wiki/File:Praezession.svg" rel="nofollow noreferrer">here</a></p>

<p><a href="https://i.sstatic.net/CC8UU.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/CC8UU.png" alt="enter image description here"></a></p>

<p><strong>below:</strong> Screenshots from Steven Senders' video <a href="https://www.youtube.com/watch?v=qlVgEoZDjok" rel="nofollow noreferrer">Precession of the earth</a>.</p>

<p><a href="https://i.sstatic.net/8XS9R.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/8XS9R.jpg" alt="enter image description here"></a></p>

<p><a href="https://i.sstatic.net/EVRS7.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/EVRS7.jpg" alt="enter image description here"></a></p>

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

CC BY-SA 3.0
2017-12-18T12:58:36.003Z
Thank you, but maybe I should clarify the question. I know about axial precession, my question is about the model and how it should be used.
Anton Gromov
CC BY-SA 3.0
2017-12-18T15:30:43.143Z
@AntonGromov First line of the abstract; "Every three years the IAU Working Group on Cartographic Coordinates and Rotational Elements revises tables giving the directions of the poles of rotation and the prime meridians of the planets, satellites, minor planets, and comets." So you should use it between 2009 and 2012. As this is 2017, look for the newest value. If you know "Which means that in about 16000 years..." is the wrong way to think about it, you might consider removing it from your question. A straight line approximation to circular motion should of course not be used forever.
uhoh
CC BY-SA 3.0
2017-12-18T16:39:43.063Z
But the fact that the tables are produced every three years doesn't mean that they are accurate for three years. Obvious example is DE ephemeris which has an applicable period of time specified for every release, and it may be thousands of years.

As for newest values, according to the [Working Group website](https://astrogeology.usgs.gov/groups/IAU-WGCCRE), the report I mentioned is currently the the most recent.
Anton Gromov
CC BY-SA 3.0
2017-12-18T18:24:39.697Z
@AntonGromov the [JPL Development Ephemerides](https://en.wikipedia.org/wiki/Jet_Propulsion_Laboratory_Development_Ephemeris) are very large tables of numbers (10's or 100's of MB up to ~2 GB) evaluated at a dense mesh of time points, and are used for *interpolation* between the time points. One uses it only for times within the range calculated, never outside of it. The triplet values $\alpha_0, \delta_0, W$ in your reference are single values, used strictly for *extrapolation*.
uhoh
CC BY-SA 3.0
2017-12-18T18:39:06.203Z
Yes, maybe VSOP87 or ELP2000 would be better examples to illustrate what I mean. They both have a recommended time span which they are optimized for.
Anton Gromov
CC BY-SA 3.0
2017-12-19T09:40:25.757Z
@AntonGromov check the edit (first paragraph).
uhoh
CC BY-SA 3.0
2017-12-19T10:14:12.533Z
A key line from the report is "Expressions for the Sun and Earth are given to a similar precision as those of the other bodies of the Solar System and are for comparative purposes only."
James K
CC BY-SA 3.0
2017-12-19T14:14:29.573Z
@JamesK thanks for pointing that out. Reading the complete paragraph leaves me wondering if the reason that Earth's values have fewer digits than Mars or Mercury is that Earth's motion is so complicated by it's shape and Moon compared to them that *the linear expansion is simply unsuitable for such precision*, rather than it being known to less accuracy. Motion of the Earth-Moon system is known to incredible accuracy.
uhoh
CC BY-SA 3.0
2017-12-18T12:52:48.037Z
2017-12-19T09:52:14.383Z
2017-12-19T09:52:14.383Z
uhoh
<p>I'm looking at this IAU WGCCRE Report: <a href="http://aa.usno.navy.mil/publications/reports/Archinaletal2011a.pdf" rel="nofollow noreferrer">http://aa.usno.navy.mil/publications/reports/Archinaletal2011a.pdf</a></p>

<p>It gives expressions for Earth orientation relative to the International Celestial Reference Frame in terms of right ascension and declination of the north pole.</p>

<p>The numbers say that the declination of the Earth rotation axis starts from 90 degrees and decreases by 0.557 degrees every century:</p>

<blockquote>
  <p>δ0 = 90.00 − 0.557T</p>
</blockquote>

<p>Which means that in about 16000 years (and 16000 years ago) Earth rotation axis will lay in ecliptic plane. It doesn't make any sense to me.</p>

<p>Is it because this model should be applied on short time scales only? I didn't find any information on the time range for which the model is adequate.</p>

<p>Update: my question is not about how Earth actually rotates, but about the model and how it should be used.</p>

<rotation><iau>
IAU rotation model
Anton Gromov
# IAU rotation model

(Asked by: username_0 on 2017-12-18)

I'm looking at this IAU WGCCRE Report: <http://aa.usno.navy.mil/publications/reports/Archinaletal2011a.pdf>

It gives expressions for Earth orientation relative to the International Celestial Reference Frame in terms of right ascension and declination of the north pole.

The numbers say that the declination of the Earth rotation axis starts from 90 degrees and decreases by 0.557 degrees every century:

> δ0 = 90.00 − 0.557T

Which means that in about 16000 years (and 16000 years ago) Earth rotation axis will lay in ecliptic plane. It doesn't make any sense to me.

Is it because this model should be applied on short time scales only? I didn't find any information on the time range for which the model is adequate.

Update: my question is not about how Earth actually rotates, but about the model and how it should be used.

**Tags:** rotation, iau

---

## 1 answers

### Answer by username_1 on 2017-12-18. Score: 1

The values

$$\alpha\_0 = 0.00 - 0.641 T$$
$$\delta\_0 = 90.00 - 0.557 T$$

provide a *first-order estimate* of the movement of the right ascension ($\alpha\_0$) and declination ($\delta\_0$) of the direction of the Earth's north pole for short periods of time after the epoch, expressed to three digits of precision only. $T$ represents the time after epoch expressed in units of Julian centuries (36525 days). The centuries unit was chosen to make the values of order unity, *not because* the values are meant to be used to extrapolate for centuries. You should be thinking of using this for a period of years, *until the next update is published*.

This is because the motion sets off in that direction, but will move in approximately a circle about the pole of the ecliptic, and in about 26,000 years return to roughly the same direction. Watch [Steven Senders' snappy video](https://www.youtube.com/watch?v=qlVgEoZDjok).

> This movie was created with Blender and is used in the Spitz Fulldome Curriculum for the SciDome planetariums around the world.
>
> Precession is the wobble of the Earth which makes the poles shift position over ~26,000 years as well as the position of the Vernal and Autumnal equinoxes in the sky. This movie illustrates the movement.
>
> Hopefully this movie gives a little more meaning to the Dawning of the Age of Aquarius.
>
> <https://www.spitzinc.com/>

The Earth's axis [precesses](https://en.wikipedia.org/wiki/Nutation) around the ecliptic pole due to gravitational interaction between the Earth's tilted equatorial bulge and (mostly) the Sun. There is also a faster and much smaller amplitude [nutation](https://en.wikipedia.org/wiki/Precession).

---

**below:** Earth's Rotation, Precession and Nutation. From [here](https://en.wikipedia.org/wiki/File:Praezession.svg)

[![enter image description here](https://i.sstatic.net/CC8UU.png)](https://i.sstatic.net/CC8UU.png)

**below:** Screenshots from Steven Senders' video [Precession of the earth](https://www.youtube.com/watch?v=qlVgEoZDjok).

[![enter image description here](https://i.sstatic.net/8XS9R.jpg)](https://i.sstatic.net/8XS9R.jpg)

[![enter image description here](https://i.sstatic.net/EVRS7.jpg)](https://i.sstatic.net/EVRS7.jpg)

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

> **Comments:**
> **username_0**: Thank you, but maybe I should clarify the question. I know about axial precession, my question is about the model and how it should be used.  
> **username_1**: @AntonGromov First line of the abstract; "Every three years the IAU Working Group on Cartographic Coordinates and Rotational Elements revises tables giving the directions of the poles of rotation and the prime meridians of the planets, satellites, minor planets, and comets." So you should use it between 2009 and 2012. As this is 2017, look for the newest value. If you know "Which means that in about 16000 years..." is the wrong way to think about it, you might consider removing it from your question. A straight line approximation to circular motion should of course not be used forever.  
> **username_0**: But the fact that the tables are produced every three years doesn't mean that they are accurate for three years. Obvious example is DE ephemeris which has an applicable period of time specified for every release, and it may be thousands of years.  As for newest values, according to the [Working Group website](https://astrogeology.usgs.gov/groups/IAU-WGCCRE), the report I mentioned is currently the the most recent.  
> **username_1**: @AntonGromov the [JPL Development Ephemerides](https://en.wikipedia.org/wiki/Jet_Propulsion_Laboratory_Development_Ephemeris) are very large tables of numbers (10's or 100's of MB up to ~2 GB) evaluated at a dense mesh of time points, and are used for *interpolation* between the time points. One uses it only for times within the range calculated, never outside of it. The triplet values $\alpha_0, \delta_0, W$ in your reference are single values, used strictly for *extrapolation*.  
> **username_0**: Yes, maybe VSOP87 or ELP2000 would be better examples to illustrate what I mean. They both have a recommended time span which they are optimized for.  
> **username_1**: @AntonGromov check the edit (first paragraph).  
> **username_2**: A key line from the report is "Expressions for the Sun and Earth are given to a similar precision as those of the other bodies of the Solar System and are for comparative purposes only."  
> **username_1**: @JamesK thanks for pointing that out. Reading the complete paragraph leaves me wondering if the reason that Earth's values have fewer digits than Mars or Mercury is that Earth's motion is so complicated by it's shape and Moon compared to them that *the linear expansion is simply unsuitable for such precision*, rather than it being known to less accuracy. Motion of the Earth-Moon system is known to incredible accuracy.  

---

