<p>@questionhang, the moon's celestial north pole is always 1.543 degrees from the ecliptic north pole (Earth's orbital pole), which, according to <a href="https://en.wikipedia.org/wiki/Orbital_pole" rel="nofollow noreferrer">en.wikipedia.org/wiki/Orbital_pole</a> was at RA 18h 0m 0.0s, D +66° 33′ 38.55″ at J2000.  </p>

<p>If an error or about 1.5 degrees if small enough for you, then use the ecliptic north pole.  </p>

<p>If not, the problem is that the moon's north pole precesses through that whole circle every 18.6 years, so it changes fairly rapidly.  If one knew accurately where it was on a given date, one could to calculate where it should be now, but I don't find those numbers either.  For my purposes, I am ok using the ecliptic north pole.</p>

CC BY-SA 3.0
2018-01-09T11:22:09.797Z
@Envite's post is right.
questionhang
CC BY-SA 3.0
2018-01-08T02:07:38.520Z
2018-01-08T02:07:38.520Z
Doguleez
<p>Here's a NASA movie showing Libration: <a href="http://svs.gsfc.nasa.gov/cgi-bin/details.cgi?aid=4000" rel="nofollow">http://svs.gsfc.nasa.gov/cgi-bin/details.cgi?aid=4000</a></p>

<p>As given in the details here, the <strong>position angle</strong> is the angle between the Moon's north and celestial north. This changes because of the inclination of ecliptic to equator + inclination of moon's orbit to ecliptic and plus, there might be some contribution from the inclination of moon's rotation axis to its orbital plane. Note that all these changes are <strong>apparent</strong>. The pole need NOT physically shift at all for these effects.</p>

<p>Having said that, whether the pole does shift, requires one to correct for all those effects and the remaining effects would be cause by some precession or nutation of the lunar poles, which is likely to be negligible given that it is tidally locked to the earth.</p>

CC BY-SA 3.0
2014-07-16T12:19:56.293Z
do you know the exact RA and Dec which the moon points at?
questionhang
CC BY-SA 3.0
2014-07-16T20:32:22.087Z
No, not really. There must be some database which has these details, but I'm not sure where you'd find it.

EDIT: As Envite pointed out in the comment on the other answer, there seems to be a better explanation with some concrete numbers in that link.
Takku
CC BY-SA 3.0
2014-09-09T12:02:24.123Z
It is empty here. http://en.wikipedia.org/wiki/Poles_of_astronomical_bodies
questionhang
CC BY-SA 3.0
2014-07-16T07:52:56.557Z
2014-07-16T07:52:56.557Z
Takku
<p>The &quot;small vibration&quot; is Libration, and it does not imply that lunar axis changes orientation. It is caused by Moon's movement not being a perfectly circular orbit parallel to Earth's Equator with aligned axis.</p>
<p>Here's <a href="http://www.rmg.co.uk/gcse-astronomy/sun-and-moon/moon-movement/the-moon%27s-movement" rel="nofollow noreferrer">a description of the causes of libration</a> from the Royal Observatory (check the linked page for graphics of each source):</p>
<blockquote>
<p>Synchronous rotation and libration</p>
<p>The 27.3 days it takes the Moon to complete one orbit around the Earth is about the same as the time taken for it to complete one rotation. This synchronous rotation means that it always shows the same face to the Earth.</p>
<p>However, libration means that it is possible to see around 59% of the surface. It has three components:</p>
<p>i) Diurnal libration</p>
<p>As the Earth rotates the view of the Moon changes. An observer on the surface of the Earth sees slightly around the eastern limb of the Moon at moonrise. At moonset the same observer sees slightly more around the western limb of the Moon.</p>
<p>This arises from the changed position of the observer because of the rotation of the Earth. A parallax effect means that the Moon looks slightly different at moonrise and moonset.</p>
<p>ii) Longitudinal libration</p>
<p>The Moon moves in an elliptical orbit around the Earth. As a result it does not move at a constant speed (this is Kepler's second law)</p>
<p>However the Moon rotates at a constant speed. When it is moving faster in its orbit, this allows observers on Earth to see around the trailing edge of the Moon. When it is moving slowly it is possible to see around the Moon's leading edge.</p>
<p>iii) Libration in latitude</p>
<p>The Moon's axis is tilted by 6.7° to the plane of its orbit around the Earth. This means that sometimes the Moon's North Pole is tilted towards the Earth and sometimes tilted away.</p>
<p>As a result it is sometimes possible to see beyond the lunar North Pole and the South Pole is hidden. Conversely it is sometimes possible to see beyond the South Pole and the North Pole is hidden.</p>
<p>The combination of the three kinds of libration allows observers on Earth to see 59% of the lunar surface. However 41% remained hidden from view until the space age.</p>
</blockquote>
<p>So in order to get Moon's poles position you just need to know where the Moon's center is, which is quite standard, and the position of the poles referenced to that center, which is always the same (not in RA/Dec but in true space).</p>
<p>There is a secondary effect of &quot;wobbling&quot; called Nutation, which is caused by the Moon on the Earth, not a movement on Moon itself.</p>

CC BY-SA 3.0
2017-05-30T21:47:12.793Z
i and ii seem like two terms for one effect.
Roger Cathey
CC BY-SA 3.0
2017-06-06T21:13:11.397Z
@RogerCathey No, you can think i accounts for observers being in different places on Earth at the same time, thus being allowed to see different portions of the back side due to perspective, on both sides (East and West) at the same time, one for each observer, while ii accounts for Moon having elliptic orbit, so its constant rotation "lags behind" its non-constant translations sometimes, for all observers on Earth at the same time, and "lies before" it, again for all observers at the same time, for the other part of the orbit.
Envite
CC BY-SA 3.0
2017-11-14T21:29:46.130Z
how rude. two numbers would be a very succinct and acceptable answer. cassini's laws might help, but there is not enough information on wikipedia to actually implement anything... and its irrelvant anyway. what is the ra/dec of the lunar north pole?
jheriko
CC BY-SA 3.0
2017-11-15T20:57:49.387Z
@jheriko "two numbers" are not an acceptable answer, at all. The Moon moves on sky, independently on any "small vibration", don't you know?
Envite
CC BY-SA 3.0
2014-07-16T06:40:43.960Z
http://en.wikipedia.org/wiki/Libration http://en.wikipedia.org/wiki/Poles_of_astronomical_bodies  The main reason should be caused by the change of lunar pole which should be very small. But why is there not position of lunar poles in the second wiki link?
questionhang
CC BY-SA 3.0
2014-07-16T12:37:12.607Z
@questionhang http://en.wikipedia.org/wiki/Orbit_of_the_Moon#Inclination
Envite
CC BY-SA 3.0
2014-07-17T01:27:59.583Z
Yes. This helps. The rotation axis changes. However I am still not able to find a value which can specify the general position of its axis direction and the circle size draw on the sky.
questionhang
CC BY-SA 3.0
2014-07-17T05:38:55.310Z
@questionhang Double check the link I have just provided. **The angle between the ecliptic and the lunar equator is always 1.543°** and **the rotation axis of the Moon precesses with the same rate as its orbital plane, but is 180° out of phase (see Cassini's Laws)**. This is all you need. You just need to follow the link to Cassini's Laws. Did you really investigate before asking?
Envite
CC BY-SA 3.0
2014-07-17T06:21:46.687Z
＠Envite Thanks, I saw this. I need a RA&Dec and a general region pjojected on the sky.
questionhang
CC BY-SA 3.0
2014-07-17T06:29:40.013Z
@questionhang Just use Cassini's Laws. If you have trouble with them that's **another** question. This one is over.
Envite
CC BY-SA 3.0
2014-07-17T06:42:41.247Z
The north pole of the moon should point at some place near north  ecliptic pole very roughly. The physical laws can not give me a precise value and region.
questionhang
CC BY-SA 3.0
2014-07-16T05:45:37.380Z
2014-07-16T22:17:42.600Z
2020-06-17T09:47:40.653Z
Envite
<p>The moon faces the earth with one fixed side. However there is a small vibration. </p>

<p>So I am not sure the south and north poles of the moon is fixed. Even if they are fixed points on the moon, the pole axis should point at different locations in the sky.</p>

<p>What are the general positions of the two points in equatorial coordinate system of our earth?</p>

<the-moon><pole>
The RA and Dec of lunar poles
questionhang
# The RA and Dec of lunar poles

(Asked by: username_0 on 2014-07-16)

The moon faces the earth with one fixed side. However there is a small vibration.

So I am not sure the south and north poles of the moon is fixed. Even if they are fixed points on the moon, the pole axis should point at different locations in the sky.

What are the general positions of the two points in equatorial coordinate system of our earth?

**Tags:** the-moon, pole

---

## 3 answers

### Answer by username_1 on 2018-01-08. Score: 0 | Accepted answer

@questionhang, the moon's celestial north pole is always 1.543 degrees from the ecliptic north pole (Earth's orbital pole), which, according to [en.wikipedia.org/wiki/Orbital\_pole](https://en.wikipedia.org/wiki/Orbital_pole) was at RA 18h 0m 0.0s, D +66° 33′ 38.55″ at J2000.

If an error or about 1.5 degrees if small enough for you, then use the ecliptic north pole.

If not, the problem is that the moon's north pole precesses through that whole circle every 18.6 years, so it changes fairly rapidly. If one knew accurately where it was on a given date, one could to calculate where it should be now, but I don't find those numbers either. For my purposes, I am ok using the ecliptic north pole.

> **Comments:**
> **username_0**: @Envite's post is right.  

---

### Answer by username_2 on 2014-07-16. Score: 3

Here's a NASA movie showing Libration: <http://svs.gsfc.nasa.gov/cgi-bin/details.cgi?aid=4000>

As given in the details here, the **position angle** is the angle between the Moon's north and celestial north. This changes because of the inclination of ecliptic to equator + inclination of moon's orbit to ecliptic and plus, there might be some contribution from the inclination of moon's rotation axis to its orbital plane. Note that all these changes are **apparent**. The pole need NOT physically shift at all for these effects.

Having said that, whether the pole does shift, requires one to correct for all those effects and the remaining effects would be cause by some precession or nutation of the lunar poles, which is likely to be negligible given that it is tidally locked to the earth.

> **Comments:**
> **username_0**: do you know the exact RA and Dec which the moon points at?  
> **username_2**: No, not really. There must be some database which has these details, but I'm not sure where you'd find it.  EDIT: As Envite pointed out in the comment on the other answer, there seems to be a better explanation with some concrete numbers in that link.  
> **username_0**: It is empty here. http://en.wikipedia.org/wiki/Poles_of_astronomical_bodies  

---

### Answer by username_3 on 2014-07-16. Score: 2

The "small vibration" is Libration, and it does not imply that lunar axis changes orientation. It is caused by Moon's movement not being a perfectly circular orbit parallel to Earth's Equator with aligned axis.

Here's [a description of the causes of libration](http://www.rmg.co.uk/gcse-astronomy/sun-and-moon/moon-movement/the-moon%27s-movement) from the Royal Observatory (check the linked page for graphics of each source):

> Synchronous rotation and libration
>
> The 27.3 days it takes the Moon to complete one orbit around the Earth is about the same as the time taken for it to complete one rotation. This synchronous rotation means that it always shows the same face to the Earth.
>
> However, libration means that it is possible to see around 59% of the surface. It has three components:
>
> i) Diurnal libration
>
> As the Earth rotates the view of the Moon changes. An observer on the surface of the Earth sees slightly around the eastern limb of the Moon at moonrise. At moonset the same observer sees slightly more around the western limb of the Moon.
>
> This arises from the changed position of the observer because of the rotation of the Earth. A parallax effect means that the Moon looks slightly different at moonrise and moonset.
>
> ii) Longitudinal libration
>
> The Moon moves in an elliptical orbit around the Earth. As a result it does not move at a constant speed (this is Kepler's second law)
>
> However the Moon rotates at a constant speed. When it is moving faster in its orbit, this allows observers on Earth to see around the trailing edge of the Moon. When it is moving slowly it is possible to see around the Moon's leading edge.
>
> iii) Libration in latitude
>
> The Moon's axis is tilted by 6.7° to the plane of its orbit around the Earth. This means that sometimes the Moon's North Pole is tilted towards the Earth and sometimes tilted away.
>
> As a result it is sometimes possible to see beyond the lunar North Pole and the South Pole is hidden. Conversely it is sometimes possible to see beyond the South Pole and the North Pole is hidden.
>
> The combination of the three kinds of libration allows observers on Earth to see 59% of the lunar surface. However 41% remained hidden from view until the space age.

So in order to get Moon's poles position you just need to know where the Moon's center is, which is quite standard, and the position of the poles referenced to that center, which is always the same (not in RA/Dec but in true space).

There is a secondary effect of "wobbling" called Nutation, which is caused by the Moon on the Earth, not a movement on Moon itself.

> **Comments:**
> **username_0**: http://en.wikipedia.org/wiki/Libration http://en.wikipedia.org/wiki/Poles_of_astronomical_bodies  The main reason should be caused by the change of lunar pole which should be very small. But why is there not position of lunar poles in the second wiki link?  
> **username_3**: @questionhang http://en.wikipedia.org/wiki/Orbit_of_the_Moon#Inclination  
> **username_0**: Yes. This helps. The rotation axis changes. However I am still not able to find a value which can specify the general position of its axis direction and the circle size draw on the sky.  
> **username_3**: @questionhang Double check the link I have just provided. **The angle between the ecliptic and the lunar equator is always 1.543°** and **the rotation axis of the Moon precesses with the same rate as its orbital plane, but is 180° out of phase (see Cassini's Laws)**. This is all you need. You just need to follow the link to Cassini's Laws. Did you really investigate before asking?  
> **username_0**: ＠Envite Thanks, I saw this. I need a RA&Dec and a general region pjojected on the sky.  
> **username_3**: @questionhang Just use Cassini's Laws. If you have trouble with them that's **another** question. This one is over.  
> **username_0**: The north pole of the moon should point at some place near north  ecliptic pole very roughly. The physical laws can not give me a precise value and region.  
> **username_4**: i and ii seem like two terms for one effect.  
> **username_3**: @RogerCathey No, you can think i accounts for observers being in different places on Earth at the same time, thus being allowed to see different portions of the back side due to perspective, on both sides (East and West) at the same time, one for each observer, while ii accounts for Moon having elliptic orbit, so its constant rotation "lags behind" its non-constant translations sometimes, for all observers on Earth at the same time, and "lies before" it, again for all observers at the same time, for the other part of the orbit.  
> **username_5**: how rude. two numbers would be a very succinct and acceptable answer. cassini's laws might help, but there is not enough information on wikipedia to actually implement anything... and its irrelvant anyway. what is the ra/dec of the lunar north pole?  
> **username_3**: @jheriko "two numbers" are not an acceptable answer, at all. The Moon moves on sky, independently on any "small vibration", don't you know?  

---

