<p>I think I found the answer to my question. The rotational axis of each planet is identical with the vector pointing from the planet's south pole to its north pole. Therefore, if I find a table that defines positions of north poles of the planets, I will also find the unique vector pointing in the direction of the planets' tilts. This page <a href="http://en.wikipedia.org/wiki/Poles_of_astronomical_bodies" rel="nofollow">http://en.wikipedia.org/wiki/Poles_of_astronomical_bodies</a> shows the positions of the north poles of major bodies in the solar system (as well as their tilt angles) projected onto the celestial sphere. The coordinates are given relative to Earth's celestial equator and the vernal equinox as they existed at the J2000 epoch. These coordinates uniquely define the tilt of each of the planets and other relatively stable bodies within the solar system.</p>

CC BY-SA 3.0
2015-02-08T15:45:35.567Z
Perfect, the PDF seems to contain exactly what I was asking for. I'll read it in more detail later :). Thanks!
pkout
CC BY-SA 3.0
2015-02-07T07:19:14.327Z
2015-02-07T07:19:14.327Z
pkout
<p>A bit too simply (but not too much), it's the angle between the planet's rotational angular velocity vector and the planet's orbital angular momentum vector.</p>

<p>Where it gets tricky is dealing with little wobbles and such. Planets don't quite orbit in a plane because of gravitational interactions amongst the planets. This means the instantaneous (osculating) orbital angular momentum vector isn't quite constant, both in magnitude and direction. There are a number of different mean orbital elements that smooth out most of those tiny wobbles. One of those mean orbital elements sets (I'm not sure which one exactly) is used to determine the  mean orbital angular momentum vector.</p>

<p>Planets don't quite rotate nice and smoothly because planets aren't perfect spheres and aren't rigid bodies. This gives the Moon, the Sun, and other planets a handle by which they can exert tiny little torques in the planet in question. The response of the planet to these torques is somewhat arbitrarily divided into two categories based on frequency. Very slow responses are called precession; faster responses, nutation. The non spherical nature of a planet means the planet undergoes a small torque-free nutation as well as the torque-induced precession, nutation, and polar motion. In addition to these, there are a number of terms (all small) that don't yet have a very good model behind them. This oddball terms, along with the torque-free nutation, are collectively called polar motion. The motion is fairly smooth if one ignores nutation and polar motion, and the effects are all small.</p>

<p>Precession, while very slow, can be quite large in magnitude. The rotational angular velocity vector that is used in determining the axial tilt incorporates precession but smooths out nutation and polar motion.</p>

CC BY-SA 3.0
2015-02-05T03:20:00.510Z
When you say "it's the angle between the planet's rotational angular velocity vector and it's orbital angular momentum vector", that's still not unique. One can rotate the rotational angular velocity vector around the angular momentum vector and always maintain the same angle. Simply said, do I tilt the planet to the left, to the right, towards the sun, away from the sun or in a combination of these? What direction do I tilt? I hope this makes sense - hard to explain.
pkout
CC BY-SA 3.0
2015-02-05T11:46:18.333Z
@pkout - You asked how "axial tilt" is defined, which is what I answered. You are now asking a different question, "How is the pole of rotation of an astronomical body defined?" I suggest you ask that as a separate question.
David Hammen
CC BY-SA 3.0
2015-02-06T01:25:49.317Z
I didn't ask a generic question of how "axial tilt" is defined. I actually defined it in my own question. I asked how do I uniquely define the tilt including its direction for the other planets? Saying that the tilt is 25.6 degrees, for example, doesn't yield a unique vector due to symmetry. My question was: "What is the proper way of determining in what direction the tilt of a planet occurs?" That wasn't answered. I know about precession and all that, but that's an answer to a different question.
pkout
CC BY-SA 3.0
2015-02-06T01:30:59.117Z
I edited the title of the question to make it more explicit.
pkout
CC BY-SA 3.0
2015-02-04T23:59:07.353Z
2015-02-04T23:59:07.353Z
David Hammen
<p>The tilt doesn't depend at all on where one is on the planet, and whether or not it is to the left or right is irrelevant.</p>

<p>The angle (excluding the wobbles and longer term effects as David mentioned) doesn't vary depending on where you measure it. See this pic from <a href="http://www.srh.noaa.gov/abq/?n=clifeatures_wintersolstice" rel="nofollow noreferrer">NOAA</a> for a simple perspective:</p>

<p><img src="https://i.sstatic.net/qr8iw.png" alt="enter image description here"></p>

CC BY-SA 3.0
2015-02-06T01:20:36.837Z
I didn't say that the tilt depends on where you stands on the planet. I said that whether one has winter or not depends on where one stand on the planet. I know the basics of the axial tilt. What I don't understand is how to determine in what direction to tilt the planets. For earth, you can determine it by putting the planet to a position in orbit corresponding to December 22nd (shortest day of the year) and then tilt the rotational axis 23.4 degrees away from the sun. That uniquely defines the tilt direction. How do you uniquely define it for the other planets?
pkout
CC BY-SA 3.0
2015-02-06T01:36:21.967Z
Say that I use the table of planetary tilts on this page: http://en.wikipedia.org/wiki/Axial_tilt Does it mean that if I model a solar system, I would tilt all these planets in the same direction? I could position them as they will be on December 22nd this year, then tilt the earth 23.4 degrees away from the sun to reflect the fact that we will have winter in the northern hemisphere, and then tilt all the other planets in the same direction by the number of degrees specified in the table? Or do they tilt in a different direction? I hope this clarifies the question.
pkout
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2015-02-06T08:36:00.187Z
No - they all tilt in different directions. I'm really puzzled now what you are asking in your question.
Rory Alsop
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2015-02-06T15:35:38.417Z
"No - they all tilt in different directions." What directions do they tilt then? That's my question. I know the angles, but I don't know the directions.
pkout
CC BY-SA 3.0
2015-02-06T18:18:03.503Z
Relative to what?
Rory Alsop
CC BY-SA 3.0
2015-02-06T19:26:19.793Z
That's a part of my question. The earth is tilted relative to its orbital plane. But providing the tilt angle relative to the orbital plane isn't enough to uniquely define the tilt direction. One also has to know the direction along which the tilt takes place because saying that the tilt is 23.4 degrees relative to the normal of the orbital plane doesn't yield a unique vector. If it still doesn't make sense, I suggest we drop it. I don't want to waste too much of our time. Thanks, though!
pkout
CC BY-SA 3.0
2015-02-05T08:33:21.987Z
2015-02-05T08:33:21.987Z
Rory Alsop
<p>The earth's axis is titled 23.4 degrees with respect to the ecliptic. Since this tilt is responsible for the seasons, it's clear that the tilt is in the direction away from the sun on the shortest day of year in the winter (on the northern hemisphere). That uniquely defines the tilt direction for me. How do we define the tilt direction for the other planets, though? What is the proper way of determining in what direction the tilt of a planet occurs?</p>

CC BY-SA 3.0
2015-02-07T16:32:17.240Z
Can you guys tell me why you're downvoting this question? It's a valid question. If you don't understand what I am asking, read my answer and you'll get it.
pkout
<planet>
How precisely is planetary tilt defined (the tilt direction, not just the angle)?
pkout
# How precisely is planetary tilt defined (the tilt direction, not just the angle)?

(Asked by: username_0 on 2015-02-04)

The earth's axis is titled 23.4 degrees with respect to the ecliptic. Since this tilt is responsible for the seasons, it's clear that the tilt is in the direction away from the sun on the shortest day of year in the winter (on the northern hemisphere). That uniquely defines the tilt direction for me. How do we define the tilt direction for the other planets, though? What is the proper way of determining in what direction the tilt of a planet occurs?

**Tags:** planet
> **Comments:**
> **username_0**: Can you guys tell me why you're downvoting this question? It's a valid question. If you don't understand what I am asking, read my answer and you'll get it.  

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## 3 answers

### Answer by username_0 on 2015-02-07. Score: 0 | Accepted answer

I think I found the answer to my question. The rotational axis of each planet is identical with the vector pointing from the planet's south pole to its north pole. Therefore, if I find a table that defines positions of north poles of the planets, I will also find the unique vector pointing in the direction of the planets' tilts. This page <http://en.wikipedia.org/wiki/Poles_of_astronomical_bodies> shows the positions of the north poles of major bodies in the solar system (as well as their tilt angles) projected onto the celestial sphere. The coordinates are given relative to Earth's celestial equator and the vernal equinox as they existed at the J2000 epoch. These coordinates uniquely define the tilt of each of the planets and other relatively stable bodies within the solar system.

> **Comments:**
> **username_0**: Perfect, the PDF seems to contain exactly what I was asking for. I'll read it in more detail later :). Thanks!  

---

### Answer by username_1 on 2015-02-04. Score: 4

A bit too simply (but not too much), it's the angle between the planet's rotational angular velocity vector and the planet's orbital angular momentum vector.

Where it gets tricky is dealing with little wobbles and such. Planets don't quite orbit in a plane because of gravitational interactions amongst the planets. This means the instantaneous (osculating) orbital angular momentum vector isn't quite constant, both in magnitude and direction. There are a number of different mean orbital elements that smooth out most of those tiny wobbles. One of those mean orbital elements sets (I'm not sure which one exactly) is used to determine the mean orbital angular momentum vector.

Planets don't quite rotate nice and smoothly because planets aren't perfect spheres and aren't rigid bodies. This gives the Moon, the Sun, and other planets a handle by which they can exert tiny little torques in the planet in question. The response of the planet to these torques is somewhat arbitrarily divided into two categories based on frequency. Very slow responses are called precession; faster responses, nutation. The non spherical nature of a planet means the planet undergoes a small torque-free nutation as well as the torque-induced precession, nutation, and polar motion. In addition to these, there are a number of terms (all small) that don't yet have a very good model behind them. This oddball terms, along with the torque-free nutation, are collectively called polar motion. The motion is fairly smooth if one ignores nutation and polar motion, and the effects are all small.

Precession, while very slow, can be quite large in magnitude. The rotational angular velocity vector that is used in determining the axial tilt incorporates precession but smooths out nutation and polar motion.

> **Comments:**
> **username_0**: When you say "it's the angle between the planet's rotational angular velocity vector and it's orbital angular momentum vector", that's still not unique. One can rotate the rotational angular velocity vector around the angular momentum vector and always maintain the same angle. Simply said, do I tilt the planet to the left, to the right, towards the sun, away from the sun or in a combination of these? What direction do I tilt? I hope this makes sense - hard to explain.  
> **username_1**: @pkout - You asked how "axial tilt" is defined, which is what I answered. You are now asking a different question, "How is the pole of rotation of an astronomical body defined?" I suggest you ask that as a separate question.  
> **username_0**: I didn't ask a generic question of how "axial tilt" is defined. I actually defined it in my own question. I asked how do I uniquely define the tilt including its direction for the other planets? Saying that the tilt is 25.6 degrees, for example, doesn't yield a unique vector due to symmetry. My question was: "What is the proper way of determining in what direction the tilt of a planet occurs?" That wasn't answered. I know about precession and all that, but that's an answer to a different question.  
> **username_0**: I edited the title of the question to make it more explicit.  

---

### Answer by username_2 on 2015-02-05. Score: 2

The tilt doesn't depend at all on where one is on the planet, and whether or not it is to the left or right is irrelevant.

The angle (excluding the wobbles and longer term effects as David mentioned) doesn't vary depending on where you measure it. See this pic from [NOAA](http://www.srh.noaa.gov/abq/?n=clifeatures_wintersolstice) for a simple perspective:

![enter image description here](https://i.sstatic.net/qr8iw.png)

> **Comments:**
> **username_0**: I didn't say that the tilt depends on where you stands on the planet. I said that whether one has winter or not depends on where one stand on the planet. I know the basics of the axial tilt. What I don't understand is how to determine in what direction to tilt the planets. For earth, you can determine it by putting the planet to a position in orbit corresponding to December 22nd (shortest day of the year) and then tilt the rotational axis 23.4 degrees away from the sun. That uniquely defines the tilt direction. How do you uniquely define it for the other planets?  
> **username_0**: Say that I use the table of planetary tilts on this page: http://en.wikipedia.org/wiki/Axial_tilt Does it mean that if I model a solar system, I would tilt all these planets in the same direction? I could position them as they will be on December 22nd this year, then tilt the earth 23.4 degrees away from the sun to reflect the fact that we will have winter in the northern hemisphere, and then tilt all the other planets in the same direction by the number of degrees specified in the table? Or do they tilt in a different direction? I hope this clarifies the question.  
> **username_2**: No - they all tilt in different directions. I'm really puzzled now what you are asking in your question.  
> **username_0**: "No - they all tilt in different directions." What directions do they tilt then? That's my question. I know the angles, but I don't know the directions.  
> **username_2**: Relative to what?  
> **username_0**: That's a part of my question. The earth is tilted relative to its orbital plane. But providing the tilt angle relative to the orbital plane isn't enough to uniquely define the tilt direction. One also has to know the direction along which the tilt takes place because saying that the tilt is 23.4 degrees relative to the normal of the orbital plane doesn't yield a unique vector. If it still doesn't make sense, I suggest we drop it. I don't want to waste too much of our time. Thanks, though!  

---

