<p>You're using the wrong terms. Engineers use yaw, pitch, and roll to describe the orientation of a vehicle. Some erroneously call these rotations Euler angles. Astronomers and physicists use true Euler angles, a rotation about the Z axis of some reference plane, followed by a second rotation about the once-rotated X axis, followed by a third rotation about the twice-rotated Z axis. Note that the Tait-Bryan angles (aka Cardano angles) use a sequence of rotations about three distinct axes. Euler angles use only two axes.</p>

<p>The first rotation is the planet's <a href="https://en.wikipedia.org/wiki/Axial_precession" rel="nofollow">axial precession</a> angle. The second rotation is the planet's <a href="https://en.wikipedia.org/wiki/Axial_tilt" rel="nofollow">axial tilt</a>, or obliquity. The third rotation represents the planet's daily rotation. The rates at which the precession and obliquity change are much smaller than the quickly-changing third angle.</p>

CC BY-SA 3.0
2015-09-03T01:11:23.487Z
Sorry, but I still don't understand, so I will rephrase. I have a reference plane (e.g. the ecliptic) with a preferred direction (corresponding to the Earth's major axis. I now have another plane, for example, that of Mars's orbit. I understand that this is inclined ("pitched") with respect to the ecliptic by about 1.85 degrees. Mars's major axis, as projected onto the ecliptic, intersects at angle ("yaw"). I am interested in rotation around the third axis, which with planes or ships is called "roll". I would appreciate a pointer to an elementary document on this topic.
Spencer Rugaber
CC BY-SA 3.0
2015-09-03T10:35:39.700Z
@SpencerRugaber - Forget the third axis. Forget yaw, pitch, and roll. That  is not how astronomers describe the orientation of a planet. They instead use proper Euler angles. Read what I wrote. Use google to search for the terms I used. I'll add links to wikipedia articles to my answer as a starting point in your understanding.
David Hammen
CC BY-SA 3.0
2015-09-01T01:56:04.010Z
2015-09-03T10:39:08.487Z
2015-09-03T10:39:08.487Z
David Hammen
<p>I have been reading about celestial mechanics and particularly about planetary orbits. I understand that a planet's orbit can be tilted (pitched) with respect to the Earth's ecliptic and that it might precess (yaw) over time. But I have not come across any indication that another planet's orbital plane might be rolled with respect to the Earth's.</p>

<p>I have also found references to Keplerian orbital elements, but I don't see that any of them indicate roll. Am I misunderstanding the situation? If not, would someone point me at an elementary resource where I can learn about this?</p>

CC BY-SA 3.0
2015-09-02T02:35:35.233Z
@barrycarter - A planet's rotation is a rotation about the instantaneous z axis. That's yaw, not roll. Roll is about the x axis.
David Hammen
CC BY-SA 3.0
2015-09-03T01:12:47.530Z
I am unconcerned with rotation, only revolution.
Spencer Rugaber
<orbital-elements><celestial-mechanics>
Roll, Pitch and Yaw of Orbital Planes
Spencer Rugaber
# Roll, Pitch and Yaw of Orbital Planes

(Asked by: username_0 on 2015-08-31)

I have been reading about celestial mechanics and particularly about planetary orbits. I understand that a planet's orbit can be tilted (pitched) with respect to the Earth's ecliptic and that it might precess (yaw) over time. But I have not come across any indication that another planet's orbital plane might be rolled with respect to the Earth's.

I have also found references to Keplerian orbital elements, but I don't see that any of them indicate roll. Am I misunderstanding the situation? If not, would someone point me at an elementary resource where I can learn about this?

**Tags:** orbital-elements, celestial-mechanics
> **Comments:**
> **username_1**: @barrycarter - A planet's rotation is a rotation about the instantaneous z axis. That's yaw, not roll. Roll is about the x axis.  
> **username_0**: I am unconcerned with rotation, only revolution.  

---

## 1 answers

### Answer by username_1 on 2015-09-01. Score: 1

You're using the wrong terms. Engineers use yaw, pitch, and roll to describe the orientation of a vehicle. Some erroneously call these rotations Euler angles. Astronomers and physicists use true Euler angles, a rotation about the Z axis of some reference plane, followed by a second rotation about the once-rotated X axis, followed by a third rotation about the twice-rotated Z axis. Note that the Tait-Bryan angles (aka Cardano angles) use a sequence of rotations about three distinct axes. Euler angles use only two axes.

The first rotation is the planet's [axial precession](https://en.wikipedia.org/wiki/Axial_precession) angle. The second rotation is the planet's [axial tilt](https://en.wikipedia.org/wiki/Axial_tilt), or obliquity. The third rotation represents the planet's daily rotation. The rates at which the precession and obliquity change are much smaller than the quickly-changing third angle.

> **Comments:**
> **username_0**: Sorry, but I still don't understand, so I will rephrase. I have a reference plane (e.g. the ecliptic) with a preferred direction (corresponding to the Earth's major axis. I now have another plane, for example, that of Mars's orbit. I understand that this is inclined ("pitched") with respect to the ecliptic by about 1.85 degrees. Mars's major axis, as projected onto the ecliptic, intersects at angle ("yaw"). I am interested in rotation around the third axis, which with planes or ships is called "roll". I would appreciate a pointer to an elementary document on this topic.  
> **username_1**: @SpencerRugaber - Forget the third axis. Forget yaw, pitch, and roll. That  is not how astronomers describe the orientation of a planet. They instead use proper Euler angles. Read what I wrote. Use google to search for the terms I used. I'll add links to wikipedia articles to my answer as a starting point in your understanding.  

---

