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?

  • $\begingroup$ I'm probably misunderstanding, but doesn't the planet's rotation constitute "roll"? $\endgroup$
    – user21
    Sep 1, 2015 at 15:07
  • $\begingroup$ @barrycarter - A planet's rotation is a rotation about the instantaneous z axis. That's yaw, not roll. Roll is about the x axis. $\endgroup$ Sep 2, 2015 at 2:35
  • $\begingroup$ OK, but the x axis is always the direction of travel, correct? So wouldn't rotation contribute to both roll and yaw? $\endgroup$
    – user21
    Sep 2, 2015 at 2:43
  • $\begingroup$ I am unconcerned with rotation, only revolution. $\endgroup$ Sep 3, 2015 at 1:12

1 Answer 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 angle. The second rotation is the planet's 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.

  • $\begingroup$ 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. $\endgroup$ Sep 3, 2015 at 1:11
  • $\begingroup$ @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. $\endgroup$ Sep 3, 2015 at 10:35

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