# Can planetary bodies have a second axis of rotation?

Is it possible for a planetary body to have a secondary axis of rotation? For example let's say there's an Earth-like body that is spinning with its North Pole facing the Sun. Imagine that the North Pole is always facing the Sun, in a somewhat tidally locked position. Is this even possible? Is it possible for the actual axis of rotation to change over time in a predictable and stable way?

I'm aware that the axial tilt can vary and oscillate with time. I guess what I'm asking is, is it possible for the axial tilt itself to be tidally locked to another astronomical body? Is it possible for the axial tilt to rotate on its own axis independent of perturbations from other bodies?

Good answers will provide me with a yes or no, as well as providing me examples of possible celestial bodies that already show this feature. Provide links or pictures for bonus points.

The relation to worldbuilding is that in my story, I'm trying to have the main planet actually be a moon of a large gas giant, yet be livable, have seasons, and have equatorial and polar differences in temperature. My original idea was using the L1 Lagrangian point of the gas giant so that it maintains a pretty consistent distance from the sun, but this point cannot be stabilized in a natural way. (See my previous question here)

• A free rotating solid body has only one axis of rotation at any given moment. This is elementary mechanics. The axis of rotation can itself rotate (= precession) or oscillate (= nutation). Moreover, a rotating body tends to react vigurously against attempts to change its axis of rotation (= gyroscopic effect). Sep 17, 2019 at 23:50
• @overlord What is the desired effect you are trying to achieve? Sep 18, 2019 at 0:42
• As others have said an object can't have multiple axes of rotation, but from your question it seems like that may not be what you're really wondering about--it sounds like you're asking whether you can have a planet that's rotating about a single axis and meanwhile the axis is itself turning in such a way that one of the poles of rotation is always facing the sun (so axis is parallel to line from sun to planet). If that's what you're asking, you should edit your question so it no longer talks about a "second axis of rotation", since that's not a correct description of the situation in physics. Sep 18, 2019 at 11:39
• Nothing to do with a second axis of rotation, but if you want an example of planet with an unconventional tilt of his rotation axis have a look at Uranus. It's axis is (almost) in the orbit plane, which cause all sorts of non intuitive day/season/year durations. Cool image for it
– Hoki
Sep 18, 2019 at 16:33
• I think what you're asking about is not a "2nd axis of rotation", but an axis of precession. Sep 18, 2019 at 20:24

Yes, it can, but not in our 3D universe (but this is not tagged hard science anyway).

It is perhaps better to think about rotation as "in a plane", instead of "around an axis". The plane of rotation has two dimensions - you cannot fit another independent plane of rotation into our three dimensional space, you lack one additional dimension.

In a 4D space, however, you can have two independent planes of rotation, and thus two axes of rotation (these are 2D planes, not 1D lines) that intersect in one point.

I asked this same question, on the physics stack. The answer is that a body can have only one axis of rotation. Below pasted is the link to the question and the answer I picked.

https://physics.stackexchange.com/questions/322200/how-many-different-axes-of-rotation-can-coexist

Q: I have questions about rotation.

There is a sphere in space. I can apply a force to cause the sphere to rotate around a central axis. An infinite number of possible central axes can be drawn.

Can I apply a force and then another force such that the sphere will rotate around 2 different central axes at the same time? I think yes....

A: No, this is not the case. Any rigid body, at any time, can only be rotating about one instantaneous axis of rotation. If you apply additional torques this axis can shift, but there's no such thing as having more than one axis of rotation.

Now, that said, if the body is asymmetric, like, say, a slab of wood, then you can think about spinning it quickly about its long axis and then more slowly about an axis orthogonal to that, but even then that's an illusion: at any given time, the block is undergoing an instantaneous rotation about a single axis, with the funky property that this axis will shift position with respect to both the body and the inertial laboratory frame.

Emilio goes on to give the formulas behind angular momentum and some examples. Go upvote his answer!

• However - appearances can suggest that rotation is about two axes if the body lacks some symmetry such as being shaped like a deck of playing cards or tennis racket. tennis racket theorem or intermediate axis theorem. When such an object is provided an angular impulse around the intermediate axis, the body tumbles around both the first and third principle axes. Why your Physics.stackexchange link mentions this in only a single comment is surprising. Sep 19, 2019 at 5:07
• Would have been better to ask this in the Astronomy forum, because they probably would have noted the important exceptions 1) Most astronomical bodies are not rigid spheres (stars, gas giant planets, black holes), and 2) External forces, like satellites, other planets, stars, etc. can induce secondary rotations (like the Earth's). In some cases, these secondary rotations can be quite extreme (but probably not on a liveable planet). Sep 19, 2019 at 12:40
• @PieterGeerkens I'm not sure exactly what you're getting at-- the intermediate axis theorem only says that rotations about an axis of intermediate moment of inertia are unstable. Regardless of this fact, the rotation of a rigid body can only be about one axis in 3 dimensional space. The axis can change with time, but the fact that there's only one at any given time has nothing to do with the intermediate axis theorem, or really mechanics at all-- its pretty much pure math. Specifically it's saying that any non identity element of SO(3) has a one dimensional eigenspace with eigenvalue 1. Sep 20, 2019 at 15:54
• @elduderino: And to an observer the object will, for many purposes, appear to be rotating about two axes because of the rotational instability. Lay observers care about appearances, not mathematical theory. Try it yourself with a deck of playing cards - it really looks bizarre. Sep 20, 2019 at 16:02
• @PieterGeerkens Ah I see what you're talking about-- I was just confused because I the answer quoted by WillK seems to address this so I had assumed you were talking about something else. But I do see how a lay person might conflate "changing axis of rotation" with "multiple axes of rotation", which I believe is something the OP likely fell prey to when asking this question in the first place. Sep 20, 2019 at 16:30

Yes it can. And Earth (and any planet) has! And even 2 more "axis", not just one

There are such a phenomena wich is called "precession" and "nutation"

• There is only one axis of rotation. Precession and Nutation are about how that axis changes in time in response to outside forces. However, given that the OP is not actually after two axes of rotation, your answer is relevant. Sep 18, 2019 at 16:49
• A Uranus-like planet, with an axis of rotation that is approximately parallel with the plane of the star system, could perhaps experience precession that is extreme enough to keep the axis pointed at the star. This would not be "tidal locking", it would be coincidental and any perturbation would easily cause this to diverge. Precession is caused by gravitational tidal forces of moon(s) and the star applying torque to the equator of an oblate spheroid. There would have to be massive tidal forces, and/or the year length of the planet would have to be very long. Sep 18, 2019 at 20:36
• A good bonus question would be how fast Precession and Nutation can occur. Sep 18, 2019 at 23:19
• With external momentum (like in gyrostabilisation) precession can occur at any speed depending on that momentum (even grater than rotation velocity). In stellar body case those momentum originats from gravitational forces from moons and other planets and typicaly is about thousands to billions times less than angular speed. But for artificial special cases (like twin-planet system) it can be hundreds times less than angular speed i.e. about a years. Nutations are much faster, but has much smaler amplitudes Sep 19, 2019 at 9:23
• @Benjamin That depends on the relation of rotational inertia of the body to the torque that causes the precession/nutation. Satellite orbits, which have a low rotational inertia compared to the torque applied to them by the sun and the moon, can precess fast enough to be sun-synchronous: One full precession per year, allowing the orbit to remain the same relative to earth and sun. (Very useful to place a low orbiting satellite in eternal sunlight!) For almost spherical bodies like planets, the torque / rotational inertia ratio is much, much worse, though. Sep 19, 2019 at 10:42

Uranus + Handwaving

The closest body I can think of to what you are describing is Uranus. Its axis of rotation is 90 degrees off of the other planets, but it is not tidally locked to the sun. So its north pole has day for 42 Earth-years, followed by night for 42 Earth-years.

This is an odd but stable configuration. It is believed that is was originally "vertical" like the other planets, but an impact with an Earth-sized object titled it.[1] Another interesting theory is that Uranus and Neptune were formed inside Jupiters orbit and the gas giants all migrated a bit.[2]

Perhaps during a period of solar system change, which could last millions of years and appear stable to human observers, the orbit/rotation you are talking about is possible.