### Is it possible for planetary rings to be perpendicular (or near perpendicular) to the planet's orbit around the host star?

• Is it possible for planetary rings to be perpendicular (or near perpendicular) to the planet's orbit around the host star?

Why might it not be, please?

Are you assuming anything about the orientation of the planet's rotational axis?

camera was sideways!

• Yes, the plane of the rings of Uranus are at about 98 degrees to the plane of its orbit around the Sun.

This means that the ring system looks as in your picture twice per orbit. As the planet orbits the Sun, the rings, although still inclined at 98 degrees to the orbital plane gradually become "face-on" when viewed from the Sun. This will happen about quarter of an orbital period after the configuration illustrated in the picture. Then another quarter of an orbital period later, Uranus will be on the other side of the Sun, but with its rings tilted as shown.

When you say "cannot be permanently in that configuration", do you mean the orientation of the rings periodically oscillates (within one orbital cycle) or that eventually the orbit of the ring will change over many orbital cycles?

@CuriousCat The orientation of the rings in space stays the same. But the planet orbits the star. The apparent orientation of the rings with respect to the star will therefore change from as shown in your picture, to the rings being "face-on" to the star, quarter of an orbit later.

Is it possible for planetary rings to be perpendicular to their planet's axial tilt?

@Mazura that is a different question.

Yeah but it's the fun part of this one. "the rings of Uranus are at about 98 degrees to the plane of its orbit around the Sun [because... that's exactly what its axial tilt is as it's the one planet that 'got tipped over']." As far as the rings are concerned, their sphere of influence is the planet, not the sun.

@Mazura and the answer is that if the rings are produced by the breakup of a captured satellite, then yes they can be. If the rings are formed at the same time as the planet, then no they can't. Some of Saturn's rings are out of the equatorial plane. None of this would change my answer.

"Some of Saturn's rings are out of the equatorial plane". Are you talking about Phoebe ring which is tilted 27 deg from the planet equatorial plane? On a unrelated note: Do other planets except Saturn has their rings in the same plane to the equatorial plane? I can ask a separate question if you want.

• I posted a few animations, just to make sure :) The image is hopefully obviously not to scale.

This is possible:

and is, in fact, not far from what Uranus is doing.

The animation above was produced using Mathematica. The camera is above the plane of the planet's orbit, but not directly above the star. The rings are perpendicular to the plane of the orbit. Because the camera is off-center, we see a little bit of the side of the rings. Because the camera is at a finite distance, the angle between the plane of the rings and the line of sight from the camera varies along the orbit.

On the other hand, the animation shown below is physically impossible. Conservation of angular momentum prohibits it:

The ring is on the plane of the orbits of the particles the ring consists of, and (the direction of the normal of) this plane does not change during the orbit of the planet. Initially I thought that the ring would automatically be on the plane of the equator of the planet. Which is the case with Saturn's main rings and those of Uranus. However, as explained here, there is no law of physics that would make this necessary. Even Saturn has a thin faint ring in a different orientation.

My limited understanding is that the origin of the ring plays a role. If a ring consists of the remains of a former satellite, then it will follow whatever orbit that satellite had. On the other hand, if the ring was formed together with the planetary system, or even ejecta from the forming planet, then it feels natural that the ring should be exactly on the equatorial plane.

We need an astronomer to give more details. After taking a peek at Wikipedia I suspect that a ring on the equatorial plane may be more stable. Particularly, if/when "shepherd moons" need to be present to keep the ring intact. Obviously the satellites tend to be near the equatorial plane of the mother planet. May be the gravity of the remaining satellites would perturb a ring in some other orientation more severely, meaning that it would not last long?

What if this planet was tidally locked to the host star?

@fasterthanlight Then the host star is on the equatorial plane of the planet, right? Implying that so are the rings (if any can survive under the circumstances). The axis of the planet is perpendicular to the plane of the ring.

Actually I'm no longer sure about that. Anyway, the direction of the normal of the plane of the ring should be (near) constant, a tidal lock notwithstanding. So it would still be the situation in the top animation. And I think that the tidal forces of the star are strong enough to lock the planet, then they would also break apart the ring. I'm afraid I don't know.

The second case is not as impossible as it may seem. In fact, the rings follow a Sun synchronous orbit https://en.wikipedia.org/wiki/Sun-synchronous_orbit which is a very real thing.

@Pere 1- The rings typically follow the equator of the planet (due to angular momentum conservation) if, as the more common case, they are formed from protoplanetary dust. The sun synchronous orbit you mentioned would be for the planet, then this means that the planet's orbit and rotation, and consequently the rings, would be in the same plane (so, all parallel). The case you mentioned, of the rings being sun synchronous, saying the second case would be possible, defy linear/angular momentum conservation. But props to Jyrki

2- To understand that it is not possible (or at least, in the planetary case, nearly impossible, but possible as in a thought experiment), just see how the rings move in relation to the planet, they spin around the planet in an awkward manner. Instead of the case like Saturn, where they spin in a disk (or like a hockey puck on ice), each particle of the rings has its own orbit, and the rings spin like a spinning coin on a table with the orbit time of the ring, being the same as the planet's orbit time. That is just weird. In this case you cannot add spin like the one of Saturn's rings...3

3- as doing so means you create a cloud of dust, where all the particles collide and slowly coalesce into the actual plane allowed by the angular momentum, which is nothing like the case of a star-synchronous orbit that you described. In other words, a ring system in a star-synchronous orbit is a highly (mega hyper) unstable equilibrium point.

@Pere An interesting possibility. At some point I had included a parenthetical remark *precession is possible, but we ignore that*. Then I removed it for I thought it would be confusing. Anyway, I'm not acquainted well enough with celestial mechanics to be able to tell whether a sizable ring can stably follow the kind of orbit you had in mind.

The point being that I did not know that fast enough precession could be feasibly achieved. What was the period with the Earth's axis again? 26000 years?

I was thinking about this again last night and noticed I made a mistake, that the parts on the rotation axis (the coin on table type) actually have no orbital speed, and would just fall onto the planet, secondly, the orbits are around the center of mass of the planet, not an axis (as in, of course you have an axis of rotation, but the projection of the rotation is on one point, not along the axis), meaning that kind of orbit is not possible

regarding precession and all other effects that come from more than 2 body mechanics, I am also not versed enough into that, but for sure that angular and linear momenta would not allow the case where the rings would align with the rotating plane including the star-planet line in the perpendicular of the orbit

Triton is closer to Neptune than the moon is to Earth. It orbits in the opposite direction of Neptune's spin and precesses between about 7 degrees and 53 degrees from the plane of Neptune's rotation. A Wikipedia source predicts that in less than 4 billion years Triton will be within the Roche limit an will break up to form a ring system. Therefore, Neptune will have rings that will not only be non-equatorial, but possibly still precess.

@Ilmari Exactly what you did to the GIFs to make them repeat indefinitely? It is a bit of a puzzle to me. Some of my old animated GIFs in Math.SE do loop infinitely, but the new ones won't. Even if I specify the parameter in Mathematica to Inifinity. I have a vague recollection that there was a SW change at some point, but I was never up to speed with that.

@JyrkiLahtonen: GIF animations have a loop count setting; if it's 0, the animation loops forever. A lot of GIF editing software allows changing the setting; I think I used gifsicle. Here's a few other options.

@IlmariKaronen Apparently you managed it, but tinkering with the AnimationRepetitions parameter with Mathematica should do the same but won't. Irrespective of whether I set that parameter to $7$, $\infty$, or $0$. The animation is shown in browser exactly twice. This before it gets anywhere near imgur and their stuff. I thought the issue is browser related. Or a site policy even? I recall a thread where it was announced that the number of repetitiions was limited on purpose because users were abusing it. I thought you know some dirty tricks.

FWIW Mac OS X tools are of no use to me. I'm on Windows, for better or for worse :-)

@IlmariKaronen I learned that it is a bug in Mathematica, introduced in version 11 that I'm unlucky to own. A fix, kind of.

@JyrkiLahtonen: Gifsicle is cross-platform. Here's a Windows build.

Thanks @IlmariKaronen