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example

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

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    $\begingroup$ Why might it not be, please? $\endgroup$ – Robbie Goodwin Jan 10 at 22:38
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    $\begingroup$ Are you assuming anything about the orientation of the planet's rotational axis? $\endgroup$ – Peter Mortensen Jan 11 at 8:42
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    $\begingroup$ camera was sideways! $\endgroup$ – blankip Jan 13 at 4:56
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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.

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    $\begingroup$ @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. $\endgroup$ – ProfRob Jan 10 at 11:02
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    $\begingroup$ Is it possible for planetary rings to be perpendicular to their planet's axial tilt? $\endgroup$ – Mazura Jan 10 at 21:36
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    $\begingroup$ @Mazura that is a different question. $\endgroup$ – ProfRob Jan 10 at 22:16
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    $\begingroup$ 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. $\endgroup$ – Mazura Jan 10 at 22:21
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    $\begingroup$ "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. $\endgroup$ – Nilay Ghosh Jan 11 at 9:16
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I posted a few animations, just to make sure :) The image is hopefully obviously not to scale.

This is possible:

Animation of a planet with rings perpendicular to its orbital plane

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:

Animation of an impossible planet with rings always sideways to the sun

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?

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    $\begingroup$ What if this planet was tidally locked to the host star? $\endgroup$ – fasterthanlight Jan 10 at 18:52
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    $\begingroup$ @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. $\endgroup$ – Jyrki Lahtonen Jan 10 at 19:24
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    $\begingroup$ The second case is not as impossible as it may seem. In fact, the rings follow a Sun synchronous orbit en.wikipedia.org/wiki/Sun-synchronous_orbit which is a very real thing. $\endgroup$ – Pere Jan 11 at 13:51
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    $\begingroup$ @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 $\endgroup$ – José Andrade Jan 11 at 15:47
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    $\begingroup$ 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 $\endgroup$ – José Andrade Jan 11 at 16:02

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