oribts as discs

[rriverstone]

I was just looking at an animation of Saturn; it reminded me of an old question I've had since I was a little girl, 45 yrs ago. Why are so many orbits flat discs? Why isn't Saturn within a bubble of snowballs, rather than rings? Why do planets orbit Sol in a relatively disc shaped order? Why is this true for what I think must be most galaxies, too?? If gravity is pretty equal in all directions, why don't things orbit in spheres, bubbles or balls of material, around the focus?

[Henning Makholm]

I was just looking at an animation of Saturn; it reminded me of an old question I've had since I was a little girl, 45 yrs ago. Why are so many orbits flat discs? Why isn't Saturn within a bubble of snowballs, rather than rings? Why do planets orbit Sol in a relatively disc shaped order?

There are really two questions here: (1) why does each individual orbit fit into a plane? (2) why do all of the orbital planes in the solar system lie in roughly the same direction?

The first one is easy to answer. Consider the Sun and a planet. At some given moment in time we can imagine two lines in space: one that connects the centers of the sun and the planet, and another one that starts at the planets and indicates the direction the planet it moving in right now, relative to the sun. These two lines are not parallel, and since they cross at the planet, there will be exactly one geometric plane that contains them both. Then, as long as the gravitational interaction with the sun is the main influence on the planet, gravity will just move the planet's velocity vector around within that orbital plane, which means that the planet itself will stay on that plane. Every orbit in a two-body system has to be plane, due to this argument.

The second question is harder. I think a good explanation will need to involve the angular momentum of the interstellar gas cloud that collapsed to form the solar system, and probably also some statistical dynamics of the collapsing cloud. But I cannot right off the cuff produce an explanation that would convince myself ...

However, note that the nice shared-orbital-plane property we see in the solar system is not universal. Globular clusters have no preferred orbital plane. Neither do elliptical galaxies. Closer to home, the Oort cloud is not thought to be particularly aligned with the Ecliptic.

[hstarbuck]

Our man-made satellites can be placed in any orbit.

Click to view full size image

I think that if initial conditions of an interstellar cloud of gas and dust are organized (i.e. one big ball collapsing, spinning, gaining angular velocity), we could expect all objects to end up in single plane and single direction (e.g. counter-clockwise when viewed facing the plane from some location in space). Saturn's rings could be the remnant of a moon or moons that turned into rubble.

Saturn's rings may be very old, dating to the formation of Saturn itself. There are two main theories regarding the origin of Saturn's rings. One theory, originally proposed by Édouard Roche in the 19th century, is that the rings were once a moon of Saturn whose orbit decayed until it came close enough to be ripped apart by tidal forces (see Roche limit).[23] A variation of this theory is that the moon disintegrated after being struck by a large comet or asteroid.[24] The second theory is that the rings were never part of a moon, but are instead left over from the original nebular material from which Saturn formed.[citation needed]

It seems likely however that they are composed of debris from the disruption of a moon about 300 km in diameter, bigger than Mimas. The last time there were collisions large enough to be likely to disrupt a moon that large was during the Late Heavy Bombardment some four billion years ago.[25]

[dougettinger]

I was just looking at an animation of Saturn; it reminded me of an old question I've had since I was a little girl, 45 yrs ago. Why are so many orbits flat discs? Why isn't Saturn within a bubble of snowballs, rather than rings? Why do planets orbit Sol in a relatively disc shaped order?

There are really two questions here: (1) why does each individual orbit fit into a plane? (2) why do all of the orbital planes in the solar system lie in roughly the same direction?
The second question is harder. I think a good explanation will need to involve the angular momentum of the interstellar gas cloud that collapsed to form the solar system, and probably also some statistical dynamics of the collapsing cloud. But I cannot right off the cuff produce an explanation that would convince myself ...
However, note that the nice shared-orbital-plane property we see in the solar system is not universal. Globular clusters have no preferred orbital plane. Neither do elliptical galaxies. Closer to home, the Oort cloud is not thought to be particularly aligned with the Ecliptic.

Why does the ecliptic plane of planetary orbits exist? I am not sure but I believe the ecliptic plane exists for star systems with exo-solar planets (?) I cannot convince myself why it occurs? Perhaps the forming core has multiple clumps that form a plane that in turn creates the inertia conditions for other clumps of matter falling toward the core of attraction to align with the same plane.

Doug Ettinger
Pittsburgh, PA

[rstevenson]

It might simply be a matter of stability. I'm not up to the math myself, but I can visualize the instability of a system where planetary orbits are crossing at all sorts of angles. Such a system would gradually fling miscreant planets and other bodies either out of the system or into more stable orbits. So it's not so much a question of why a more or less planar system, but why not a multi-planar system.

... [later] ...

I see you posted the same question within another thread, and Chris answered it better than I could. I'll post your question and his answer here for completeness.

How does a disk form from groupings of matter randomly located in three-dimensional space? Why don't different accretion disks form with various alignments in the same region of several square AUs? These accretion disks could develop substantial angular momentum that should resist being pulled into a common accretion disk that could form a solar system like ours or a typical binary star system.

A disc is the only possible solution when you have material that interacts, as normal matter does. As material comes together, it becomes fluid-like, subject to the laws of fluid dynamics. Angular momentum is transferred between particles, and is conserved. Material is either brought into the dominant plane, or is ejected from the system.

Rob

[Chris Peterson]

It might simply be a matter of stability. I'm not up to the math myself, but I can visualize the instability of a system where planetary orbits are crossing at all sorts of angles. Such a system would gradually fling miscreant planets and other bodies either out of the system or into more stable orbits. So it's not so much a question of why a more or less planar system, but why not a multi-planar system.

... [later] ...

I see you posted the same question within another thread, and Chris answered it better than I could. I'll post your question and his answer here for completeness...

This explains why spherical accumulations can happen as well. Globular clusters, some small galaxies, dark matter halos- these are all cases where there is limited interaction between the material, so there is little transfer of angular momentum. But spinning systems like stellar systems and spiral galaxies presumably form from a medium consisting primarily of gas, and it becomes dense enough to behave as a fluid- you have collisions, friction, drag, and other effects that very efficiently transfer momentum.

[dougettinger]

Allow me to add another question to this discussion after Chris presented a convincing arguement. As for the Sun, its ecliptic plane is almost perpendicular to its direction of travel around the galaxy. Does the plane of orbiting planets or stars or galaxy spiral arms reveal the direction of travel of the main core or gravity source to be approximately perpendicular to the subject plane in all cases ?

Doug Ettinger
Pittsburgh, PA

[Chris Peterson]

Allow me to add another question to this discussion after Chris presented a convincing arguement. As for the Sun, its ecliptic plane is almost perpendicular to its direction of travel around the galaxy. Does the plane of orbiting planets or stars or galaxy spiral arms reveal the direction of travel of the main core or gravity source to be approximately perpendicular to the subject plane in all cases ?

I think the ecliptic plane of a stellar system (and some may not even have a well defined ecliptic) is unrelated to the galactic orbit. Our orientation is completely accidental.

[dougettinger]

I was not trying to establish a relationship between galactic orbit and ecliptic plane. I was checking to confirm any relationship between direction of travel (no matter what the location) and any established ecliptic plane.

So the ecliptic plane for our solar system could have been just as easily laid along the vector of the Sun's travel ?

Doug Ettinger
Pittsburgh, PA

[Chris Peterson]

I was not trying to establish a relationship between galactic orbit and ecliptic plane. I was checking to confirm any relationship between direction of travel (no matter what the location) and any established ecliptic plane.

I'm not quite sure of the distinction, since all stars in the galactic disc have the same direction of travel- they are traveling on the galactic plane, all in the same direction, with a period determined by Keplerian elements. The orientation of their spin axes is random with respect to their orbit.

So the ecliptic plane for our solar system could have been just as easily laid along the vector of the Sun's travel ?

Yes.

[dougettinger]

Please be patient with this science officer. I am trying to gain a complete understanding of these relationships.

In the case of the ecliptic plane being along the vector of the Sun's travel - then the planets would have to increase their orbital velocities when going against the direction of the Sun's path and decrease their orbital velocity when going with the Sun's direction which is independent of the differences of Keplerian velocities. This is not to say that Keplerian velocity changes would also be a factor. Is this correct ?

Doug Ettinger
Pittsburgh, PA

[Chris Peterson]

In the case of the ecliptic plane being along the vector of the Sun's travel - then the planets would have to increase their orbital velocities when going against the direction of the Sun's path and decrease their orbital velocity when going with the Sun's direction which is independent of the differences of Keplerian velocities. This is not to say that Keplerian velocity changes would also be a factor. Is this correct ?

No. What are you considering these orbital velocities with respect to?

Think about the Earth-Moon-Sun system. Do you think that the Moon's orbital velocity around the Earth changes depending on whether it is in a part of its orbit that is in the direction of Earth's solar orbit, or a part that is against that direction?

[dougettinger]

If one is able to look downward on the moon and Earth from a far place above the Sun's north pole, you should see that the moon takes a wavelike path about the Earth's orbital path. I then suppose the moon's absolute velocity about the Sun should be unchanging.

I suspect the planets in the same way would take planar wavelike paths about the Sun's orbital path around the galaxy. Since the planetary ecliptic plane is more perpendicular to the Sun's path, the planets travel more in a spiral fashion like DNA with respect to the galaxy's center. But the absolute velocity of each planet should remain unchanged regardless of the planetary ecliptic angle to the plane of galaxy disk. Is my logic improving ?

I guess I was thinking of a simple Copernician system with the orbits being a set of gearing.

Doug Ettinger
Pittsburgh, PA

[Chris Peterson]

If one is able to look downward on the moon and Earth from a far place above the Sun's north pole, you should see that the moon takes a wavelike path about the Earth's orbital path. I then suppose the moon's absolute velocity about the Sun should be unchanging.

The Moon is actually in its main orbit around the Sun, which exerts several times greater gravitational force on it than the Earth does. If you view the motion of the Moon relative to the Sun it does wiggle (because it is perturbed by the Earth). But if you view it with respect to the Earth, it is a perfectly ordinary orbit. It isn't speeding up or slowing down in some odd way, depending on which side of the Earth it is on. The travel is uniform elliptical motion.

I suspect the planets in the same way would take planar wavelike paths about the Sun's orbital path around the galaxy. Since the planetary ecliptic plane is more perpendicular to the Sun's path, the planets travel more in a spiral fashion like DNA with respect to the galaxy's center. But the absolute velocity of each planet should remain unchanged regardless of the planetary ecliptic angle to the plane of galaxy disk.

It's the same as with the Moon. From the reference frame of the galaxy center, the path of the planets, and even the Sun, is complex. But if we use the Sun as a reference, the planets are all in ordinary orbits. Those orbits would be exactly the same regardless of the orientation between the ecliptic plane and the galactic plane (or the direction of the Sun's orbit, if you prefer).

[dougettinger]

I now have a much deeper and more accurate understanding. Using the moon as an example for the planets was very helpful. Thanks.

Doug Ettinger