Why do all the planets orbit in the same plane?

[QEDrpf33]

Hello,
I was just curious why do all of the planets in the solar system orbit in approximately the same plane? Why is it not random? This is not a homework question, but if possible I would like to see the math that accompanies the explanation.
thanks

 

[chollapete]

You'll get better answers, I'm sure, but what I recall reading is that planets that orbit in planes at large angles to one another create gravitational perturbations that cause instability in one or more planets' orbits. The instability is evinced by planets changing their orbits to either collide or fly off into deep space. An alternative view is that the nearly-same-plane configuration is a least-energy configuration and hence favored. Sorry, I don't know the math. While it is not accessible in the least, I've heard the Herbert Goldstein's _Classical Mechanics_ covers celestial mechanics in excruciating detail. Again, I'm not recommending it for someone at my level, but it's good to know about it as a goal. HTH.

 

[mikelepore]

The plane of the solar system (the ecliptic) preserves the average of the angular momentum of the original gas and dust that formed the accretion disc. Gravity made the big blob flatten into a spinning disc, but that didn't change the angular momentum. Then gravity made clumps separated by spaces appear in the disc, and these became planets, and that didn't change the angular momentum either. The law of conservation of angular momentum says that the total angular momentum of a system of objects won't change as long as no torques are applied to the system.

 

[nonequilibrium]

Hey mikelepore, nice answer. So I get how you go from the spinning sphere to a spinning disc, but how did we get the spinning sphere in the first place?

 

[mikelepore]

but how did we get the spinning sphere in the first place?

When gravity makes gas and dust from far away converge, there would be a very small probability that the total angular momentum would be zero. It would be zero if the particles would were all headed directly towards a common point that forms the center of the new solar system, but that's not a probable initial condition. You even have angular momentum, with respect to any reference point, when a particle is moving in a straight line path past that point, not only in a curved path. Therefore, let gravity pull in a lot of particles from over a wide distance, and, after they converge into a group, that group will probably be spinning.

 

[nonequilibrium]

I get that the angular momentum is probably non-zero, but how would you explain the mass coherence? I'd expect a chaotic whirling.

 

[Chronos]

Look at galaxies, that is the preferred plane of accretion. A few are spherical, the great majority are disc shaped.

 

[mikeph]

Quick question on going from spinning sphere to spinning disk,

Does this happen because at the "poles" there is no centrifugal force so the gas goes inwards, but at the equator the gas stays out?

But then, why does the gas which started at the poles not just oscillate up and down?

 

[mikelepore]

Quick question on going from spinning sphere to spinning disk,

Does this happen because at the "poles" there is no centrifugal force so the gas goes inwards, but at the equator the gas stays out?

But then, why does the gas which started at the poles not just oscillate up and down?

Gravity is sufficient to make the spinning sphere flatten into a spinning disc. That the particles are attracted toward each other is the only cause you need.

Movement doesn't occur in the radial direction, that is, the particles don't suddenly fall toward the center of mass, because the particles have velocity vectors that have components that are perpendicular to the gravitational force from the center of mass.

 

[mrchristr]

I have always wondered and figured the answer was taught in physics 201. I dropped out of 101 because the math was ahead of my advanced calc class so I don't know the math or the terminology. Yesterday I poured beet juice into a slowly draining sinkful of water and thought I understood as such: The spinning sun's gravity distorts space into a similar shape as the magnetic field. I watched the beet juice split, some going down the drain and some spinning out into a flat orbit horizontal to the spin. I don't understand the math but it must be known to solve the three body problem. .... My question: Why isn't the sun flat?

 

[mrchristr]

But how could the components be perpendicular if gravity was equal in all directions, or is it just a known fact that gravity distorts space. Crap! It has been two years since this was visited. Will I get a reply at all.

 

[mikeph]

Coincidentally this is my first visit for a while.

My understanding is this: the sun has radiation pressure which opposes gravity at all polar angles, so it can preserve its (nearly) spherical shape. The solar system has no radiation pressure so it collapses due to gravity, but it must still conserve angular momentum. Objects at constant radius in the solar system experience equal force due to gravitation, but objects far out of the solar plane have very small velocity components perpendicular to this force, so they tend to be drawn into the plane from above/below, whereas equidistant objects that already lie in the plane have large perpendicular velocities and tend to maintain circular or elliptical motion in that plane.

 

[D H]

Gravity is sufficient to make the spinning sphere flatten into a spinning disc. That the particles are attracted toward each other is the only cause you need.

Gravity is not sufficient to make the spinning sphere flatten into a spinning disc. You also need dissipative/dispersive forces such as inelastic collisions. Without such forces, the sphere would not collapse. For example, the conjectured dark matter halo that surrounds a galaxy remains spherical rather than disc shaped because of the lack of such forces.

What those dissipative/dispersive forces do is provide a mechanism by which the gas cloud can settle to a state that minimizes mechanical energy while conserving angular momentum. That minimal energy configuration is a flattened disc.

My question: Why isn't the sun flat?

For one thing, the Sun is spinning very, very slowly. One revolution per 25 days at the Sun's equator, one per 34 days near the Sun's poles. There's not much there to flatten the Sun out.

More importantly, the conditions of the Sun and the gas cloud are quite different from one another. The mean free path of particles in the Sun, even near it's surface, is very small. Particles in the Sun aren't orbiting the Sun. They instead move a tiny bit and collide, move a tiny bit and collide. The underlying physics is that of hydrostatic equilibrium. The mean free path of particles in the interstellar gas cloud is huge. The physics that describes the particles in the gas cloud is orbital mechanics with infrequent collisions that reset the orbits.

 

[mrchristr]

I kind of thought my little experiment with the beet juice and slowly draining dish water was cool. Does it demonstrate any of the principles we are talking about?

 

[rbj]

The plane of the solar system (the ecliptic) preserves the average of the angular momentum of the original gas and dust that formed the accretion disc. Gravity made the big blob flatten into a spinning disc, but that didn't change the angular momentum. Then gravity made clumps separated by spaces appear in the disc, and these became planets, and that didn't change the angular momentum either. The law of conservation of angular momentum says that the total angular momentum of a system of objects won't change as long as no torques are applied to the system.

Hey mikelepore, nice answer. So I get how you go from the spinning sphere to a spinning disc, but how did we get the spinning sphere in the first place?

maybe not a spinning sphere but maybe a spinning cylinder of stuff. whatever is this swirl that is in the turbulence of condensing matter in the early life of the universe.

i think it's the same reason that most galaxies that hadn't collided with another are nice spiral disks of matter. there are these swirls of turbulence at many levels of scale in the universe (what one might expect after a big bang). perhaps the largest scale is what makes these groups of galaxies. then the scale of turbulence just smaller than that is what makes galaxies. then the scale smaller than that is what makes solar systems, and then probably the planets are the last leftover eddy currents. except for Uranus which is tipped at lot (and that might be evidence for a lower-scale swirl that is not an eddy of the solar system) i think the rest of the planets spin on an axis that is roughly perpendicular to the sort of common plane of the planets' orbits. maybe some spectacular collision is what tipped Uranus. and i think that the sun's spin is also along roughly the same direction.

so think of a big turbulent volume of gas with big swirls and little swirls and all sorts of swirls in between. and the swirls swirling in all sorts of random directions. but within each swirl, not every direction is random and things line up a lot with the axis of rotation of the swirl more often than not.

and the spinning is what keeps the galaxy or solar system from collapsing due to gravity along a radial direction. but along the direction of the axis of rotation, nothing is opposing gravity. so the mass collapses along the axis of rotation and you'll get something sort of flat.

 

[Anti-Crackpot]

then the scale of turbulence just smaller than that is what makes galaxies. then the scale smaller than that is what makes solar systems, and then probably the planets are the last leftover eddy currents. except for Uranus which is tipped at lot (and that might be evidence for a lower-scale swirl that is not an eddy of the solar system)

Star clusters, then, will, presumably, also tend toward a disk-like formation pattern? Sounds a lot like fractals. Self similarity and repeating shape across all levels of organization...

- AC

 

[Drakkith]

Star clusters, then, will, presumably, also tend toward a disk-like formation pattern? Sounds a lot like fractals. Self similarity and repeating shape across all levels of organization...

- AC

I don't believe star clusters tend to fall into disk-like shapes. I think the reason is that even in hugely dense globular clusters the stars are still extremely far apart compared to their actual sizes, so impacts that would cause loss of momentum don't happen. Some stars are thrown out by gravitational effects, but overall the cluster retains a spherical shape.

 

[ahadley]

So this post is old, but I would like to offer a thought:

Our solar system is old since it has heavy matter (elements greater than iron) meaning it had to have been formed by a supernova that formed these elements.

Say there was a super-giant star. This star was spinning (due to previous conditions to its formation, as most stars spin). This star exploded.

Exploding a star that is spinning will cause matter to 'generally' shoot out from the center of the explosion. Matter from the poles will shoot straight up from the center of the star and matter at the equator will shoot out from the direction of the equator.

Matter from the poles will shoot up and some or most of it will fall back down to the center of the core of the star that remains. Matter from the equator will not 'fall back to the stars core center' because it has an angular velocity and will orbit the core of the star that remains.

This explanation would explain why a spinning supernova would result in an accretion disk that would eventually form a sun and an orbital plane that contains planets, would it not?

This is more or less a thought that I had this morning (03apr14) and was wondering if it had merit or not.

 

[Drakkith]

This explanation would explain why a spinning supernova would result in an accretion disk that would eventually form a sun and an orbital plane that contains planets, would it not?

No, that isn't how the formation of our solar system occurred. The elements ejected from the supernova were dispersed into interstellar space and mixed with clouds of hydrogen gas to form large clouds of gas and dust. It is these clouds of hydrogen gas and "dust" that collapse to form new stars. (Typically many new stars will be formed from a single cloud)

 

[Sabin Ionescu]

Gravity and angular momentum are indeed the key to the answer.

But, how about the Super Massive Black Holes(SMBH) geometry...
We know now what in the '60 it was just a theoretical and matematical issue, that galaxies have in their center super massive black holes, responsible for the existence and the shape of the galaxies itselves(mainly the spiral ones). One year ago one of the SMBH in Milky Way started to feed with a nearby massive star. Now is a orbiting gas formation and in one year will be completely consumed. It's still live recording...
What's interesting, the SMBH are seeming to eject in a perpendicular plane to the galaxy's disk plane, in two opposing directions powerfull jets of gamma and other radiations, particules and photons.
My question is not why the SMBH is doing that(although this is a big question too), but why these twin opposing ejected jet streams are perpendicular to the galaxy's plane? I mean it's obvious that gravity has to do with that, but how is this matematicaly possible? And from where these ejections are emerging? From event horizon? Nothing can escape the event horizon, not even the light. Home come "something" is ejected?

 

[Subluminal]

@Sabin Ionescu, check out Doug Finkbeiner's work at http://arxiv.org/a/finkbeiner_d_1. In particular, read arXiv:1205.5852

It's my understanding that matter/energy (as we know it) never escapes the event horizon, but magnetic fields do. As a SMBH feeds on clouds and stars, the accretion disks that form prior to entering the black hole are not 100% consumed. Some of the ionized material (electrons and plasma) gets spun off instead and caught up in cork-screw shaped fields emanating along the N and S poles of the SMBH, accelerating away to escape velocity (~0.999c) in both directions.

Leptons speeding along these paths bombard low frequency photons in the regions above and below the galactic disk, bumping up their energies and causing the observable X-rays and gamma rays (inverse Compton scattering). A large object feeding into the SMBH is rare and would create intense beams of radiation called "jets", while broad "bubbles" form from slower, more steady dose accumulation from all the more common, less-massive clouds that get sucked in all the time.

In the case of the Milky Way, our "Sagittarius" black hole has a magnetic field axis tilted 15° from the disk (not perpendicular), and we apparently see one pair of old jets shooting off at this angle in opposite directions. Either due to precession (the black hole axis wobbles around the disk axis), or the black hole's magnetic poles simply don't coincide with its rotational axis, (or both?) the cork screw fields kind of spray around like a lawn sprinkler, so the bubbles result from a more even dose of low-intensity, high-energy radiation over time.

 

[marcus]

The original question was answered. The density in a gas cloud varies and over dense regions tend to collapse. Any random over dense region is likely to have some angular momentum. Will be turning, eddying, swirling with some overall rotational motion. For simplicity imagine the cloud is spherical, with some average rotation around some axis, and starts to collapse.

Quick question on going from spinning sphere to spinning disk,

Does this happen because at the "poles" there is no centrifugal force so the gas goes inwards, but at the equator the gas stays out?

But then, why does the gas which started at the poles not just oscillate up and down?

Mike had two intelligent questions. The answer to the first was basically YES. the equatorial plane has more rotational momentum ("centrifugal force" if you like) and that keeps it spread out. Stuff at the poles tends to fall into the equatorial plane.

But then why doesn't it keep on yo-yoing up and down thru the plane? why does it eventually stay in the plane and join in the circulation there? the answer is the matter falling into the plane keeps BUMPING---having collisions which heat it up and make it radiate away the up-and-down oscillation energy as heat. This getting rid of surplus energy is called DISSIPATION.

DH explained that

Gravity is not sufficient to make the spinning sphere flatten into a spinning disc. You also need dissipative/dispersive forces such as inelastic collisions. Without such forces, the sphere would not collapse. For example, the conjectured dark matter halo that surrounds a galaxy remains spherical rather than disc shaped because of the lack of such forces.

What those dissipative/dispersive forces do is provide a mechanism by which the gas cloud can settle to a state that minimizes mechanical energy while conserving angular momentum. That minimal energy configuration is a flattened disc.

Somebody else asked, given that the rotating spherical cloud can collapse to a planar solar system, why doesn't the SUN collapse to form a pancake? DH also answered that one.

For one thing, the Sun is spinning very, very slowly. One revolution per 25 days at the Sun's equator, one per 34 days near the Sun's poles. There's not much there to flatten the Sun out.

More importantly, the conditions of the Sun and the gas cloud are quite different from one another. The mean free path of particles in the Sun, even near it's surface, is very small. Particles in the Sun aren't orbiting the Sun. They instead move a tiny bit and collide, move a tiny bit and collide. The underlying physics is that of hydrostatic equilibrium. The mean free path of particles in the interstellar gas cloud is huge. The physics that describes the particles in the gas cloud is orbital mechanics with infrequent collisions that reset the orbits.

I don't understand the recent posts that do not seem to address the question which is the topic of this thread. Some of the most recent posts seem off topic.

 

[Subluminal]

I'm not convinced by the explanation that the initial angular momentum of the gas cloud develops by random chance, density anisotropies, or whatever, as it collapses into a disk. After reading http://arxiv.org/pdf/astro-ph/0512046.pdf, it's more plausible to me that, early on, Coriolis forces affect the paths of the dust particles as the cloud tightens and flattens out. This is where the initial angular momentum comes from, and is simply conservation of the angular momentum of all the particles that had been already rotating as they orbited around a galactic center. From simple orbit mechanics, dust particles closer to this center travel, on average, faster than particles further out. As particles move towards the center of mass of the cloud, they cross these isolines of velocity, if you will, causing their paths to curve similar to how we observe particles of a hurricane system curve as they move toward the eye of the storm, across lines of latitude where the surface of the Earth is passing underneath at varying speeds. A hurricane gets its angular momentum from the rotation of the Earth, and a dust cloud get spinning thanks to the rotation of the galaxy it forms in.

Once the disk develops shear and gravitational forces that overcome the Coriolis effect, then the random inelastic collisions dominate things like planet sizes, axis tilt, orbit inclination and such. With the slight exceptions of Venus (very slow backspin) and Uranus (axis tilt ~90°) all planets turn in the same general direction, as each in turn derived its angular momentum from the spinning of the accretion disk, thanks again to the Coriolis force.

 

[D H]

I'm not convinced by the explanation that the initial angular momentum of the gas cloud develops by random chance, density anisotropies, or whatever, as it collapses into a disk. After reading http://arxiv.org/pdf/astro-ph/0512046.pdf, it's more plausible to me that, early on, Coriolis forces affect the paths of the dust particles as the cloud tightens and flattens out.

Your conjecture is falsified by observation. Whether astronomers look at nearby planetary nebulae, nearby binary star and triple star systems, and the newly discovered exoplanetary systems, they see a purely random orientation. They even see that in galactic clusters, which presumably formed from a common base.

The one possible exception to that is planetary nebulae close to the galactic core. These do appear to have a non-random orientation. That was a rather startling discovery because it makes no sense. Perhaps it's the Milky Way's magnetic field that was responsible for this when the stars that have since died and made those nebulae first formed (so several billions of years ago). Maybe the galactic magnetic field was stronger back then. Magnetism does appear to have some effect on star formation, but it's still more than a bit of an unknown as to how and why.

 

[Subluminal]

The hurricane was a bad example - in that analogy, the Earth's atmosphere is about the same thickness as the storm, but the galactic disk is very thick compared to a cloud that will form a solar system. It still makes sense to me, if no one else, that particles drawn toward the center of the dust cloud, from all directions in 3D space, will curve as they pass across the velocity gradient of the galactic disk, but these will enter micro orbits in random inclinations and directions. It won't be a disk at first, just this bunch of grains in orbital type trajectories like electrons around a nucleus, and not all plunging straight into the stellar object. I see now that there's no reason the overall angular velocity should have any relationship to the galactic core axis. This spherical mess of orbiting grains would flatten as previous commenters explained, with Monsieur Coriolis having nothing to say about determining the overall average inclination that will become the equatorial plane.

Turbulence seems to play the major role, see http://iopscience.iop.org/0004-637X/582/2/869/pdf/52083.web.pdf. This could explain those disks near the core where they do seem to line up?

This was helpful: http://www.circumstellardisks.org/resolved.php?key=incl
As observed from our location, here's the inclination (disk axis vs. line of sight) of 170 disks we've been able to resolve. I don't know what probability distribution applies to these angles observed from our position, but it looks to me that formed disks are pointed in no particular direction as you said. A few point at us, but most point in other directions...

Thanks for your reply!

 

[Jimster41]

Is there any speculation that there may be interference patterns in orbital mass ensembles like planetary or solar or galactic systems?

In other words has it ever been hypothesized that there may be physical (as opposed to just visual appearance) similarity between Saturn's rings and a Poisson interference pattern, or a super-massive black hole at a galactic core and a Poisson spot?

I don't mean to try and hijack this thread. This thread got my attention because the same question was bothering me... Do we believe we have accounted for everything that causes orbital structure in mass ensembles?