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 momemtum 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

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

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 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.


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

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 sorta 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 sorta flat.

Anti-Crackpot

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

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.