Planet Formation: Unsolved Questions in Solar System Origin

[Shubert]

In a recent theological discussion, I came to realize that there is a point in question regarding planet formation in the current model of the origins of the Solar System. The question itself is not theological, but has some theological ramifications. It goes like this:

Planets are believed to have formed through accretion in a solar nebula of dust and gases. Planetoids swept through this dust cloud, accumulating material until they reached their present size and character.

But, it is apparent that the mass of the dust particles and the mass of the planetoid (or planet) are quite different. Ye the orbital distance of a given body around its central star will be a function of the mass and orbital velocity of the body.

So, as planetoids acquire mass, they must also experience a change in either velocity or distance from the central star. It seems to me that a change in orbital velocity will not occur spontaneously, so one would expect that, as the planetoids increased in mass, they would spiral into their host star. If the planetoids eventually reached a stable orbit, I would expect it to be highly eccentric.

I cannot envision a scenario in which dust-cloud aggregation will result in a stable planetary system consisting of multiple, nearly-circular orbiting planets.

What am I missing?

 

[mathman]

Ye the orbital distance of a given body around its central star will be a function of the mass and orbital velocity of the body.

So, as planetoids acquire mass, they must also experience a change in either velocity or distance from the central star.

This doesn't feel right. Why should mass affect velocity or distance? I think Galileo's work contradicts this idea.

 

[Kurdt]

The distance is merely a function of velocity and not mass. The velocity of a body revolving around a central mass assumed to be much greater than that of the body can be derived by equating the force from circular motion and Newtons gravitational law as so:

$$F=\frac {GmM} {r^2} = \frac {mv^2} {r}$$

this reduces to

$$v = \sqrt {\frac {GM} {r} }$$

Thus as a planet acquires mass the velocity does not change.

 

[Shubert]

This doesn't feel right. Why should mass affect velocity or distance? I think Galileo's work contradicts this idea.

Sorry, I must not have put that very well.

I'm not saying that the mass affects the velocity or distance.

What I am saying is that the distance of a given mass, in a stable orbit, from the sun is a function of its velocity and mass - proportional to velocity, and inversely proportional to mass. Any given body can orbit at any given distance so long as the mass and velocity are balanced against each other.

(Can anyone help by inserting the equation for the distance/mass/velocity relationship for an orbiting body?)

Anyway, I am not saying that the mass results in a given velocity, or that the distance does - only that the velocity and mass will be balanced against each other for a body orbiting at a given distance from its sun.

Hope I cleared that up.

 

[Shubert]

Thus as a planet acquires mass the velocity does not change.

Right. And thanks for adding a little math to the discussion.

So, if the mass increases while the velocity remains the same, then the orbit will decay into the sun.

Right?

 

[Kurdt]

The last equation I gave shows how the velocity of an object in orbit is related to M which is the mass of the sun in your example (and not the mass of the orbiting object) and also the distance from the sun. The mass of the actual planet cancels out in the derivation and so the velocity bears no relation to the mass of the planet and thus the radius of the orbit only depends on the velocity the object is travelling.

I apologise if you took the first equation to be the statement of what was happening. This is actually conveyed in the second equation. I added the first to show you where the second was derived from.

EDIT: I know this is rather pedantic but cosmology is concerned with scales greater than that of galaxies and this is in the wrong forum. Perhaps you would receive more guidance if it were relocated to astrophysics or general astronomy.

 

[Shubert]

EDIT: I know this is rather pedantic but cosmology is concerned with scales greater than that of galaxies and this is in the wrong forum. Perhaps you would receive more guidance if it were relocated to astrophysics or general astronomy.

Kurdt - thanks for this guidance. I was wondering about that. But if you would go one more step with me, that will probably be sufficient.

The last equation I gave shows how the velocity of an object in orbit is related to M which is the mass of the sun in your example (and not the mass of the orbiting object) and also the distance from the sun. The mass of the actual planet cancels out in the derivation and so the velocity bears no relation to the mass of the planet and thus the radius of the orbit only depends on the velocity the object is travelling.

So, what you are saying is that the only variable which determines orbital distance is orbital velocity - that the mass of the orbiting object is unrelated to the orbital distance/period. Thus, two completely dissimilar masses can occupy the same orbital pattern, so long as they share the same velocity. And that a change in a body's mass will not change its orbital distance.

Right?

 

[SpaceTiger]

So, if the mass increases while the velocity remains the same, then the orbit will decay into the sun.

Normally, no. If the planet is much less massive than the sun (as all planets and planetoids are), then the semimajor axis of the orbit can be determined from the planet's velocity and the sun's mass.

However, if the process of accreting mass results in a net torque to the planet/planetoid, then the planet's orbit will change with time. This is called planet migration and is still not entirely understood by the astronomical community. We think it occurs, but there are several competing explanations being thrown around.

Something we're even less sure of is exacty how "probable" the observed configuration of planets is. I think it's unlikely that it formed in exactly the configuration we see today -- what you see is probably just a semi-stable equilibrium that it happened to fall into. That this configuration allows for the formation and healthy evolution of life may simply be a consequence of the anthropic principle; i.e. that it would have to be that way or we wouldn't be here to ask the question.

We're still in the process of discovering extrasolar planetary systems, so answers to some of these questions are forthcoming. Theorists are also working hard on the question. My roommate is doing his thesis on simulating the long-term evolution of planetary systems and I suspect that I'll have a reference for you sometime in the next six months that will include, for example, eccentricity distributions.

 

[Kurdt]

So, what you are saying is that the only variable which determines orbital distance is orbital velocity...Thus, two completely dissimilar masses can occupy the same orbital pattern, so long as they share the same velocity. And that a change in a body's mass will not change its orbital distance.

Right?

That is correct.

that the mass of the orbiting object is unrelated to the orbital distance/period. ?

This is not entirely true but it has nothing to do with the original question. The mass of a planet is related to the orbital distance through Newton's law of gravity. The mass of a planet around the sun for example does contribute slightly to the period also but we normally neglect the planets mass because it is small compared with the sun. Perhaps you would like to look up Newton's form of Kepler's third law. I know this last bit may seem strange but if you have any questions post away.

 

[Shubert]

I guess I confused myself by trying to think in tensor terms. I was remembering the motorcyclist on the conical wall: The faster he went, the higher up the wall he went. And the more mass you put on the motorcyclist, the faster he had to go to make it to his "orbit". Right?

But I guess that may be a poor analogy.

Now, I just have to figure out why.

 

[tony873004]

In the process of accumulating dust and small objects, the overall net bias of collisions that slow you down and collisions that speed you up should be close to 0. So your orbit will not acquire much eccentricity, and may even circularize as a result.

Likewise, when an a planet encounters small debris, but does not collide with it, some angular momentum is transfered. If the planet boosts the object inward, the planet must respond by moving outward, but at a proportional rate to their masses. And if the planet boosts the object outward, then it must respond by migrating inward. If the net bias of a large amount of such encounters is 0, then the planet does not migrate.

There's a theory that Saturn, Neptune and Uranus are thought to have migrated out, while Jupiter migrated in slightly. As Saturn, Uranus, and Neptune scattered the objects in their vicinity they would often encounter the same objects. Sometimes it boosted them outward, sometimes inward. The net bias would have been 0 except some of the outward boosted objects reached escape velocity, tilting the bias towards inward migration. And some inward boosted objects encounterd Jupiter and were ejected by Jupiter from the solar system. Unable to encounter Saturn, Neptune or Uranus again, there was a net bias of inward boosted objects which pushed the planets out. "Feeding" the objects to Jupiter was a much more efficient way to eject them from the solar system, so the outward bias of these 3 planets dominated. Jupiter, however, with its mighty gravity that could eject objects with ease migrated inward as a result.

As planets migrate they can capture objects into resonances. This is one reason why some feel that Neptune migrated a large distance. It has many objects trapped in 3:2 (Plutinos) and 2:1 (Twotinos)resonances, as well as a smaller collection of objects in the weaker resonances. We're just starting to discover a population of 1:1 (Trojans) as well. The populations in these resonances, combined with their eccentricities, as well as whether an object in a 2:1 resonance is in a leading resonance or a trailing resonance provides a signature of Neptune's migration that gives clues about how far and how fast it migrated.

 

[russ_watters]

I didn't read throught the last couple of responses, but I think what you may be missing is that the disk is already orbiting the sun, so as it coalesces, there is no net change in kinetic or potential energy of the orbiting dust/planetoids and no net change in the mass of the solar system.

If the dust were not orbiting the sun, but perhaps falling into it, then as planetoids swept it up, there would be an accompanying increase in required orbital energy, but no gain in orbital energy, and thus it would spiral in.

 

[Kurdt]

The nebula you are referring to is a planetary nebula which means it is formed from the atmosphere of a dying star. The Nebula that created our solar system is most likely long gone. When whatever stars an planets formed from it were relatively complete the remaining gas would be pushed into space from the strong solar winds of the newborn stars. This gas will now be spread throughout space at a very low density do no 'mother' nebula exists.

 

[Shubert]

I didn't read throught the last couple of responses, but I think what you may be missing is that the disk is already orbiting the sun, so as it coalesces, there is no net change in kinetic or potential energy of the orbiting dust/planetoids and no net change in the mass of the solar system.

If the dust were not orbiting the sun, but perhaps falling into it, then as planetoids swept it up, there would be an accompanying increase in required orbital energy, but no gain in orbital energy, and thus it would spiral in.

So, then, in order to form a stable planetary system, the original nebula must have been rotating stably.

I remember reading that the rotation of the original nebula was thought to have been the result of gravitic attraction within the nebula. But based on what you are saying, this could not have been the case, since rotation of this kind (whirlpool) would have necessarily meant that all planetoids forming in the mix would fall toward the center of the cloud, becoming part of the solar mass.

Of course, regardless of the cause or character of the original rotation, the following question remains on the table: Since the sun is thought to have formed from the coalescence of the original cloud, then the overall motion of material in the cloud must have been toward the center; the gravitic force which formed the sun from the cloud must also have been drawing all of the material to the center.

So, then, what balancing forces could have existed in the original protostellar nebula which would have countered the force of gravity sufficiently to result in planets in stable orbits, rather than all material being either swept into the sun or blown away by the cosmic wind?

It seems that the formation of stable orbits of any degree of regularity is the least likely outcome from the collapsing cloud model of the formation of the Solar System.

(By the way, I realize that these questions may be very basic, but I would appreciate any help anyone can give. I'm afraid that the materials I've read on the subject are not much more sophisticated than a Sunday supplement.)

 

[russ_watters]

So, then, in order to form a stable planetary system, the original nebula must have been rotating stably.

I remember reading that the rotation of the original nebula was thought to have been the result of gravitic attraction within the nebula. But based on what you are saying, this could not have been the case, since rotation of this kind (whirlpool) would have necessarily meant that all planetoids forming in the mix would fall toward the center of the cloud, becoming part of the solar mass.

No, it doesn't have to be (really, can't be) stable. If it were, then all matter would have stayed in orbit around its center of mass. Instead something like 99.9% of the matter did spiral into the center and become the sun or got blown out of the solar system. What's left is what did settle into a stable disk.

 

[Kurdt]

The rotation of the nebula is differential. Because all the disc is at first essentially of a uniform density it tends to ad a drag factor to developing planets. Some of these planetoids will fall into the star but once most of the nebula has turned into planetoids remaining gasses are blown off the resistance tends to zero and whatever velocity the remaining planetoids have is conserved.

 

[Shubert]

No, it doesn't have to be (really, can't be) stable. If it were, then all matter would have stayed in orbit around its center of mass. Instead something like 99.9% of the matter did spiral into the center and become the sun or got blown out of the solar system. What's left is what did settle into a stable disk.

Right - that's a given, assuming the original conditions. But I still don't see how any of the matter in the original cloud ended up in stable orbits. It would seem that all of it was on the move inward, and should have continued in that direction, until fusion began in the center and a solar wind formed - then everything small enough would have been blown out of the heliosphere.

Is there a standard explanation for how a collapsing cloud produced stably-orbiting planets?

 

[Shubert]

The rotation of the nebula is differential. Because all the disc is at first essentially of a uniform density it tends to ad a drag factor to developing planets. Some of these planetoids will fall into the star but once most of the nebula has turned into planetoids remaining gasses are blown off the resistance tends to zero and whatever velocity the remaining planetoids have is conserved.

But if the original disc is coalescing, shouldn't all of the dust have been on its way into the center of the nebula? And if so, shouldn't all of the planetoids thus formed also be heading for the center?

 

[Kurdt]

To Vogue: The sun does not travel in a straight line, it orbits the galactic centre.

To Schubert: Think of the gasses in the disc between planetoids as a kind of 'treacle'. When the gasses are present they slow the planetoid down. When the gasses get pulled into the planetoids and eventually get blown off by the birth of the star there is nothing to slow the planets down and they maintain their orbit.

 

[Shubert]

To Vogue: The sun does not travel in a straight line, it orbits the galactic centre.

To Schubert: Think of the gasses in the disc between planetoids as a kind of 'treacle'. When the gasses are present they slow the planetoid down. When the gasses get pulled into the planetoids and eventually get blown off by the birth of the star there is nothing to slow the planets down and they maintain their orbit.

Kurdt,

Okay, that's a good analogy, and it helps model the idea that you are getting across.

So, it seems that you are saying that, as soon as the surrounding dust is gone, a planet which was in a decaying orbit will simply stabilize in whatever orbit happens to match its velocity. So, it may migrate to a new orbital distance after the nebular cloud is purged, but only so that its orbit matches its tangential velocity.

Is this right?

 

[Kurdt]

Pretty much; I hope this analogy agrees with you?

 

[SpaceTiger]

Because all the disc is at first essentially of a uniform density it tends to ad a drag factor to developing planets.

I'm not quite sure the origin or reasoning of your claims here. The disk likely begins with a smooth density distribution, but I don't see why it should be uniform. Also, please elaborate on how this "drag" mechanism that you're proposing works.

 

[Kurdt]

I'm not quite sure the origin or reasoning of your claims here. The disk likely begins with a smooth density distribution, but I don't see why it should be uniform. Also, please elaborate on how this "drag" mechanism that you're proposing works.

Yeah sorry uniform was a slip on my part. The drag factor on planetesimals comes from the gas rich medium in which they orbit which provides a sort of 'atmospheric' drag if you will circularising the orbits and bringing them closer to the parent star. As you can imaging this depends greatly on the density of the disk and the stage of planetesimal formation.

 

[SpaceTiger]

The drag factor on planetesimals comes from the gas rich medium in which they orbit which provides a sort of 'atmospheric' drag if you will circularising the orbits and bringing them closer to the parent star.

The gas in the disk is orbiting with the planetesimals (i.e. the planetesimals are not moving "through" the medium), so at lowest order, there should be no drag.

 

[Kurdt]

The gas in the disk is orbiting with the planetesimals (i.e. the planetesimals are not moving "through" the medium), so at lowest order, there should be no drag.

Thats assuming the planetesimals form in perfect orbits.

 

[SpaceTiger]

Thats assuming the planetesimals form in perfect orbits.

It's not really an assumption. A planetesimal on an elliptical orbit will be moving through the disk material and will experience a drag. This will result in a net energy loss, but it will also cause the orbit to circularize. The final result, a circular orbit, should be a stable, "dragless", configuration. Again, to lowest order, the planetesimal should not spiral into the sun.

However, the planetesimal is massive and exerts a local influence on the protoplanetary disk. If it accretes material orbiting at slightly larger radii (which is orbiting more slowly), there will be a net loss of angular momentum. If it accretes material orbiting closer in, there will be a net gain. To lowest order, there should be no net change in angular momentum because material is accreted from both directions. However, if there is an imbalance in the accretion process, the planetesimal can lose or gain angular momentum and spiral in or out. There are a variety of ways to create an imbalance and thus cause the planet to migrate. There is no consensus in the community as to which mechanism or mechanisms are most important, if any.

 

[Kurdt]

It's not really an assumption. A planetesimal on an elliptical orbit will be moving through the disk material and will experience a drag. This will result in a net energy loss, but it will also cause the orbit to circularize. The final result, a circular orbit, should be a stable, "dragless", configuration. Again, to lowest order, the planetesimal should not spiral into the sun.

However, the planetesimal is massive and exerts a local influence on the protoplanetary disk. If it accretes material orbiting at slightly larger radii (which is orbiting more slowly), there will be a net loss of angular momentum. If it accretes material orbiting closer in, there will be a net gain. To lowest order, there should be no net change in angular momentum because material is accreted from both directions. However, if there is an imbalance in the accretion process, the planetesimal can lose or gain angular momentum and spiral in or out. There are a variety of ways to create an imbalance and thus cause the planet to migrate. There is no consensus in the community as to which mechanism or mechanisms are most important, if any.

It was to the circularisation I was referring to in a previous post but I should have been more explicit. Apologies

 

[SpaceTiger]

Note that part of this thread was split off into another:

https://www.physicsforums.com/showthread.php?t=125616"

 

[Andre]

...
However, the planetesimal is massive and exerts a local influence on the protoplanetary disk. If it accretes material orbiting at slightly larger radii (which is orbiting more slowly), there will be a net loss of angular momentum. If it accretes material orbiting closer in, there will be a net gain...

Are you sure? I thought that the velocity of an orbiting mass is proportional to the inverted square root of the radius, however the angular momentum is directly proportional to the radius, resulting in a increase in angular momentum proportional to the square root of the radius. From this it appears that the particles orbiting at larger radii have a bigger angular momentum.

 

[SpaceTiger]

Are you sure? I thought that the velocity of an orbiting mass is proportional to the inverted square root of the radius, however the angular momentum is directly proportional to the radius, resulting in a increase in angular momentum proportional to the square root of the radius. From this it appears that the particles orbiting at larger radii have a bigger angular momentum.

You're correct, but my description made the interaction sound a bit simpler than it is. Rather than simply conserving angular momentum between the accreted material and the planetesimal, we also need to consider the effect the accretion process has on the nearby disk.

Now, I admit I'm not an expert in this area and could have it wrong, but I think about the process as being similar to the tidal effects between the Earth and moon. Perturbations induced in the material in the outer disk are moving more slowly than the planetesimals, so will lag behind it and produce a negative torque. The opposite for material in the inner disk.

Ultimately, it comes down to a gravitational interaction between planetesimal and disk, this much is clear. Some references:

http://adsabs.harvard.edu/cgi-bin/n...pe=HTML&format=&high=445b02ffde30341"
http://adsabs.harvard.edu/cgi-bin/n...pe=HTML&format=&high=445b02ffde13664"

Perhaps someone with more time can read through those and give a more detailed description.

 

[stanz123]

I donʻt believe that a low-density nebula can rotate stably. Looking at a particle at high "latitude", in order to have stable rotation of the nebula as a whole, that particle would have to rotate in a small circle about the rotation axis. But there is no axial force that would maintain a small-circle rotation. Such a high-latitude particle with a non-zero velocity would, in fact, orbit around the center of mass of the nebula, in an inclined orbit (that is, inclined to the mean angular momentum of the nebula). I know this is an unpopular conclusion, but it appears to be unavoidable if one believes in the laws of physics. I would be happy to hear counter-explanations, but hopefully with more rationality than some of the popular ones!

 

[DaveC426913]

I donʻt believe that a low-density nebula can rotate stably. Looking at a particle at high "latitude", in order to have stable rotation of the nebula as a whole, that particle would have to rotate in a small circle about the rotation axis. But there is no axial force that would maintain a small-circle rotation. Such a high-latitude particle with a non-zero velocity would, in fact, orbit around the center of mass of the nebula, in an inclined orbit (that is, inclined to the mean angular momentum of the nebula). I know this is an unpopular conclusion, but it appears to be unavoidable if one believes in the laws of physics. I would be happy to hear counter-explanations, but hopefully with more rationality than some of the popular ones!

1] This thread is 4 years old.

2] Who suggested that nebulae behave the way you are saying?? You are describing the solar system as a spinning top - with all masses - including those above and below the protoplanetary disc - orbiting the common protoplanetary axis! No sane scientifically-educated person thinks that. Certainly no one in this thread suggested such a thing.

 

[Chronos]

It does appear logical the inner planets could not retain much of the original gasses that seeded the solor system. The atmosphere of earth, for example, is probably almost entirely self generated. The preponderance of rocky and metallic meteroids and asteroids in the solar system is indicative of the types of materials available to the inner planets during the accretion phase.

 

[D H]

I donʻt believe that a low-density nebula can rotate stably. Looking at a particle at high "latitude", in order to have stable rotation of the nebula as a whole, that particle would have to rotate in a small circle about the rotation axis. But there is no axial force that would maintain a small-circle rotation. Such a high-latitude particle with a non-zero velocity would, in fact, orbit around the center of mass of the nebula, in an inclined orbit (that is, inclined to the mean angular momentum of the nebula). I know this is an unpopular conclusion, but it appears to be unavoidable if one believes in the laws of physics. I would be happy to hear counter-explanations, but hopefully with more rationality than some of the popular ones!

You are creating a red herring. A nebula does not rotating as a sphere. The formation of a protostar causes the nebula to form a protoplanetary disk.

 

[stanz123]

Rather than name-calling, please read my post more carefully. It was written in response to an earlier post that did, in fact, talk about rotation of the proto-nebula. There are an unfortunate number of relatively sane people who discuss or imply nebula rotation, usually when discussing the evolution of the quasi-spherical nebula into the proto-planetary disk. Stephen Hawking, for example, mentions in passing the creation of a disk by the spinning of the nebula ("like sitting on a piano stool"). Others talk about gravitational collapse into a disk, which violates other physical laws (gravitational attraction). I could describe my own conclusions, which arenʻt much different from those of V. S. Safronov in his book and papers from the 70ʻs. It describes a very large number of inelastic collisions that eventually mutually cancel all out-of-plane angular momentum components, leaving a disk-shaped residue of high-angular-momentum aggregates and particles, and a large mass of low-angular-momentum particles added to the central proto-solar mass.