# Planet Formation

1. Jul 6, 2006

### 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?

Last edited: Jul 6, 2006
2. Jul 6, 2006

### mathman

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

3. Jul 6, 2006

### Kurdt

Staff Emeritus
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 aquires mass the velocity does not change.

4. Jul 6, 2006

### Shubert

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.

Last edited: Jul 6, 2006
5. Jul 6, 2006

### Shubert

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?

6. Jul 6, 2006

### Kurdt

Staff Emeritus
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.

7. Jul 6, 2006

### Shubert

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.

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?

8. Jul 6, 2006

### SpaceTiger

Staff Emeritus
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.

9. Jul 6, 2006

### Kurdt

Staff Emeritus
That is correct.

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.

10. Jul 6, 2006

### 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.

11. Jul 6, 2006

### 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.

12. Jul 6, 2006

### Staff: Mentor

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.

13. Jul 7, 2006

### Kurdt

Staff Emeritus
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.

14. Jul 7, 2006

### Shubert

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.)

Last edited: Jul 7, 2006
15. Jul 7, 2006

### Staff: Mentor

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.

16. Jul 7, 2006

### Kurdt

Staff Emeritus
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.

Last edited: Jul 7, 2006
17. Jul 7, 2006

### Shubert

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?

18. Jul 7, 2006

### Shubert

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?

19. Jul 7, 2006

### Kurdt

Staff Emeritus
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.

20. Jul 7, 2006

### Shubert

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?