Exploring the Formation of Planets and Moons

[lealla]

I have for a long time now wondered about how the planets and moons actually congealed into their current forms. How can loose mass and gas develop the gravity to pull themselves together? Could the cause of these actions been related from the "big bang" which threw out micro black holes of differing sizes, which are captured by solar gravity (this includes what created the gravitational force to form suns) which then sweep their gravitational areas clear of debris which then form the bodies we know about today?

Could these "micro" black holes then somehow find stability and the gravitational forces they exert are then related to their size? Could this then cause the warping the in fabric of space?

I know this is a simple question with a not so simple answer, one that most theorists to my knowledge have never outwardly questioned. What are your thoughts?

 

[Vanadium 50]

Actually, it does have a simple answer. There is no evidence at all that black holes are involved in planetary formation. (And evidence against - the fact that we have planets and not bigger black holes)

 

[lealla]

Vanadium, I appreciate your answer, but it does not provide anything regarding the possibility of a micro black hole finding a way to stabilize itself, nor explaining how drifting mass and gas could find a way to create the gravitational pull necessary to coalesce into suns, planets or other heavenly bodies. It does in fact provide a possible explanation for a solar collapse into a black hole and how it could grow in size, but if the new reactor tests in the spring are expected to create black holes that "might" last for only seconds, isn't it possible that the "big bang" created micro black holes that could possibly find stabilization? Such is the quandry of the question I put out there! Would not this type of eventuality also create the shifts in time and space as described by Einstein?

 

[SpiffyKavu]

I don't know anything about the black hole question, but it has been shown that isolated gas clouds can collapse without outside influence. For a roughly homogeneous cloud of gas, there exists a maximum size before the cloud cannot support itself from gravitational collapse. If the cloud becomes too large, there is not enough thermal pressure to maintain hydrostatic equilibrium. In this case, gravity pulls the cloud together, eventually forming a protostar.


http://en.wikipedia.org/wiki/Jeans_instability


Now the Jeans length includes some false assumptions, but it has been shown that the corrections lead to essentially the same result.


It is worth noting that $$R_J = {1 \over \sqrt {G \rho}}$$. If we assume that the collapse occurs adiabatically, the temperature will remain the same. As the cloud collapses, the density increases, and as a result, the Jeans length decreases. It can be the case where the collapse happens slower than the decrease $$R_J$$. If this is the case, the collapsing cloud fragment. Smaller portions of the cloud can begin to collapse under their own gravity. This can be a natual explanation for why stars are typically found in clusters.

 

[Vanadium 50]

Lealla, there are a number of misconceptions in your post. Probably the root one is that objects cannot coalesce on their own - that's not true. Any initial density fluctuation is unstable and will grow, and that's why you end up with planets, stars and galaxies. So there is not only no evidence for micro black holes, there is no need for them.

 

[Widdekind]

I have for a long time now wondered about how the planets and moons actually congealed into their current forms. How can loose mass and gas develop the gravity to pull themselves together? ...?

In the proto-Sun's Protoplanetary Disk, dust grains stuck together by building up Static Charges, from frictional forces:

Laboratory experiments on sticking of dust have been reviewed by Blum (2000), who concluded that sticking microscopic grains together w/ static & Van der Waals forces to build millimeter-sized compact objects was entirely feasable*.​

Then, "some as yet uncertain mechanism" caused those millimeter-sized grains to accrete into meter-sized, & ultimately kilometer-sized, bodies**. After bodies become about 1 kilometer across, "gravity plays a major role" in further accretion***.

* A.M. Davis, Heinrich D. Holland, Karl K. Turekian. Meteorites, Comets, and Planets, pg. 516. (Google Books)
** ibid., pg. 517.
*** ibid., pg. 516.​

The planets then formed from these mountain-sized meteorites:

In the Protoplanetary Disk, the dust particles collided & stuck together. As more & more stuck together, larger particles were formed. This is called Accretion. Then objects several meters across, and before long kilometers across, would have formed. These objects, called Planetesimals, were the 'building blocks' of the planets. Collisions between the numerous planetesimals then built a fewer number of larger bodies, called Planetary Embryos... Eventually, one planetary embryo will have dominated and accreted all the other significantly sized bodies in its region of the disc. When all the material in that region had been exhausted, the planet was 'complete'. This whole process would have taken in the region of 10⁸ years*.​

This Accretion has decayed (approximatley) exponentially across the ages:

The impact flux was extremely high during the first few 100 million years of the Solar System as the planets finished accreting -- as well as smaller collisions, impacts between Mars-sized objects may have occurred several times... Since approximately 3.8 billion years ago, the flux has declined -- probably exponentially -- and is now declining at a low rate**.​

Thus, the Impact Rate was higher, in Earth's past, than it is today.

* Neil McBride & Iain Gilmore. An Introduction to the Solar System, pg. 23.
** ibid., pg. 149.​

We can (crudely) model this Accretion process, for the Earth. For, the Earth accretes approximatley 80 kilotons of cometary & meteoric debris, per year* (on average). The (probable) exponential decay of this Accretion process (above) suggests that:

$$Accretion \approx T_{0} \times e^{- \, t / \tau}$$​

We impose, as constraints, that: (1) that Accretion accumulates one Earth Mass over the age of the Solar System (~4.6 billion years); and, (2) that Accretion amounts to ~80 kilotons yr^-1 at the current age of the Solar System. This System of Equations can be solved numerically**, and yields:

$$T_{0} \approx 3 \times 10^{10} \, kilotons \, yr^{-1}$$
$$\tau \approx 200 \, million \, yrs$$​

Perhaps surprisingly, this simple model reproduces the ~10⁸ year Time Scales cited above. The "Important Physics", to observe, is that Accretion rates were much higher in Earth's past. For example, during the days of the Dinosaurs (~200 million years ago), Earth's Accretion could have been ~3x (e¹) higher than today. And, back at the Cambrian Explosion (~600 million years ago), Earth's Accretion could have been ~20x (e³) higher than today. Indeed, major Mass Extinctions, like those at the close of the Permian Period (~250 million years ago) and Cretaceous Period (~65 million years ago) were probably caused by Impactors***.

* Iain Gilmore & Mark A. Sephton. An Introduction to Astrobiology, pp. 23 & 303.
** https://www.physicsforums.com/showthread.php?t=281660 . NOTE: This present post, based upon a Print Source (above), uses the more accurate Accretion Rate of ~80 kilotons yr^-1, and corrects an algebra mistake. These numbers have been rounded to one (1) Significant Figure.
*** Discovery Channel The Day the Earth Nearly Died (DVD) ; National Geographic Naked Science -- Dino Meteor (TV)​

I hope this is clear (eg., all the 'footnotes') for you.

 

[Widdekind]

There is some kind of error. Despite what is being displayed in the above post, here is what I typed in:

$$T_{0} \approx 3 \times 10^{10} \, kilotons \, yr^{-1}$$
$$\tau \approx 200 \, million \, yrs$$​

If you quote my post, you will see, that what is actually written, is the above.

 

[Widdekind]

Verifying the quote:

$$T_{0} \approx 3 \times 10^{10} \, kilotons \, yr^{-1}$$
$$\tau \approx 200 \, million \, yrs$$​

 

[D H]

We can (crudely) model this Accretion process, for the Earth. For, the Earth accretes approximatley 80 kilotons of cometary & meteoric debris, per year* (on average). The (probable) exponential decay of this Accretion process (above) suggests that:

$$Accretion \approx T_{0} \times e^{- \, t / \tau}$$​

We impose, as constraints, that: (1) that Accretion accumulates one Earth Mass over the age of the Solar System (~4.6 billion years); and, (2) that Accretion amounts to ~80 kilotons yr^-1 at the current age of the Solar System. This System of Equations can be solved numerically**, and yields:

$$T_{0} \approx 3 \times 10^{10} \, kilotons \, yr^{-1}$$
$$\tau \approx 200 \, million \, yrs$$​

Perhaps surprisingly, this simple model reproduces the ~10⁸ year Time Scales cited above.
The "Important Physics", to observe, is that Accretion rates were much higher in Earth's past. For example, during the days of the Dinosaurs (~200 million years ago), Earth's Accretion could have been ~3x (e¹) higher than today. And, back at the Cambrian Explosion (~600 million years ago), Earth's Accretion could have been ~20x (e³) higher than today. Indeed, major Mass Extinctions, like those at the close of the Permian Period (~250 million years ago) and Cretaceous Period (~65 million years ago) were probably caused by Impactors***.

* Iain Gilmore & Mark A. Sephton. An Introduction to Astrobiology, pp. 23 & 303.
** https://www.physicsforums.com/showthread.php?t=281660 . NOTE: This present post, based upon a Print Source (above), uses the more accurate Accretion Rate of ~80 kilotons yr^-1, and corrects an algebra mistake. These numbers have been rounded to one (1) Significant Figure.
*** Discovery Channel The Day the Earth Nearly Died (DVD) ; National Geographic Naked Science -- Dino Meteor (TV)​

Stop that!

The thread to which you linked was locked, and for good reason. You were being overly speculative there, and you are continuing the same speculation here.

You have not recovered the 10⁸ year time scale cited in texts. That time scale refers to the time period when the formation of the Earth was, for all practical purposes, 100% complete. Your derived 10⁸ year time scale refers to the time period when the formation of the Earth was 63% complete. With an exponential decay model with decay time $\tau$, the Earth would have required roughly $6\tau$ to become 99.75% complete. Moreover, recent evidence suggest an even faster time scale for planet formation. If the 10⁸ year time scale cited in older texts does not jibe with your overly-simple exponential model, an even faster time scale does not jibe with it at all.

Your simple model does not reflect that terrestrial planet formation involves a number of different stages, including dust (micron sized particles) to rocks (size on order of centimeters to meters), rocks to planetesimals (100 meter to 10 km size), runaway growth, oligarchic growth. Each of these parts of the overall planet formation process has its own time scale. Applying a single time constant to the overall process leads to incorrect results, such as the planet being only 63% formed 100 million years into the process and 3x higher impact rates 200 million years ago.

Some reading material:
Yin, Q., et al, "A short timescale for terrestrial planet formation from Hf–W chronometry of meteorites", Nature 418, 949-952 http://www.nature.com/nature/journal/v418/n6901/full/nature00995.html

Our measurements indicate that, contrary to previous results, the bulk of metal–silicate separation in the Solar System was completed within <30 Myr. These results are completely consistent with other evidence for rapid planetary formation and are also in agreement with dynamic accretion models that predict a relatively short time (10 Myr) for the main growth stage of terrestrial planet formation.​

Johansen A., et al, "Rapid planetesimal formation in turbulent circumstellar disks", Nature 448, 1022-1025 http://www.nature.com/nature/journal/v448/n7157/full/nature06086.html

During the initial stages of planet formation in circumstellar gas disks, dust grains collide and build up larger and larger bodies. How this process continues from metre-sized boulders to kilometre-scale planetesimals is a major unsolved problem: boulders are expected to stick together poorly, and to spiral into the protostar in a few hundred orbits owing to a 'headwind' from the slower rotating gas. Gravitational collapse of the solid component has been suggested to overcome this barrier. But even low levels of turbulence will inhibit sedimentation of solids to a sufficiently dense midplane layer, and turbulence must be present to explain observed gas accretion in protostellar disks. Here we report that boulders can undergo efficient gravitational collapse in locally overdense regions in the midplane of the disk.​

Armitage, P., "Lecture notes on the formation and early evolution of planetary systems"
http://arxiv.org/pdf/astro-ph/0701485v1

 

[DaveC426913]

I have for a long time now wondered about how the planets and moons actually congealed into their current forms. How can loose mass and gas develop the gravity to pull themselves together?
...
I know this is a simple question with a not so simple answer, one that most theorists to my knowledge have never outwardly questioned. What are your thoughts?

The physics of accretion into planetoids all the way up to stars is well-understood, and no call for black holes is required.

We can see evidence of all these stages currently in progress when we look into the night sky - yes, even the birth of stars.

 

[Widdekind]

Comets often contain "water-bearing clays"*.

* Caleb A. Scharf. Extrasolar Planets & Astrobiology, pg. 339.​

CONCLUSION (?): Intermediate mass bodies (1m to 1km), made of mud & clay, thus could collisionally accrete, b/c of the "stickiness" of clay.

 

[Vanadium 50]

As DaveC said, the physics of accretion into planetoids all the way up to stars is well-understood. Small bits of clay in comets is not where planets come from.