Solar System Planet Formation Times

[Widdekind]

Planetary Mass Growth Rates, in Proto-Planetary Disks, are calculated to be (C.A.Scharf. Extra-Solar Planets & Astrobiology, pg. 89):

[math]\frac{dM}{dt} = \pi \; R^{2} \left(1 + \left( \frac{v_{esc}}{v_{rel}} \right)^{2} \right) \; \rho_{disk} \; v[/math]

And (ibid., pg. 102):

[math]\rho_{disk} \; v \approx \sigma_{disk} \; \omega[/math]

where:

[math]\sigma_{disk} \approx 1700 \; \left( \frac{D}{1 AU} \right)^{3/2} \; g \; cm^{-2}[/math]

We assume that the average Relative Impact Velocity (v_rel) is equal to the Keplerian Disk Velocity (v)*.

*

This can be verified, by assuming that all potential

Impactors

possess, at the beginning of their planet-ward trajectories, the

Keplerian Disk Velocity

at that

Orbital Distance

; and, that said potential Impactors impinge upon the

Proto-Planet

from all directions equally. Then, by integrating over

Velocity Space

, the

Average Relative Velocity

turns out to be just the

Keplerian Disk Velocity

.

 

We may now estimate the Planetary Formation Time-Scales:

[math]\tau \equiv \frac{M}{\frac{dM}{dt}}[/math]

for the Planets & Dwarf Planets* in our Solar System.

*

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

 

 

RESULTS:

 

Planet Formation Time-Scales are plotted against Planet Orbital Distances in the attached figure. We find that:

• Terrestrial Planets -- formed over hundreds of thousands of years
  
• Gas Giants -- formed over tens of millions of years
  
• Ice Giants -- formed over hundreds of millions of years
  
• Kuiper Belt Objects -- formed over billions of years
  

In particular, please ponder the pronounced "dips" corresponding to both the Asteroid- & Kuiper- Belts. This may imply, that the Giant Planets "stole" material from adjacent disk regions, thereby "strangling" Planetary Growths there.

 

Note, too, that the Outer Kuiper Belt Dwarf Planet Eris, with an estimated Planetary Formation Time-Scale exceeding the age of the Solar System, may still be (albeit slowly) accumulating material through collissions.

 

 

ANALYSIS:

 

The Ice Giants, being depleted in Hydrogen & Helium compared to the Gas Giants, are thought to have formed after the Sun's Solar Wind blasted out the Lighter Elements from the Planetary Disk (citation needed). That "sweeping out" happened when the Solar System was tens of millions of years old*. This is completely consistent with the above results, which indicate that the Ice Giants took hundreds of millions of years to form.

*

http://www.scienceforums.net/forum/showthread.php?t=40703

The roughly-linear main trend indicated has a slope of roughly 5/2, indicating that [math]\tau \propto D^{5/2}[/math].

Edited June 23, 2009 by Widdekind

[Widdekind]

Deleted

Edited June 23, 2009 by Widdekind

[Ophiolite]

Planet Formation Time-Scales are plotted against Planet Orbital Distances in the attached figure. We find that:

Terrestrial Planets -- formed over hundreds of thousands of years

Gas Giants -- formed over tens of millions of years

Ice Giants -- formed over hundreds of millions of years

Kuiper Belt Objects -- formed over billions of years

 

Simplistic.

 

Let's examine just the figure for the gas giants. You claim tens of millions of years. This is not possible. The hydrogen and helium in the nebula was dissipated by T Tauri and FU Orionis activity within one million years. The gas giants have to form within that time span, or they do not form at all.

 

Your speculation is falsified by this inconvenient observation.

[Klaynos]

Simplistic.

 

Let's examine just the figure for the gas giants. You claim tens of millions of years. This is not possible. The hydrogen and helium in the nebula was dissipated by T Tauri and FU Orionis activity within one million years. The gas giants have to form within that time span, or they do not form at all.

 

Your speculation is falsified by this inconvenient observation.

 

IIRC this is one of the problems with the accretion model of planet formation...

 

There are two main models, their formal names escape me right now, and I'm too tired to go find my UG lecture notes on it, but they both have different problems and don't quite fit the observed evidence.

[granpa]

whats the escape velocity of an ice giant. if earth can hold hydrogen and helium even today then I doubt that an ice giant could when it was forming (and was very very hot)

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Merged post follows:

Consecutive posts merged

Simplistic.

 

Let's examine just the figure for the gas giants. You claim tens of millions of years. This is not possible. The hydrogen and helium in the nebula was dissipated by T Tauri and FU Orionis activity within one million years. The gas giants have to form within that time span, or they do not form at all.

 

Your speculation is falsified by this inconvenient observation.

the nebula may have been disapated in one million yrs but what about the protoplanetary disk itself?

[Widdekind]

According to McBride & Hughes (pg. 7):

Hoyle (1978)... expected the lower limit for the formation time of the inner terrestrial planets to be about 2 x 10⁶ yr, whereas the outer ones, Neptune & Uranus, to be about 3 x 10⁸ yr to aggregate.

However, this ignores the sudden increase in solids at the Snow Line, in the Sun's Proto-Planetary Disk:

This scenario indicates that the large planetesimals in the the asteroid region would have formed before similar sized objects in the Jupiter region...

 

The asteroids were at a chemical boundary. The varying temperature of the pre-planetary nebula was such that snows & ices could condense beyond the asteroid belt, but could not condense w/in it, or in the region closer to the Sun. Cosmic material contains 2.2 times (by mass) more snow & ice than it does rock and metal. In volume terms, the snow-ice / rock-metal ratio is around 90. It is this factor that helped the Jovian planetesimals to grow faster than the asteroidal ones.

My original analysis (OP) did not account for the Snow Line's effects on the density of solids in the Proto-Planetary Disk. Perhaps all of the Outer Planets' formation times should be divided by some factor — such as 2.2.

[Klaynos]

This is a very active area of research, the knowledge has moved forward fantastically in the last 10 years... With alot of observational evidence of planet forming disks being taken in recent years.

[Widdekind]

According to the National Geographic Channel documentary Direct from the Moon (TV), Dr. Fumi Yoshida et al. have shown, that the size distribution of Main Belt Asteroids precisely matches the size distribution of craters on Moon, dating to the Late Heavy Bombardment period (4.0 to 3.8 billion years ago). This "fingerprint" establishes the Main Belt — and not comets — as the source of the LHB of the Inner Solar System.

 

These results are described in detail here.

 

Planet Formation Times could conceivably play some part in said analysis — for example, the Ice Giants apparently finally formed after hundreds of millions of years... about the same time as the LHB.