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Under reconstruction below:
streaming instability,
Arrokoth (AKA Ultima Thule)
Lee Billings, 2020 Feb20, "New Horizons May Have Solved Planet-Formation Cold Case".
- Sticky Accretion:
In this theory the colliding grains stick together through some chemical bonding or cohering force.
But there is NO obvious sticky force strong enough to bond grains as we think they were when they are bouncing off each other at tens of meters per second.
Possibly tarry, organic compounds containing carbon helped sticky accretion (Se-419).
- Collective Self-Gravity Accretion:
The grains CANNOT grow through binary gravitational collision accretion as argued above.
But if enough grains are compacted into a thin enough layer, then their collective self-gravity might lead to a gravitational runaway to largish lumps of compacted grains that are at rest or at very low velocity with respect to each other.
Then chemically bonding and cohering forces fuse the lumps into lumps of rock (i.e., silicates with metals) and/or astro ices (i.e., water ice (H_2O), carbon dioxide (CO_2), nitrogen (N_2), ammonia (NH_3), methane (CH_4), etc.).
It was once thought that turbulence in the protoplanetary disk would prevent this process.
But some calculations suggest the process should happen (Youdin, A. N. 2003, astro-ph/0311191).
- Collective Self-Gravity Accretion:
Condensation is an atom by atom or molecule by molecule growth of a solid or liquid phase sample from a gas phase sample.
Once you have large grains some kind of accretion of grains must have occurred to get larger bodies.
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Somewhere there must be an argument as to why
condensation can't make objects
much larger than micron-sized grains, but
I can't seem to locate it.
Maybe the accretion by condensation is just to slow or maybe most of the metals are exhausted in grain formation.???
The orbits were mostly very similar circles about the Sun in the plane of the protoplanetary disk of grains and gas.
Still there was a lot of random motion, and so collisions were frequent.
Orbital speeds relative to the inertial frame of the Sun are of order of a few to a few tens of kilometers per second.
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For circular orbits
around the Sun, the orbital speed is given by
v = (GM_☉/r)**(1/2) = 29.789 km/s * (1 AU /r_AU)**(1/2) ,
where G=6.67384*10**(-11) is the gravitational constant,
M_☉=1.9891**30 kg is the solar mass,
and
1 AU=1.49597870700**11 m is the astronomical unit (AU)
which is an exact value in modern convention.
No correction has been made for finite planet mass
or gravitational perturbations
or other kinds of perturbations.
Such corrections probably cause changes of order 0.03 % since
Earth's mean orbital speed is
29.78 km/s, NOT 29.79 km/s as our formula implies: (0.01/30)*100 % & ≅ 0.03 %.
Our orbital speed formula shows that all objects in orbit around the Sun out to the orbit of Neptune (orbital radius 30.10 AU, mean orbital speed 5.43 km/s) have orbital speeds of order a few to a few tens of kilometers per second (km/s). But the random relative speeds of particles in the protoplanetary disk in similar orbits were probably only a few or few tens of meters per second (Youdin, A. N. 2003, astro-ph/0311191).
Two grains of micron or millimeter size are much too small to feel any significant gravitational attraction if their relative speeds are even a few or few tens of meters per second: i.e., their relative escape speed is much smaller than their actual relative speed---the figure below illustrates this situation.
Caption: A cartoon of a binary gravitational collision of grains.
Credit/Permission: ©
David Jeffery,
2004 / Own work.
Image link: Itself.
So binary gravitational collision accretion of grains is RULED OUT: i.e., two grains don't coalesce under their mutual gravitational attraction.
How did growth of grains occur?
Two theories have been discussed:
The two theories are NOT mutually exclusive. Both COLLECTIVE SELF-GRAVITY ACCRETION and sticky accretion may occur.
Sticky accretion could be a secondary process. In fact, in the compaction of COLLECTIVE SELF-GRAVITY ACCRETION relative velocities are lowered and a sort of sticky accretion must happen at some point though that may be under gravitational compression.
Actually, other processes have been considered from getting from grains to kilometer-size objects.
There seem to be no consensus resolution yet.
Whatever, the exact process somehow clumps of solids of order a kilometer in size scale are reached.
It is conventional to call these kilometer-size objects planetesimals (see Wikipedia: Planetesimal: Definition ofj planetesimal).
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Planetesimal means
itty-bitty planet I'd guess.