The Collision between Earth and a planet-size body

[dougettinger]

Art, you posted an interesting data point, 54.3 % of orbital ratios are 5:2. Did you determine that percentage yourself ?

It is simply applying Kepler's 3rd law:

Pluto has an orbital period of 248 years so it lies out at (248)^2/3 ~ 39.5 AU (i.e., = it's semi major axis)].
If an object has an orbital period of 2/5 years it lies at (2/5)^2/3 ~ 0.543 AU.

(Learning to do a few math tricks is much more fun than speculating in the abstract, IMO.)

Art, I am really asking whether you computed the 54.3 % figure or whether it was reference data. You already taught me how to play with Kepler's Third Law.

Doug Ettinger
Pittsburgh, PA

[dougettinger]

The Titius-Bode theory deals with approximating the orbital radii.
There is no such theory. Titius-Bode merely provides an observational fit to the positions of some (but not all) the major bodies in the Solar System. It has no theoretical basis at all, and there's no real reason to think it would apply to other systems. It is very likely a coincidence, or at best an inadvertent consequence of other factors, such as resonances.

"Theory" is definitely an overstatement. Perhaps you would be OK with the Titius Bode Rule. This rule helped to find Neptune and the Asteroid Belt. My suspicions are that a theory is lurking inside the protostar disk for orbital radii. This rule or mathematical series can actually be represented by other equations that are more meaningful.

My hypothesis is that as a protostar grows in size, the central gravity force attracts the disk materials into circular bands or steps of increasing gradients of density. Vortices somehow peel off at the edges of these bands to initiate clumping or density gradients occurring circumferentially.

Unless you can support this idea with some solid math, I'd say "hypothesis" is an inappropriate word.

"Hypothesis" is an overstatement. I was being sloppy with that very important word. More correctly, I am presenting my "ideas". Some math will follow; I am not sure how solid it will appear.

Art, you helped significantly by emphasizing the importance of orbital resonance.
Don't confuse different resonance effects, however. Large bodies can find themselves in resonant orbits with other bodies, because such orbits can be stable. That means that the bodies gradually move into these resonances, and then stay there. But there are thousands of "virtual" resonances in the Solar System: orbital radii where there would be constructive or destructive resonances. These are most apparent in the asteroid belt, giving it its ring-like structure. But in considering the way the Solar System came together, you need to consider these virtual resonance zones (which are by-and-large empty). Indeed, that's a key component of the numerical simulations that are relied on today for explaining planetary system formation and dynamics.

I was proposing that some orbital resonances both bring clumps together to form planetoids "and" maintain existing planets in their presence position "and" can eject planetoids that have already formed. I recognized the "virtual resonances" because I accepted the reason for the Kirkwood Gaps in the asteroid belt. I recognized the empty resonance zones because I stated the randomness of planetary orbital resonances. The first planetoids to form are random and the initial clumping in adjacent bands of dust is also random. But any existing planetary and asteroidal periods should demonstrate some type of orbital resonance.

I agree with all the points that you made.

Doug Ettinger
Pittsburgh, PA
12/22/10