Arrg, screwed up my original posts. Here is the corrected version:
I see quite a few issues with your hypothesis:
1) I think you need to re-consider he forces involved in even the slowest of two ~0.5 earth masses coming together. You wouldn't have pangea being forced apart; you'd have total fragmentation of both bodies, leading to complete destruction of the both planets. Its not a matter of heat, or anything like that, but rather is a simple issue that even if the relative velocity of the two bodies is zero upon their contact, you still have two massive object whose centers of mass are separated by an enormous distance. Ergo, the potential energy is huge, and since the earth is only marginally elastic, that energy is not going to be absorbed nicely.
For example, using your model (and using the over simplification that mass is linearly equal to radius):
[note: for simplicity the "subscript" p-e = pre-earth, h = heaven, e = earth; so Mp-e would be mass of the pre-earth)
Mass:Mp-e = 0.52(5.9736 × 10^24 kg) = 3.11 x 10^27 g
Mh = 0.48(5.9736 × 10^24 kg) = 2.87 x 10^27 g
Gravitational EnergyU=[G(Mp-e + Mh)]/R, where:
U = potential energy (joules)
G = gravitational constant
R = dist. between centers of gravity
U=[6.67x10^-11(3.11 x 10^27 + 2.87 x 10^27)]/(5200+4800)
U = 5.94 X 10^40JTo put that into perspective, the meteor that wiped out the dino's was though to have had ~10^23 joules, thats ~100,000,000,000,000,000 LESS energy than you situation without the planets being in relative motion to each other. In fact, I believe we're on par here with the collision that is though to have created the moon (and also melted the earth).
Even a slow closing speed ups the ante significantly - kinetic energy is a real bitch.
2) The other problem you have is that in your model the flow of surface material during the collision is inwards, not towards or away from the site of impact. This is due to the fact that surface area does not increase linearly with volume.
For simplicity I'll assume both the pre-earth and heaven have the same volume, that being 50% that of earth. I'll also ignore compression and assume that this means that the volume of the final planet will be the sum of the two starting volumes. I'm using this calculator:
http://www.calculatorsoup.com/calculators/geometry-solids/sphere.phpVolume earth = 1.052 X 10^12 m^3
Volume (p-e & h) = 0.5(1.052 X 10^12) = 0.526 X 10^12 m^3
SA (each) = 3.15 X 10^8 m^2
In contrast, earth is:
SAe: 5.00 X 10^8 m^2
What this means is upon merger, earth is
missing ~26% of the surface area of the old pre-earth and heaven.
This means is you have a net flow of the surface *inwards*, as surface must be subducted to maintain a spherical shape as the new earth forms. This inwards flow will occur at the site of contact (assuming fluid bodies), meaning you'll loose land area in the region of contact, while (in theory) having little effect in the areas outside of the contact sites.
You may argue that upwelling of new material from the interior would force the plates apart, but keep in mind that in this merger you are putting an equal volume into a region containing much less surface area, meaning that there will be tremendous force keeping the surface where it is. Your proposed expansion of the surface runs, in fact, in complete opposition to what physics dictates will happen when you merge two smaller objects into one.
Assuming a perfectly fluidic impact, you'd end up with the heavenly and earthly continents (assuming they both faced away from the impact) pretty much where they were, while the surface area of the contact itself would now be in the interior.
3) I didn't go through all your numbers, but I think a molten earth is a given in this situation. You have two tremendous sources of heat - the initial collision, and the heat as the new earth compresses down to a smaller size.
4) Ignoring the "stationary earths" for a moment, there is yet another source of heat and mass destruction in your system - any closely passing heavenly bodies of the size you envision will exert tremendous tidal forces on each other. Not "oooh, look at the big wave" tidal forces, but rather "holy s..t, who ripped north america in half" tidal forces. Assuming a close pass or two before collision (your model, I believe), the surface would be slice-and-diced into oblivion, long before the collision, which'll destroy whatever is left.
Bryan
