How how fast, in a relative sense, did Theia and Proto-Earth collide?

If you are asking at what velocity did these two stellar objects colide... the answer is we can only make assumptions. We can imagine what may or might have happened. The formation of Earth and moon from the accretion disk of matter after a Mars size object I think you are calling Theia collided with the early Earth. For some reason I am unable to confirm the velocity of the early inner planets around the solar disk. All I do know is that. The early solar system was a chaotic place. The four and a half billion years have allowed a thinning of debris and coalescing of material. A as best as stable system we now have... As to what was that early velocity ? It can not have been too different from what it is today. If it were the planets would not be were they are now. We can make assumptions regarding the object. They are not proven... Mark.

At least 11 km/s, as that's Earth's escape velocity, and nothing unbound to Earth can strike slower than this.

It could have been as high as 30 or 40 km/s if it had a highly-eccentric or inclined orbit. I'd guess 15-20 km/s.

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Is there actually any geological data that is seen as a confirmation of this hypothesis, as I suppose,Theia and proto-earth were of different chemical composition?

The axial tilt of Earth, rotational period of Earth and the heavy metal poor and water poor composition of the Moon.

And the unusually large iron core of the Earth (as compared to Mars and Venus.

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I would have though that as they formed in the same orbit from the same proto-cloud they should have had roughly the same chemical makeup.

The escape velocity of Earth at that time would have been something less than 11 km/s, because the mass was smaller.

The most thorough models of this moon-forming giant impact come from Robyn Canup at the Southwest Research Institute. See here for her abstract for this years Lunar and Planetary Science Conference in Houston:

http://www.lpi.usra.edu/meetings/lpsc2008/pdf/2429.pdf

There you have your answer.

There are no good constraints on the core of Venus. It could be as large as the Earths, even a little bit larger (relatively speaking). Besides, a large iron core is hardly indicative of a giant impact origin of the moon: where would all the non-iron material have gone, if, say, Earth and Theia had comparable core mass fractions? The moon has only ~1% of the Earths mass, so this doesn't really make any difference.

As radial mixing in the protoplanetary disc is extensive, the chemical composition of Earth and Theia would have been almost identical. There are though processes within the disc (like giant impacts) that can change the composition towards fewer volatile elements, while other processes (like delivery of icy comets from the outer system) can increase volatile content.

The isotopical composition, on the other hand, can vary in narrow amounts (the exact reason for this is unknown). Since most of the material of the moon must have come from the impactor (Theia), it is suprising that the moon has exactly the same oxygen isotope ratios as the Earth. But new work shows that the oxygen isotopes of the Earth and Moon could have been homogenized in the aftermath of the giant impact, when both objects were still surrounded by a super-hot silicate vapor cloud.

Actually, the escape velocity with respect to Theia was probably greater.

Although proto Earth's mass may have been less, the combined mass of proto Earth and Thiea was probably larger, since proto Earth/Thiea had enough combined mass to form the Earth, the Moon, with pleanty of additional mass probably escaping to interplanetary space after the collision.

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The Moon has a significantly lower density than Earth. This is due to most of the cores of both the proto Earth and the impactor remaining with the Earth.

__________________
"I'm as accurate as any psychic. And I'm a cartoon!" -- Squidward

"Arrrgh, the laws of physics be a harsh mistress!" -- Bender

@tony873004: You are right. What I said is true for massless particles, but I guess Theia was far from massless...

@aurora: Yes, but even when the moon (mass = 1.23e-02 Earth masses) was pure mantle material, and the impactor had a core / mantle mass ratio of ~1:1 (as the Earth has, in a very rough approximation), then the mass of the core of the Earth is only increased by 1.23% compared to what the situation would be if the moon had the same core / mantle mass ratio as the Earth. Instead of a core / mantle mass ratio of ~1:1, the Earth would have a ratio of ~1:1.01. That's what I meant when I said it doesn't make any difference.

Mars sized, not moon sized.
10%-12% additional core, some additional mantle, the Moon, and a fair amount of lost debris would result.

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Of course the impactor itself is Mars sized, but this only means that the majority of its mantle also went into the Earth. Only a fraction of the impactors mantle (~20%) formed the moon - so the Earths Core is only "overabundant" in iron regarding to the relatively small mass lost to the formation of the moon.

Look at this example. All mass units in multiples of a Moon mass (where Moon mass = 1% of an Earth mass, Mars mass = 10% of an Earth mass for simplicity). Most of the debris is picked up in later collisions (see the Canup-Papers), so it is neglected here.

Theia: 6 mantle, 4 core.
Earth: 60 mantle, 40 core
Moon: 1 mantle
Proto-Earth (before Theia impact) = 60-5 = 55 mantle, 40-4 = 36 core.

Core-mass-ratio of proto-Earth: 36/(55 + 36) = 39.56%
Core-mass-ratio of Earth today: 40/(40+60) = 40%

So the impact increased Earths core-mass-ratio only by 0.44%. As I said: it makes no difference.

This raises the question, where is the lost debris? I would guess that, being in a similar orbit, much of it would have re-impacted at a later date, but might some of it be preserved in the form of Earth Trojans, the Asteroid Belt, or NEOs? It would be a marvelous thing to study, I would think.

As far as we know, there are no Earth Trojans (that is, none have been found despite extensive searches). NEOs are comparatively short-lived: their orbits decay slowly (on a timescale of some millions of years) due to non-gravitative forces acting on them. Some of them are eventually picked up by planets, the other ones by the sun. I would guess that the asteroid belt is to far away to have retained a significant portion of the collision debris.

It would certainly be interesting, although I wonder if there would be any difference to material from the moon. We probably couldn't tell the difference.

interesting article here http://news.bbc.co.uk/2/hi/science/nature/7497715.stm