Why isn't it possible that the earth formed outside the solar system and got attracted later by the Sun?
I just need arguments to defeat this hypothesis.
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I'm sure there are plenty of arguments that could be added to the list, but that's a good start I think.
Edit: I didn't expect such a spirited debate in response to this answer. First off, I want to say that none of my arguments above are bullet-proof. I'm going to incorporate some of the comments below to help round out this answer. This will be easier than creating a long conversation of comments.
Matthew Whited - [It] is possible that other rouge planets could have formed outside of their own solar systems. It is also possible that they could form within solar systems and be ejected.
This is certainly true. One cannot soundly reject the hypothesis that Earth formed elsewhere (be it in free space or around another star) and was later captured by our Sun. My arguments are mostly ways to point out that the chance of such an occurrence is diminishingly small due to the unlikely circumstances that must occur for that hypothesis to be true. The betting man would not side with the hypothesis that the Earth formed outside our solar system and was later captured.
Rob Jeffries - Almost the only way Earth could be captured is during the clustered star formation stage (well established theoretical possibility). In which case it would have the same age and metallicity as if it had formed around the Sun. So age and metallicity are weak arguments.
I don't know if they're as weak as that. If the Earth did come from another stellar system, it would of course come from a nearby one, which would of course have a similar metallicity as our Sun. But I think a point which makes the above arguments stronger is the specific composition of the Earth. If it formed around a star which was slightly different in nature (say an M Dwarf) or at a different distance from the star I think we'd notice that the Earth seemed "out of place" in our solar system. As it is, its iron content agrees quite well with it forming where it currently resides. Again, none of this is bullet-proof, but it cast's doubts on the validity of Earth forming elsewhere.
Rob Jeffries - Planet capture in the nascent cluster also nullifies arguments 2 (since the Moon would have to be formed after capture) and 4.
jwenting - The moon argument isn't a valid one. The moon could have been formed out of the earth after capture. Which doesn't make that capture a more likely scenario of course.
I wouldn't say nullifies. In fact, I would think it makes them a bit stronger. The process of the Earth forming elsewhere, being flung out of its stellar system and captured by ours (and put in its proper place), then forming a Moon and life, requires that these events happened extremely quickly. While not impossible, it is improbable, especially when you add in your argument for the Earth being in a very precise orbit unlikely to have been achieved if it had been captured. If you argue that the Moon/Life formed after capture you're really limiting the time and chances that the Earth didn't form in our system.
I think the Earth's orbit is by far the strongest argument you have that the Earth formed around the Sun. The orbit is nearly circular and almost in the Sun's equatorial plane, similar to the other planets. These facts are naturally accounted for if the Earth formed from material that coagulated in the Sun's primordial disc, where circularisation and collapse to a plane perpendicular to the Sun's rotation axis are expected.
Capture of planets is possible and is thought to be reasonably common in the early dense environments of star forming clusters. A captured planet would therefore have a similar age and metallicity to one born around the Sun, since star clusters are empirically almost coeval and chemically homogeneous. The problem is that terrestrial, rocky planets take some tens of millions of years to form. Most dense star clusters have dispersed on much shorter timescales than this. Even if the Sun was born in a rare, long-lived cluster, its primordial disk of gas would have already dispersed within ten million years and thus there would be no mechanism to circularise a captured Earth's orbit or enforce an orbit in the same plane as the other planets.
It would be really difficult for the Earth to end up in a nearly circular orbit if it came from outside the solar system. Effectively falling from infinity, it would have a hyperbolic orbit and make one swerve around the Sun and depart back into the blackness of interstellar space.
What mechanism could get rid of precisely enough energy to keep the Earth from exiting and get it into such a nice orbit? (The eccentricity is .0167, which is too close to a perfect circle to distinguish with the naked eye.) I can't think of anything. At best it should have an orbit that has the outer point way out in the outer solar system and a closest approach near the sun.
Occam's razor defeats the hypothesis. There are no astronomical anomalies about earth's obit or position that require the complication of earth's insertion from beyond the solar system. Unless some difficulties in known fact are brought forth requiring such a hypothesis as their simplest solution, then the idea may simply be rejected as unnecessary. The other observations given (orbital circularity, consistency in solar plane, rotation, composition, etc.) lend credibility in that they show how much an insertion hypothesis would need to account for that the born-in-place model already handles. NB: This doesn't mean that it isn't possible--only that, scientifically, there's no reason proposed to think it did, and many reasons to think it didn't. Occam's razor isn't a proof; its a methodological principle.