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As a follow-up to this question: Could an asteroid aerocapture around Earth?

The answers seem to indicate that it would be possible for such a thing to happen (an asteroid aerocapturing using the Earth's atmosphere, and then getting a gravity assist from the moon to stabilize the orbit), even though it would be very unlikely.

If such a thing did happen, what would it seem like to people on Earth who happen to be watching that part of the sky at that time? Could the asteroid be big enough for this to be noticeable? What about big enough for even laypeople to know something is different about this time?

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Assuming your asteroid is large enough to be interesting - tens of metres or bigger - and goes deeply enough into the atmosphere to lose significant velocity, then it would be seen as an Earth-grazing fireball. This is a large, bright meteor which fades out because it's left Earth's atmosphere. These are very rare, but noticeable if they happen over a populated area.

It wouldn't be obvious to the casual observer that the asteroid had been or was going to be, captured, but since we started getting worried about asteroid hits on earth, there are astronomers who keep track of these things, and they'd realise rapidly after the event.

If the asteroid had been detected and tracked before the event, there might even have been a prediction that a capture was possible, although certainty wouldn't be available until after the encounter. Many asteroids aren't single solid rocks, but rock-piles held together by their very weak gravity, and those would come apart rapidly in the atmosphere.

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Asteroid 2009 BD passed between Earth and the Moon at a distance of 346,000 km. Scientists concluded that if it were to impact Earth's atmosphere, it would cause a multi-megaton explosion in the atmosphere killing everyone within a 10 - 20 km radius, and this rock was only about 10 m across.

http://sservi.nasa.gov/articles/asteroid-pass-between-moon-and-earth/

I understand that this data is for an asteroid impact, and not an aerocapture, but for an asteroid to be caught in Earth's gravitational field, it would need to dig very deep into our atmosphere, so needless to say it would be a spectacular event, one I would not want to be directly underneath. It would involve much fire (something I like) and falling pieces of asteroid (something I don't like) as pieces would break off during atmospheric entry. Also, asteroids have the unfortunate habit of exploding in the upper atmosphere, and even laypeople know what that looks like.

Reference: https://en.wikipedia.org/wiki/Tunguska_event (Just the first paragraph)

The speculation from the original question seemed to point to the fact that the asteroid would need a few passes through our atmosphere to slow down enough, so chances are we would witness this several times (unless it exploded). Also, if this theoretical asteroid was big enough to be interesting, the results could also include ablation (Dissipation) of a good portion of our atmosphere. NASA is so afraid of this that scientists have devised some interesting methods to stop an asteroid from colliding with our atmosphere, something most people can agree is a good use of tax dollars :)

http://www.planetary.org/explore/projects/laser-bees/Gibbings-Laser-Bees-201202.pdf

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