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The conference call with Bill Bottke (MP3 plus other documents) about "minimoons" presents an alternative to Asteroid Redirect first got me interested in orbital mechanics. The idea is that there are enough small asteroids that approach the earth-moon barycenter (EMB) that it seems likely there are frequent temporary captures of small asteroids into chaotic 3-body orbits in EMB system, that last for a few months to a few years.

Here is an example of one theoretical orbit from here or here:

enter image description here

One can read more in Granvik, Vaubaillon and Jedicke 2012 (The population of natural Earth satellites Icarus, 218 (1) March 2012, pp262-277) available without paywall in ArXiv.

Only one "minimoon" 2006 RH120 was known by 2012, but it seems there should be new ones regularly, according to Granvik et al. 2012.

Have there been others that were detected and reported?

enter image description here

uhoh
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    One has just been discovered, but it looks like it's been here for at least 50 years, so far longer than the type of orbit you're referrring to. http://www.jpl.nasa.gov/news/news.php?feature=6537 – Hobbes Jun 17 '16 at 07:33
  • @Hobbes that is great to know about! They call 2016 HO3 a "quasi-moon" because it's in orbit around the sun in a 1:1 resonance with earth. Watch here. They go around together, sort-of like a Trojan asteroid would. I'll have to read more - this is really interesting, at about 2.2 million miles a moon of earth would have a period of about 1 year, although that's if there were no sun. This one stays around 9 million miles away, so it's really in orbit around the sun, but in resonance with the earth. Curiouser and curiouser! – uhoh Jun 17 '16 at 12:37
  • @Hobbes here's a crazy video of the trajectory, it just does a big figure-8 in a patch of the Celestial Sphere, bisecting Virgo and Leo The Trajectory of the Strange Object 2016 HO3. – uhoh Jun 17 '16 at 13:04
  • Remember, that's just the view from Earth. Just like the planets and their weird retrograde loops. – Hobbes Jun 17 '16 at 13:15
  • @Hobbes yep. But this would be the first ever thing that moves around a lot during the year, and yet always stays in one area relative to the stars - for at least an entire human lifetime. There's nothing that I can think of that has ever done that before. If it was bright enough to be visible - and if it had come a few hundred years earlier - it would be really quite unique, and forced Newton and Galileo to think scratch their heads a bit. I'm sure Newton would have caught on to resonances earlier. – uhoh Jun 17 '16 at 13:35
  • @Hobbes http://arksky.org/images/2016_ho3_5000_day_orbit.png – uhoh Jun 17 '16 at 14:11
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    Not really an answer, but I would expect mini-moons to be commonplace around Earth. Because we have our big Moon, a body coming from interplanetary space effectively undergoes a three-body interaction when it encounters Earth. Energy can be transferred from an incoming body to the Earth-Moon pair, allowing the small body to be captured, and perhaps vice versa allowing the small body to later escape. – Oscar Lanzi Feb 27 '20 at 22:11

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Possibly the earliest documented mini-moon was the one associated with the 1913 Great Meteor Procession.

After 2006 RH120, that you mentioned, another was identified on October 3, 2015 and designated WT1190F. It impacted Earth on November 13, 2015. It was probably space debris, and not natural.

There's only one other potential candidate that I know of so far: S509356. It was identified on April 8, 2016. It may yet be an artificial satellite, but there are none known that match its orbital period, and it has a color associated with S-type asteroids.

Update 5/16/2018:

S509356 turns out to be 2015-019C, 41929, upper stage from a Long March carrying a BeiDou satellite.

Update 2/27/2020:

Now we have an official confirmed mini-moon (temporary natural satellite): 2020 CD3. It was discovered February 15, 2020, and announced February 25. It is estimated to have been orbiting Earth since around 2017-2018, and it is expected to depart April 2020.

called2voyage
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