A study conducted by Cornell University astronomers has concluded that Earth must have a second moon, calculated via counting the population of "irregular natural satellites that are temporarily captured by Earth." This has also been backed up by a sighting of one of these 'orbiters' by the Catalina Sky Survey in Arizona.
In the research paper titled "The population of natural Earth satellites," conclusions are made around a set of secret moons which disappear faster than you can say 'that’s no moon, that’s a temporarily captured orbiter of a few metres in diameter.'
This is all fair and good as a theoretical, experiment based perspective; but there's been at least one instance where we've detected one. In 2006, the Catalina Sky Survey in Arizona identified a 'mysterious titanium white object' revolving around the Earth.
“Our results are consistent with the single known natural [temporarily-captured orbiter] 2006 RH120, a few-meter diameter object that was captured for about a year starting in June 2006.”
It turned out to be a small asteroid that was pulled into the Earth's gravitational field, which acted as a second moon until June 2007, when it left orbit. It's consistent with the findings from the study, and could pose a breakthrough for space travel and specimen collection. Having 'orbiters' in our gravitational field could mean that we could send astronauts nowhere near as far to retrieve an asteroid for analysis, cutting a great deal of cost around a space mission and making it a much quicker process to understand what is around the planet.
It's quite the opportunity.
Source: Cornell University