I posted a notice sent by Dr. Tony Phillips of SpaceWeather.com about the asteroid 2009 FH that passed Earth few nights back. The notice was titled "Small Asteroid Buzzes Earth Tonight". The asteroid was 85,000 km away from Earth. The reason why Dr. Phillips decided to use the phrase "Small Asteroid Buzzes Earth Tonight" is because 85,000 km is quite close in astronomical terms.

NASA has classified objects that are less than 1.3 AU as Near-Earth Objects (NEOs)¹:

In terms of orbital elements, NEOs are asteroids and comets with perihelion distance q less than 1.3 AU. Near-Earth Comets (NECs) are further restricted to include only short-period comets (i.e orbital period P less than 200 years). The vast majority of NEOs are asteroids, referred to as Near-Earth Asteroids (NEAs).

1 AU = 149.60 million km
An object orbiting around the Sun, the closest distance in its orbital path is called the Perihelion.

NEOs closer than 0.05 AH (about 7.5 million km) are further grouped as PHAs¹ (see citation below). There are over 1000s of PHAs and to satisfy your curiosity I have posted a link giving their details ⁴.

The asteroid 2009 FH that passed Earth two nights ago was a mere 85,000 km away from earth. This is why Dr. Phillips decided to use the phrase "Small Asteroid Buzzes Earth Tonight".

Potentially Hazardous Asteroids (PHAs) are currently defined based on parameters that measure the asteroid's potential to make threatening close approaches to the Earth. Specifically, all asteroids with an Earth Minimum Orbit Intersection Distance (MOID) of 0.05 AU or less and an absolute magnitude (H) of 22.0 or less are considered PHAs.

In other words, asteroids that can't get any closer to the Earth (i.e. MOID) than 0.05 AU (roughly 7,480,000 km or 4,650,000 mi) or are smaller than about 150 m (500 ft) in diameter (i.e. H = 22.0 with assumed albedo of 13%) are not considered PHAs.

There are currently 1044 known PHAs.

This potential to make close Earth approaches does not mean a PHA will impact the Earth. It only means there is a possibility for such a threat. By monitoring these PHAs and updating their orbits as new observations become available, we can better predict the close-approach statistics and thus their Earth-impact threat.

A relatively small number of near-Earth objects pass close enough to Earth and are large enough in size to warrant close observation. That's because the gravitational tug of the planets could, over time, cause an object's orbital path to evolve into an Earth-crossing orbit. This allows for the possibility of a future collision.

Potentially hazardous asteroids are about 150 meters (almost 500 feet) or larger, roughly twice as big as the Statue of Liberty is tall. They approach Earth to within 7.5 million kilometers (about 4.6 million miles). By comparison, when Mars and Earth are at their closest, they are about 53 million kilometers (about 33 million miles) apart.

Links

1. NASA: Near-Earth Object Groups
2. NASA: Keeping an Eye on Space Rocks
3. List Of The Potentially Hazardous Asteroids (PHAs)