2.1 kilometers!
Cruithne is an asteroid about 2.1 kilometers (1.3 miles) across that travels around the Sun on a path linked to Earth's. That width comes from infrared measurements made by a NASA space telescope in 2010. An earlier estimate, based only on how bright the asteroid looks, put it at about 5 kilometers.
Cruithne's size is worked out from the sunlight it reflects and the heat it gives off. In 1997, the team that uncovered its unusual orbit estimated a width of about 5 kilometers (3 miles) from its brightness. That method depends on how much sunlight the surface is assumed to reflect. A wrong guess can give a badly wrong size.
In 2010, NASA's WISE space telescope measured the infrared light, or heat, coming from Cruithne. That heat depends mainly on an asteroid's size and only weakly on how dark its surface is. The measurements give an effective diameter, the width of a sphere that matches them, of about 2.1 kilometers. They also show that its surface is highly reflective, and with that reflectivity the brightness method gives the same 2.1 kilometers.
Cruithne turns once about every 27 hours. Its brightness rises and falls strongly as it turns.
Cruithne goes around the Sun once every 364 days, almost exactly the length of Earth's year. Its orbit is a stretched oval, tilted about 20 degrees to Earth's. Its distance from the Sun ranges from 0.48 to 1.51 astronomical units. An astronomical unit is Earth's average distance from the Sun, about 150 million kilometers.
Seen from Earth, Cruithne traces a loop shaped like a kidney bean each year, and the loop slowly creeps along Earth's orbit. As it nears Earth, Earth's gravity changes its orbit slightly, and it starts to drift back the other way. Astronomers call this a horseshoe orbit. The last reversal happened around 1900, and the next is expected around 2285.
Cruithne is not a moon of Earth, because it orbits the Sun rather than Earth. It never comes very close, either. At its closest approaches, which come only about once every 385 years, it passes about 0.1 astronomical units from Earth, roughly 40 times the distance to the Moon.
J. D. Waldron discovered Cruithne on October 10, 1986, at Siding Spring Observatory in Australia. It had been observed three years earlier in Chile, but not followed for long enough to work out its orbit. Its horseshoe path was recognized only in 1997, when Paul Wiegert, Kimmo Innanen and Seppo Mikkola simulated its motion on computers.
Its full name is 3753 Cruithne, and 3753 is its number in the catalog of known asteroids. Cruithne is the most common Irish name for the Picts, one of the ancient peoples of Scotland. In their legends, Cruithne was also the ancestor of the Picts, and his seven sons gave their names to the seven parts of the Pictish kingdom.