It’s sometimes possible to obtain a reliable result (from observations on a single night) for an object zooming close to Earth. And astronomers can make a comparable computation for an asteroid in the main belt, between Mars and Jupiter, as it moves a few Moon-diameters relative to the background stars over the course of several nights.
However, the slow across-the-sky movement of a distant object usually requires astronomers to observe two successive oppositions in order to determine and follow an object’s orbit.
But even if the orbit is a guess, a typical TNO orbiting the Sun will move only a Moon-diameter roughly every year. Usually, a careful search will recover the object.
In the case of 2003 UB313, the discovery team observed the 18th-magnitude object over an arc of sky extending little more than a single Moon-diameter during 6 weeks beginning in September 2003 and on three consecutive nights in January 2005.
Based on these positions, a computed orbit conclusively showed the object is near its farthest point, 97 AU from the Sun, and has an orbit with a period of 550 years and inclination of 44° to the ecliptic.
Once astronomers knew where it was, they could determine where it had been. Astronomers searched for earlier observations on sky surveys. The oldest known images of 2003 UB313 were identified on plates exposed as part of the original Palomar survey in September 1954. In fact, these images were made using the same telescope (Samuel Oschin 48-inch) that was used to discover the object. — BRIAN G. MARSDEN, HARVARD-SMITHSONIAN CENTER FOR ASTROPHYSICS, CAMBRIDGE, MASSACHUSETTS