Prairie Grass Observatory Campus
Update!  With the new 16" LX200R, we're now discovering asteroids at PGO!  Scroll to the bottom for details.
Prairie Grass Observatory is an official asteroid discovery/tracking station.  With the recent concern about the possibility of an asteroid colliding with the earth, there are now large professional "surveys" being done to try to find and catalog as many asteroids as possible.  It takes a few years of regular monitoring of an asteroid's position to accuartely determine its orbit.  The surveys, however, are set up to use pre-arranged search patterns to try to find new asteroids. While follow-up observations of most newly discovered asteroids will result as a side benefit of the survey's searches, in many cases deliberate follow-up is needed.  For example, if a (relatively speaking) small asteroid is first discovered while passing very close to earth, it may quickly become too dim for observation as it moves away, so immediate follow-up is needed, so that its orbit can be determined at least well enough to have a good chance of being able to find it the next time it gets near earth, so further positional measurements can be made to refine its orbit.  In other cases, a newly discovered asteroid may simply slip through the net of further follow-up via the surveys.  In both cases, much of the the follow-up is done by several smaller professional observatories and many amateurs.
1999 XN207
Asteroid 1999 XN207
This asteroid was "recovered" on the morning of October 14, 2002 at PGO. It was first discovered in late 1999, and observered many times in the following weeks. But such faint asteroids are only readily observed when they are near opposition i.e., when they are lined up with the earth on the same side of the sun, where they are closer to the earth than in other parts of their orbits. This asteroid is at opposition about every 19 months, but at the next opposition after 1999 it was almost completely missed, except for a pair of measurements by one observatory on one night in May, 2001. So by the time it returned in late 2002, the uncertainty in the orbit was growing and there was a possibilty that it might not be found again. Fortunately, the orbit determined at the first opposition turned out to be just accurate enough to find it on a first attempt. This image shows only the lower right quarter of the original image frame, which was centered near the expected position (at the upper left corner of this image). As you can see, if it had been much farther away from the expected position, it would have been missed. Initially it was detected as a point of light that didn't match star charts or older archival images (from the Digitized Palomar Observatory Sky Survey). More exposures of the same area showed that the object was indeed moving and matched the expected direction and rate of motion. This animated image was made from six 1 minute exposures at f/6 on the 12" scope, taken at about 5 minute intervals. The asteroid is at lower right, moving northeast towards a galaxy known as PGC 177306. The field is about 4'X6' (1º = 60' = 60 arcminutes). The field is in the constellation Eridanus, about 10º WSW of Rigel, the star marking Orion's west foot. There is a huge galaxy cluster centered about 1º southwest of here, which is why there are three galaxies in this image.

Asteroid data is correlated by the Minor Planet Center (MPC) at Harvard.  The MPC operates under the auspices of Commission 20 of the International Astronomical Union.  PGO is observatory number H59 on the MPC's list.
J002E3=Apollo 12
One of the most interesting objects tracked at PGO occurred right at the start.  As I was preparing a first "test batch" of measurements, Bill Yeung, one of the world's most accomplished amateur asteroid hunters, sent word out via the Minor Planet Mailing List (an internet email list for asteroid hunters) that he had detected an odd object.  After a few nights of observations, the MPC determined that this object was orbiting the earth, and took it off their lists, assuming it was space junk.  But then satellite experts determined that this object, dubbed J002E3, could not be matched to any known man made object.  At this point NASA got interested and added it to their list of solar system objects.  One obvious question was why hadn't the object been detected previously?  It was relatively bright compared to most asteroids discovered in the last few years, so if it had been in orbit around the earth for any period of time it should have been detected by the current asteroid surveys several times already. 
The only answer was that it had only recently entered earth's orbit.  Over the next several days, dozens of measurements from many observatories, including PGO, allowed NASA to determine the object's path accurately enough to extrapolate backwards a few months in an attempt to find out where it had come from.  The object was in a very high orbit, sometimes further than the moon, and since the moon is a significant fraction of the earth's mass, its gravity also has a significant effect on the orbit of any object orbiting that far out, so the orbit was somewhat unstable.  NASA found that the object had only orbited a few times and before that had come from near a point in space known as the L1 Lagrange point (Lagrange was an 18th century French mathematician who first determined the position of the "Lagrange points").  Orbits occur because the centrifugal force from the curved orbital path balances the gravity from whatever an object is orbiting around, and Lagrange points are places near the earth's orbit where the earth's gravity combines with the sun's to allow an object to orbit the sun at the same rate as the earth, even though the distance to the sun from that point is not the same as the distance from the earth to the sun.  In this case the L1 Lagrange point is on a line between the earth and the sun, about 1 million miles closer to the sun than the earth is.  Here the sun's gravity is stronger than at the earth, so an object would normally have to orbit faster so that the centrifugal force on the object will be stronger, but since an object at that point will have the gravity of the earth pulling opposite the sun's gravity, the gravity will be partly cancelled and the object can orbit slower, at a rate that matches the earth's orbit.  Lagrange points are common "transition points" between an orbit around the sun and an orbit around a planet.  Several of Jupiter's smaller moons are thought to have been pulled in from (Jupiter's) Lagrange points.
At this point NASA could not reliably estimate where the object had been any earlier, but another few weeks of observations allowed increased accuracy of the backward projections, and NASA found that before the object was pulled in from the L1 point, it had orbited the sun not exactly at the L1 point, but had been orbiting the sun just slightly closer to the sun than the earth and slightly faster than the earth, and had "lapped" the earth every 15 years.  The projection showed that 15 years ago, the last time the object was near earth, it did not get near the L1 point, but that 15 years before that, it had.  Just as objects can get pulled in from the L1 point, they can also leave that way, so it was possible that this object was a lost spacecraft, but which one?
A final piece of evidence proves that J002E3 is man-made:  A very large observatory telescope was aimed at J002E3 to obtain spectrographic data.  The evidence showed considerable amounts of titanium oxide (TiO). TiO has a definite significance in astronomy- most molecules will break down into individual atoms if they're in the atmosphere of a star, but TiO is one of the most heat-resistant molecules known, so it is one of the most frequently detected molecules in the atmospheres of stars (only small cool stars, others have no molecules at all).  But in this case TiO was significant for another reason: it is also an extremely white material, and is one of the most common pigments in white paint, including the paint NASA used to paint the huge Saturn V rockets used in the Apollo missions.
That question turned out to be easy to answer.  First, from the brightness it was clear that this was a sizable object, not a typical small satellite.  When the Apollo missions went to the moon, a large upper stage was used to boost the craft from a low earth orbit to the moon.  These would eventually separate from the rest of the craft and be sent into orbit around the sun.  (Actually, after the Apollo 11 and 12 astronauts put seismographs on the moon, the later upper stages were deliberately crashed into the moon- an impact from a known object of a known mass and speed made a good test for calibrating the seismographs).  But on Apollo 12 there was a glitch that left the upper stage in a very high earth orbit, about as far away as the moon.  It was tracked for awhile, but was soon lost.  Again the moon's gravity would have affected the orbit, so it is likely that the moon eventually flung the Apollo 12 upper stage to the L1 point and into solar orbit.  So our mystery object appears to be the long lost upper stage from the second manned moon landing.
Asteroids discovered at PGO
Asteroids 2007 TA3 and 2007 TB3
This animation, made from three images taken at PGO on the night of October 4 (the 5th, in GMT/UT), 2007, shows the discovery images of asteroids 2007 TA3 and 2007 TB3, both at left center of the images, moving towards the lower right.  Using an Apogee AP47p CCD camera (which is a significant improvement over my old Meade Pictor 416) on loan from Purdue, the sensitivity with our new 16" scope is so good that it's easy to find new asteroids- sometimes even 2 or 3 in one set of images.

As of November 13, 2007, 10 asteroids have been discovered at PGO:
2007 TA3 2007 TV4
2007 TB3 2007 TX7
2007 TC3 2007 TD18
2007 TD3 2007 TP225
2007 TE3 2007 UJ6
Press release from PGO
Story in the Frankfort Times

All of these objects appear to be ordinary main belt asteroids, with diameters of 1 to 2 miles (except for two which may be as small as 1/2 or even 1/3 mile).  You can see their orbits and positions relative to the Earth at any given time with JPL's neat 3D comet/asteroid orbit viewer.  Just enter any of the designations from the above list.

2008 Update
2008 QO6
2008 QP6
2008 QR13
2008 QZ19
2008 QS23
2008 SR11
2008 SR84
2008 SU84
2008 SW84
2008 TJ3