  Asteroid detections in astronomical images may appear as trails due to a
combination of their apparent rate of motion and exposure duration. Nearby
asteroids in particular typically have high apparent rates of motion and
acceleration. Their recovery, especially on their discovery apparition, depends
upon obtaining good astrometry from the trailed detections. We present an
analytic function describing a trailed detection under the assumption of a
Gaussian point spread function (PSF) and constant rate of motion. We have fit
the function to both synthetic and real trailed asteroid detections from the
Pan-STARRS1 survey telescope to obtain accurate astrometry and photometry. For
short trails our trailing function yields the same astrometric and photometry
accuracy as a functionally simpler 2-d Gaussian but the latter underestimates
the length of the trail - a parameter that can be important for measuring the
object's rate of motion and assessing its cometary activity. For trails longer
than about 10 pixels (> 3xPSF) our trail fitting provides 3-times better
astrometric accuracy and up to 2 magnitudes improvement in the photometry. The
trail fitting algorithm can be implemented at the source detection level for
all detections to provide trail length and position angle that can be used to
reduce the false tracklet rate.
