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Astrometry of minor planets is done for the MPC (Minor Planet Center at Harvard University)
The software which is used comprises:
PinPoint (by Bob Denny; dc-3-Software; "email@example.com")
Astrometrica (by Herbert Raab; "firstname.lastname@example.org")
CHARON from Guide-CD-ROM (by Bill J, Gray; "email@example.com")
Some star catalogs which are used for "plate-solving":
USNO SA2.0 (US Naval Observatory)
USNO A2.0 (US Naval Observatory)
The quality of plate-solving my images aquired with a focal lenth of f=2950 mm usually is in the order of 0.2 arcseconds (rms).
The standard deviation of a position of a minor planet (15-19 mag) is typically in the order of 0.5 arcseconds.