Precise measurement for differential color refraction and its application to the astrometry of faint natural satellites

Differential color refraction (DCR) is a major limiting factor in the astrometric accuracy of ground-based telescopes. Conventional strategies to mitigate DCR involve restricting observations to near-meridian transits or employing near-infrared filters. However, even under these optimized conditions, DCR remains non-negligible when the zenith distance is nonzero. In this study, we present a method to determine both color indices (CIs) and precise astrometric positions using a single Clear filter. By iteratively modelling the DCR-CI relation in the equatorial coordinate system with reference stars from Gaia DR3, we correct for DCR effects and obtain accurate positions of natural satellites. This method was applied to eight nights of observations of the Jovian irregular satellites Himalia and Carme, observed between 2024 December 21 and 2025 January 24 with the 80 cm telescope at the Yaoan Station of Purple Mountain Observatory. The derived color indices are 0.847 ± 0.010 for Himalia and 1.028 ± 0.072 for Carme. The mean observed-minus-computed (O-C) offsets and standard deviations relative to the JPL ephemeris are -0.\!\!002 ± 0.\!\!013 and 0.\!\!000 ± 0.\!\!015 in right ascension and declination for Himalia, and 0.\!\!015 ± 0.\!\!029 and -0.\!\!022 ± 0.\!\!026 for Carme. This approach significantly improves ground-based astrometric accuracy and efficiency and offers a practical method for providing high-precision data to improve the ephemerides of faint solar system satellites.