Geomagnetic declination derived from the positional records of Martian retrograde motion in 1491

Abstract

Mars exhibited retrograde motions from January 4 to March 26 in 1491 CE. The Annals of the Joseon Dynasty has more than 40 records of observations with 38 lodge angles and 4 polar angles corresponding to the equatorial coordinates measured with an observing device called a small abridged armilla, as well as 34 angular separations of Mars with respect to neighboring stars estimated by eye. Accurate positions for Mars are calculated for comparison with the records, and we find a number of interesting aspects to those observations. A length unit of chi, used for reporting angular separations, is equivalent to 1 du or a Chinese angular unit. We find that the axis of the observing device might have been misaligned with the north celestial pole (NCP), and that some court astronomers might have rounded down their measurements while other astronomers might have rounded them up. In order to correct the misalignment, we apply a χ2 minimization scheme to the lodge and polar angles simultaneously, and find that the device was misaligned with the NCP by −0.°8 ± 0.°3 in elevation and −1.°3 ± 0.°3 in azimuth if the measurements had been rounded down, while it was misaligned with the NCP by −0.°4 ± 0.°3 in elevation and −2.°2 ± 0.°3 in azimuth if the measurements had been rounded up. The axis of the device was off from the NCP and aligned with a point below and to the west of the NCP. Since a magnetic compass was used for the alignment, the misalignment angle of the polar axis in azimuth is equal to the geomagnetic declination at Seoul in 1491 CE. The misalignment angles in azimuth we have obtained are in agreement with recent geomagnetic models within the 1–2 σ uncertainties of the models. Moreover, the single measurement error characterizing the observing device is estimated to be 0.°3.