Photometric analysis for asteroid (81) Terpsichore using convex inversion and phase function fitting methods

Abstract The shapes and rotation states (periods and pole orientations) of main-belt asteroids are important for understanding their formation and evolution. In order to obtain sufficient photometric data covering different apparitions for asteroid (81) Terpsichore, ground-based photometric observations in 2020 and 2021 have been carried out. By combining published and newly obtained photometric data, we calculated the shape and spin parameters for (81) Terpsichore using the convex inversion method. With this method, we have derived a best fitted pole orientation -- ($22.2\pm{_{3.1}^{3.3}}^{\circ}, 17.5\pm{_{5.5}^{10.8}}^{\circ}$) with a spin period of 10.94 $\pm_{0.01}^{0.01}$ h. Based on the derived convex shape of (81) Terpsichore, we have fitted the $ H $, $ G_{1} $, $ G_{2} $ phase function using the calibrated TESS data and Gaia data after accounting for the light-curve amplitude correction. As a result, we've derived its absolute magnitude $H$ = 8.68 $\pm_{0.19}^{0.22}$ mag with corresponding phase function parameters $G_{1}$ = 0.82 $\pm_{0.10}^{0.09}$ and $G_{2}$ = 0.02 $\pm_{0.02}^{0.03}$.