e outer region with the dominant hot dark matter (the parabolic orbit of the test particle). It was assumed that the hot dark matter consists of hypothetical Planck neutrinos arising in the decay of the protons at the Planck scale. Galaxies formed from the baryonic matter, and the hot dark matter appears in the galaxies later. The rotation curves of the galaxies were studied in the model, including Milky Way, M33, NGC 2366 and IC 2574. In the present paper, the hot dark matter model is further investigated, with the application to M31, the system of M31 and the Milky Way, the globular clusters NGC 2419 and MGC1, the dwarf spheroidal galaxy Sculptor, ultra-massive quiescent galaxies from the COSMOS and UDS fields. The baryonic matter mass of M31 was estimated from the rotation curves, with the average value 1.6 × 10 11 m ? . The gravitational interaction of the Milky Way and M31 is considered. In the hot dark matter model, the dynamical masses of the Milky Way and M31 are twice their baryonic matter masses that gives the radial velocity of M31 toward the Milky Way, 106 km s −1 . The hot dark matter mass in the globular clusters NGC 2419 and MGC1 is estimated. The value is small compared to the stellar mass in both the clusters. The hot dark matter mass within the half-light radius of the dwarf spheroidal galaxy Sculptor is estimated, 0.5 × 10 6 m ? . The sum of the stellar and hot dark matter mass within the half-light radius is consistent with the dynamical mass within the half-light radius of the Sculptor derived from the kinematics of the metal rich stars. The instability of the baryonic matter due to the influence of the hot dark matter and some perturbations flattens the velocity profile of the metal poor stars which is unsuitable to derive the dynamical mass. The evolution of ultra-massive quiescent galaxies from the COSMOS and UDS fields is considered. The dynamical to stellar mass relation is doubling during the evolution from z = 2 to 0 that can be explained by the absence of dark matter at z = 2 and the presence of the hot dark matter at z = 0.