  To solve some problems of celestial mechanics and astrophysics, three new
models of an elliptical galaxy (EG) have been created, which are in good
agreement with modern understanding of the structure of such galaxies. Based on
these models, the total gravitational (potential) energy and rotational kinetic
energy of an EG, as well as the velocity dispersion at a distance of its
effective radius, are determined. A new method is proposed for determining the
average values of the scale radius of an EG and the density at its center, as
well as the average value of its key parameter density $\beta$ and its value at
a distance corresponding to the effective radius of the galaxy. The results
obtained are applied to sixty EGs and presented in the form of tables for ten
galaxies.
