CALCULATIONS OF THE CONSTANTS OF APSIDAL MOTION - A CRITICAL CONSIDERATION

The rate of the periastron's motion caused by the mutual tidal distort ion of the components of a binary system depends on the constants of a psidal motion k(2) specifying the density distribution in each of the components. In the surface layers of the star, where the density is sm all, the parameters k(2) are inversely proportional to the 5th power o f the radial distance r. Hence, the value of k(2)R(5) in the surface l ayers is nearly constant and does not depend on the structure of the s tar's outer layers and on the way the position of the star's surface i s chosen. Since the expression for the rate of apsidal motion contains the product k(2)R(5) (R is the star's radius), there is a possibility to avoid errors introduced by the calculations of star's surface laye rs into the predicted rates of the motion of the lines of apsides. For this aim it is appropriate to use the theoretical radii from the same calculations as the constants of apsidal motion. The k(2)R(5) paramet ers calculated by various authors are consistent with each other bette r than the constants k(2) For the stars of the initial main sequence, the dependence of log(k(2)R(5)) on the logarithm of the star's mass is linear and changes slightly with the opacities used and hydrogen cont ent. For stars with mass lower than 1.5 M. there is a small deviation from the linear dependence. Based on the calculations of evolutionary changes of the constants of apsidal motion, the least squares approxim ation of k(2)R(5) as a function of the mass and the age of the star wa s obtained.