Dynamics of double galactic system on the background of dark substance

In this article we searched the dynamics of double galactic system (the Local Group of galaxies, as example) on the background of dark substance, including both dark energy and dark matter. For modern cosmology the study influence on the dynamics of the Local Group not only the dark energy, but also the second most important component of dark substance dark matter is rather actually today. The study of dark energy in nearby Universe becomes significant and perspective for the observations at large space scales where it was discovered for the first time. That is why we constructed the Lagrangian of such dynamical system for more correctly searching the dynamics of Local Group. Such approach allowed, instead of the initially forwarded rectilinear trajectory found its more realistic one. Talk about the real elliptical trajectory, more accurate resulting expression for the revolving time and the relaxation time due to accounting the contribution of the dark substance. The results show that the contribution of the dark substance in the total amount of revolving time of galaxies is about 10%. All these results are astronomically observable quantities and testify the strict accounting of the dark substance properties within the Local Group of galaxies.