Perturbations in the external orbit of the multiple star system ${\xi}$Ursa Major

Perturbations are calculated in the external orbit of the multistar system ${\xi}$Ursa Major using formulas from a theory developed by the authors. A comparison is performed of the changes in the $i_{2}$, $\omega_{2}$, and $\Omega_{2}$ elements calculated using formulas from the theory and deduced by Heintz from observation. The comparison shows that the order of magnitude of these changes in any case is the same, although their numerical values are different. For a more precise comparison of the results, new processing of observations of the ${\xi}$Ursa Major system must be performed, with which the perturbations of the external orbit should be calculated using the authors' formulas.