Investigations of trajectories of various objects orbiting the Milky Way (MW) halo with modern precision, achievable in observations by Gaia, requires sophisticated, nonstationary models of the Galactic potential. In this paper we analyze the evolution of the spherical harmonics expansion of MW analogs potential in constrained simulations of the Local Group (LG) from the HESTIA suite. We find that at distances $r\ge 100\mathrm{kpc}$, the nonspherical part of the potential demonstrates a significant impact of the environment: ignoring the mass distribution outside the virial radius of the MW results in $>20\%$ errors in the potential quadrupole at these distances. Account of the environment results in a noticeable change of the angular momenta of objects orbiting MW analogs. Spherical harmonics vary significantly during the last 6 Gyr. We attribute variations of the potential at $r\ge 30\mathrm{kpc}$ to the motions of MW satellites and LG galaxies. We also predict that the nonsphericity of the real MW potential should grow with distance in the range $r_{\mathrm{vir}}<r<500\mathrm{kpc}$, since all realizations of simulated MW-like objects demonstrate such a trend.

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• Formation & evolution of stars & galaxies
• Galactic halos
• Milky Way
• Astronomical masses & mass distributions
• Astrophysical & cosmological simulations