We investigated the evolution of HS Hya system’s inclination based on analysis of its light curves in the period 1964–2021. HS Hya is EA type eclipsing binary star, belonging to separate group with changing orbital inclination. We used our recent observations as well as the data from sky surveys.

We studied the problem of two spherical celestial bodies in the general case when the masses of the bodies change non-isotropically at different rates in the presence of reactive forces. The problem was investigated by methods of perturbation theory based on aperiodic motion along a quasi-conic section, using the equation of perturbed motion in the form of Newton’s equations. The problem is described by the variables a, e, i, π, ω, λ, which are analogs of the corresponding Keplerian elements and the equations of motion in these variables are obtained. Averaging over the mean longitude, we obtained the evolution equations of the two-body problem with variable masses in the presence of reactive forces. The obtained evolution equations have the exact analytic integral ${a^3 e^4 = a^3_0 e^4_0} = {const}$.

We investigated the influence of the variability of the masses of planets and the parent star on the dynamic evolution of n planetary systems, considering that the masses of bodies change isotropically with different rates. The methods of canonical perturbation theory, which developed on the basis of aperiodic motion over a quasi-conical cross section and methods of computer algebra were used. 4n evolutionary equations were obtained in analogues of Poincare elements. As an example, the evolutionary equations of the three-planet exosystem K2 − 3 were obtained explicitly, which is a system of 12 linear non-autonomous differential equations. Further, the evolutionary equations will be investigated numerically.

We model evolution of exoplanets of S-type in close binary systems at the stage when the companion starts to lose mass via a slow stellar wind. At this stage an accretion disc is formed around the planets’ host. Detailed structure of such discs is calculated in quasi-stationary and non-stationary approaches. We model migration of planets embedded in these discs.

Generally it is thought that shaping of planetary nebula from initially spherical envelope of asymptotic giant branch stars into non-spherical morphologies is a consequence of binary interactions. However, post asymptotic giant branch stars HD 235858 and HD 161796 seem to be at odds with this idea and perhaps the non-spherical nebulae surrounding them arose from intrinsic change in the nature of the stellar wind which is poorly understood for this evolutionary phase. Spectroscopic monitoring of these two stars has revealed signatures in the spectra that point to variable outflow. This indicates the prospect of spectroscopic monitoring to advance the knowledge of wind launching mechanism in post asymptotic giant branch stars and other dynamical processes in their extended atmospheres.