A tiny satellite, like a swimmer, cuts through invisible layers of gas in the bloated envelope of a red giant. Each orbit excites an acoustic wake — compression waves traveling through plasma. According to Law of Universal Gravitation, the satellite attracts the gas, and the gas attracts the satellite, creating this wake. This is how gravity works — a key mechanism in the evolution of close binary star systems and the fate of exoplanet planets falling into stellar interiors. As early as Fritz Zwicky realized that dynamical friction governs the motion of galaxies in clusters, and Subrahmanyan Chandrasekhar derived its formula for stars. However, classical recipes assumed a homogeneous medium and rectilinear motion. For a satellite orbiting in a stellar evolution giant's envelope, this is too crude.

The author constructs a linear barotropic acoustic model. The orbit obeys Kepler's third law. The enthalpy perturbation is expanded in spherical harmonics and Fourier modes, and the force is written as a sum over multipoles. The key tool is a retarded Green's function. The calculation is performed for single and binary satellites on circular orbits in power-law density profiles and realistic models of stellar evolution. It turns out that stellar evolution changes dynamical friction not only through local density and Mach number but also through the global structure of the acoustic wake. The radial component of the force is determined by large-scale wave asymmetry and can differ from the homogeneous case even in sign. The azimuthal component, responsible for braking, retains sensitivity to small scales — the so-called Coulomb logarithm. In binary systems, a companion satellite can noticeably alter the radial force and weaken the braking. A local Coulomb-type contribution is absent, so the effect appears only on large scales.

For astrophysicists, this means that the inspiral time of a satellite into a giant's envelope cannot be estimated by knowing only conditions at the orbital point. The wave pattern throughout the entire envelope must be taken into account. The computed infall time for red giant and supergiant models turned out to be shorter than standard homogeneous formulas give. Planetary migration in stellar envelopes proceeds faster than previously thought. The next step is to couple the acoustic response with orbital evolution, allowing the satellite to migrate and change eccentricity. Furthermore, it is necessary to go beyond the linear approximation: where waves become shocks, three-dimensional numerical simulation hydrodynamic simulations will be required. Then it will become clear how law of conservation of angular momentum exchange between waves and orbit shapes the fate of the system. And then the acoustic wake in the stratified ocean will no longer be a mystery.