Tidal interactions in stellar and planetary systems

Gravitational tidal interactions drive long-term rotational and orbital evolution in planetary systems, in multiple (particularly close binary) star systems and in planetary moon systems. Dissipation of tidal flows in Earth's oceans is primarily responsible for producing gradual expansion of the Moon's orbit at a few centimetres per year as the Earth's day lengthens by a few milliseconds per century. Similar processes occur in many astrophysical systems. For example, tidal dissipation inside (slowly rotating) stars hosting short-period planets can cause the orbits of these planets to decay, potentially leading to planetary destruction; tidal dissipation inside stars in close stellar binary systems -- and inside short-period planets such as hot Jupiters in planetary systems -- can cause initially eccentric orbits to become circular. To model these processes, explain many current observational results, and make predictions for future observations, we require a detailed theoretical understanding of tidal flows and the mechanisms by which -- and how efficiently -- they are dissipated inside stars and planets. This article will introduce our current understanding of tidal flows and dissipation inside stars (and to a lesser extent giant planets), as well as highlight some unsolved problems.