Outcomes of Tidal Evolution

Abstract

When tides raised by a satellite dissipate energy in a spinning planet, the planet-satellite system evolves dynamically toward one of three possible final conditions. The satellite orbit may decay inward until the satellite is destroyed ; the orbit may decay outward toward escape, although at an ever decreasing rate ; or the satellite's orbital and planet's spin periods may approach stable synchronism. Which of these outcomes of tidal evolution is approached depends on the satellite-planet mass ratio and on the initial spin an orbital angular velocities. A simple criterion is derived which tells the outcome, and a universal diagram is constructed which shows the actual path of evolution for a system with arbitrary masses and angular velocities. The possibility that certain retrograde satellites have been lost from the solar system is reexamined by means of this diagram.