  When a planetary tidal disk -like Saturn's rings- spreads beyond the Roche
radius (inside which planetary tides prevent aggregation), satellites form and
migrate away. Here, we show that most regular satellites in the solar system
probably formed in this way. According to our analytical model, when the
spreading is slow, a retinue of satellites appear with masses increasing with
distance to the Roche radius, in excellent agreement with Saturn's, Uranus',
and Neptune's satellite systems. This suggests that Uranus and Neptune used to
have massive rings that disappeared to give birth to most of their regular
satellites. When the spreading is fast, only one large satellite forms, as was
the case for Pluto and Earth. This conceptually bridges the gap between
terrestrial and giant planet systems.
