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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.