Roche's proof of the existence of a critical distance for a satellite, within which it would be broken up by tidal action, assumed the satellite fluid. It is shown that a solid satellite, or a small solid body making a casual near approach, would not be broken up even close to the surface of a planet unless its diameter was less than a critical value, which is unexpectedly large, of the order of 200 km. It appears in particular that small bodies of the sizes of the majority of the asteroids could not have been formed by close approach to Jupiter, and that fragments of ice consistent with the maximum possible thickness of Saturn's rings could not have been formed by disruption of a solid mass by tidal action.