Tidal force and Roche limit
Tidal force:
On Earth, we are all familiar with the tidal force, which causes the ocean’s tides. The oceans are deformed by the attraction of the Moon and the Sun, the currents respond to these forces and move around the continents, leading to highly variable tide times and heights depending on the location on Earth and the time of the year.
The tidal force acts between all pairs of celestial bodies if close enough to each other, in particular a planet and a satellite ? or a star and a planet.
Roche limit ? :
Around a planet, the tidal force is what makes the rings stable.
The Roche limit ? is the minimum distance from the centre of a planet at which a satellite ? can orbit without breaking up, despite the tidal forces. if the planet and the satellite ? have the same density, the Roche limit ? is 2.5 times the radius of the planet. Inside this limit, the satellite ? is broken up by tidal forces.
In 1994, the comet ? Shoemaker-Levy 9 broke up as it passed within the Roche limit ? of Jupiter (figure below).
All the rings around the planets in the Solar System are inside the Roche limit ? of the planets.
Solid satellites ? can exist inside the Roche limit ? if they are small enough and the cohesion forces within the rocks prevent them from breaking up.
In a debris disc surrounding a recently formed planet, the matter located beyond the Roche limit ? can agglomerate into satellites ? , while in a zone closer to the planet, the tidal forces prevent any satellite ? from forming.
This mechanism also applies in the vicinity of a star: there can be no planets closer than 2.5 times the radius of its star.
