In science fiction novels and movies, we occasionally see a planet or a moon being teared into pieces due to it being to close to a star or a larger planet. In the newly premiered Chinese sci-fi movie The Wandering Earth II, our moon potentially gets torn into chunks as it moves closer to the Earth and passes its Roche limit. You might wonder, what exactly is this limit and why would it tear objects apart?
We know that tidal forces exist due to the differences in gravity on the near and far sides of a planet or a satellite. We also know that tidal forces become more extreme as an object gets closer to the source of the tidal effect (due to the object’s radius occupying a larger portion of the distance between the object and the source). The Roche limit, first calculated by French astronomer Édouard Roche, is the distance to a (larger) celestial body when an approaching (smaller) celestial body disintegrates due to extreme tidal effects that exceed the self-gravity that holds the smaller object together.
A completely rigid object would maintain its shape up to the point of the Roche limit, while a more fluid object will tend to get elongated due to tidal forces as it approaches its Roche limit, and this elongation further increases the tidal effects and rips the object apart. The Roche limit depends on the ratio of the density (or mass) of the two objects, and the calculation of this limit for rigid bodies is shown below.
One example of a celestial body being torn apart in the Solar System is the comet Shoemaker-Levy 9, which unfortunately traveled too close to Jupiter, got past its Roche limit, and was broken into over 20 pieces and eventually bombarded the cloudy surface of Jupiter (See figure below).
Within the Roche limit of a planet, chunks of rock and ice will not tend to coalesce to form moons, which is why rings of planets generally lie within this radius, as asteroids and moons that enter this radius disintegrate into small pieces. In contrast, larger moons of planets generally orbit beyond this radius to stay in one piece.
There are several exceptions, though. Saturn’s moon Pan, a ring shepherd in Saturn’s Encke division, and Jupiter’s moons Metis and Adrastea all lie within their Roche limits, since forces other than their self-gravity holds themselves together. Another exception is the minor planet 50000 Quaoar in the Kuiper Belt which has a ring far beyond its Roche limit. Astronomers are still investigating why Quaoar’s ring did not amalgamate into a satellite.
