The Roche Limit Is A Mathematical Formula That Explains?
Answer: Planetary Rings
The Roche limit is, in the field of celestial mechanics, the distance at which a celestial body—such as a moon, comet, or asteroid—will disintegrate due to the overpowering tidal forces of the larger nearby body.
Objects outside this limit maintain integrity and either pass by the larger celestial object or are captured as a moon or other satellite. Objects within the limit are torn apart by the tidal forces exerted by the larger body and, in most cases, become rings around that planet. Almost all known planetary rings, including those around Jupiter and most of those around Saturn (the E-Ring and Phoebe ring being exceptions), are a result of satellites drifting past the boundary. Once torn apart, there is no chance the smaller parts of the once larger satellite will be able to coalesce back into a larger object as the smaller objects are too firmly controlled by the greater gravitational force of the host body.
The term is named after French astronomer Edouard Roche who first calculated the then theoretical limit in 1848. Later observations confirmed his calculations were correct, and the mass of the planets in our solar system, the distance of their planetary rings (if present), and their moons, conform to the calculations.
Image courtesy of NASA.