Rouche limit
The Roche limit, also known as the Roche radius, is the minimum distance at which a celestial body, such as a moon or planet, can exist without being torn apart by tidal forces due to the gravitational pull of a larger celestial body, such as a planet or star.
The Roche limit is determined by the balance between the gravitational pull of the larger body and the self-gravity of the smaller body. If the smaller body comes within this limit, the tidal forces exerted by the larger body will overcome the self-gravity of the smaller body, leading to its disintegration.
The formula for the Roche limit is given by:
R = 2.44 * (M / m)^(1/3) * Rb
Where R is the Roche limit, M is the mass of the larger body, m is the mass of the smaller body, and Rb is the radius of the smaller body.
The Roche limit has important implications for celestial bodies in close proximity to each other, such as binary star systems, planetary rings, and the formation and stability of moons around planets. If a moon or ring system comes within the Roche limit of its parent planet, it will be pulled apart by tidal forces, leading to the formation of rings or the breakup of the moon.
The Roche limit was named after the French astronomer Edouard Roche, who first derived the concept in the 19th century.