The Roche limit (pronounced /ʁoʃ/ in IPA, similar to the sound of rosh), sometimes referred to as the Roche radius, is the distance within which a celestial body, held together only by its own gravity, will disintegrate due to a second celestial body's tidal forces exceeding the first body's gravitational self-attraction. Inside the Roche limit, orbiting material disperses and forms rings whereas outside the limit material tends to coalesce. The term is named after Édouard Roche, who is the French astronomer who first calculated this theoretical limit in 1848. == Explanation == Typically, the Roche...

In mathematics, a saddle point is a point in the range of a function that is a stationary point but not a local extremum. The name derives from the fact that the prototypical example in two dimensions is a surface that curves up in one direction, and curves down in a different direction, resembling a saddle or a mountain pass. In terms of contour lines, a saddle point in two dimensions gives rise to a contour that appears to intersect itself. == Mathematical discussion == A simple criterion for checking if a given stationary point of a real-valued function F(x,y) of two real variables is a saddle...