By transformingto an abstract 'shape-sphere', researchers in 2013 discovered the first new families of solutions to this problem since the Brouke-Henon family.  Expanding the coordinates as a function of the cube root of t was the technique used by Sundman to create a series expansion for this problem.  Another family of solutions is named after Euler and a mathematician who lends his name to their solutions, known as 'Lagrange points'. A third family is named for their characteristic motion pattern, the figure-eight. For 10 points, name this celestial mechanics problem, which requires calculating the motions of three masses influenced by each other's gravity from a given position and velocity.
By transformingto an abstract 'shape-sphere', researchers in 2013 discovered the first new families of solutions to this problem since the Brouke-Henon family.  Expanding the coordinates as a function of the cube root of t was the technique used by Sundman to create a series expansion for this problem.  Another family of solutions is named after Euler and a mathematician who lends his name to their solutions, known as 'Lagrange points'. A third family is named for their characteristic motion pattern, the figure-eight. For 10 points, name this celestial mechanics problem, which requires calculating the motions of three masses influenced by each other's gravity from a given position and velocity.
By transformingto an abstract 'shape-sphere', researchers in 2013 discovered the first new families of solutions to this problem since the Brouke-Henon family.  