The three-body problem is to take the initial positions and velocities of three point masses orbiting each other in space, and calculate their subsequent motion.
The three-body problem has no general closed-form solution. But, if you have read the novel by the same name you already knew that.
This tool introduces the special case of the circular restricted three-body problem, CR3BP. In this, Euler found three periodic solutions in 1767 where the three masses are in a straight line. Five years later, Lagrange found two more where the three masses form an equilateral triangle. Together, these solutions known as L1 to L5 form the basis of our understanding of the CR3BP.
Test unit of the James Webb Space Telescope, which is in a halo orbit at L2 Lagrange point, sunshield stacked and expanded at the Northrop Grumman facility in California in 2014.
The tool shows contours of the so-called Jacobi constant, a value conserved in the CR3BP with the units of energy per unit mass. However, as is standard, the tool uses a normalised, dimensionless unit system. The user can switch between different pre-defined three-body systems or vary the mass and distance between the two primary bodies to see how this changes the Jacobi contours. The location of the five Lagrange points is illustrated, with the distance of each from the two primary bodies detailed.
You can read more Nibbles in Space at 
SpaceProf.xyz 
. And, if you want to go into more depth at The International Handbook of Space Technology which is a definitive modern text on space technology with contributions from globally leading agency experts from NASA, ESA, JAXA, and CNES, as well as European and North American academics and industrialists. This comprehensive handbook provides an overview and a holistic understanding of the system-of-systems that is a modern spacecraft.