The three-body problem, unlike the two-body problem, lacks a general closed-form analytic solution. This means explicit formulas for the positions of three orbiting bodies over time cannot be derived using Newton's laws. The governing differential equations are not integrable, making prediction difficult for most initial conditions. Typically, the three-body system exhibits chaotic behavior, requiring numerical methods for motion estimation. Despite this, thousands of stable three-body orbits, which repeat predictably, have been discovered. The Three Body Orbits website showcases a collection of these stable orbits, displaying diverse and intricate patterns. It also allows users to search for new stable solutions directly within their browser. An example of an unsuccessful search showed two bodies in a gravitational spiral while the third moved independently. This highlights the complexity and the often unstable nature of three-body interactions. The website serves as an atlas and an interactive tool for exploring this physics challenge.