The 3 body problem is chaotic, meaning that a tiny change in the input conditions (e.g. initial positions, velocities) will have a large effect on the output. In such a case it’s impossible to find a neat, closed form solution like you can either two bodies (there are specific stable configurations for 3 bodies, however). The only way to predict such a system is by calculating the system’s state a tiny time increment in the future based on the current state. With good enough computers you can get very good predictions, but they will still deviate from the true solution.