The 3-body problem is one of the most important problems in dynamical systems. The perenial question on the (in)stability of Earth’s orbit is unsolved to this day. It turns out that certain problems concerning the stability of solutions are easier to solve in spatial dimension 4 then in dimension 3. The goal of this project is to study the particular case where the angular momentum tensor has degenerate eigenvalues in 4D. A combination of numerical and analytical tools will be used.