  We consider two particles interacting via a contact interaction that are
constrained to a sphere, or $S^2$. We determine their spectrum to arbitrary
precision and for arbitrary angular momentum. We show how the non-inertial
frame leads to non-trivial solutions for different angular momenta. Our results
represent an extension of the finite-volume L\"uscher formulas but now to a
non-trivial geometry. We apply our results to predict the spectrum of select
two-nucleon halo nuclei and compare with experimental results.
