Evaluated distance between the MW and M 31 at t = 0 for different masses of the LG. The model predicts the correct mass when r(t = 0)=0. The first minimum (4 − 5 × 10¹² M_⊙) points to the predicted mass according to the TA. The second minimum points to the predicted mass with one PE (9 − 10 × 10¹² M_⊙). The dashed blue line corresponds to the solution without Λ, and the orange line corresponds to the solution with Λ.