Small-mass-ratio collinear Lagrange points ($x_{L_1,L_2}=1\mp (\alpha /3{)}^{1/3}+O({\alpha }^{2/3})$)

In barycentric coordinates with unit primary separation, a small secondary mass fraction $\alpha$ gives distances $(\alpha /3{)}^{1/3}$ from that secondary to the two neighboring Lagrange points at leading order. This is the dimensionless Hill radius. The opposite exterior L3 Lagrange point has coordinate $-1-5\alpha /12+O({\alpha }^2)$.