# Why is there a singularity in Lambert solutions for transfers of pi-multiple degrees?

Lambert provides a solution as long as the transfer angle is not 0, 180 or 180-multiple degrees. Why is that?

An integral multiple of 180° means that the initial point $$r_1$$, the central point, and the target point $$r_2$$ all lie on the same line. This in turn means the cross product between the displacement vector from the central point to the initial point and from the central point to the final point is zero. Note that except for these special cases, the cross product point between these two vectors indicates the orbital plane of the transfer orbit. But in the special case where the cross product is zero, the orbital plane of the transfer orbit is undefined.