Gravitational scattering between particles 1 and 2 in the center-of-mass frame. The initial velocities υ₁, υ₂ are scattered in the directions , along the asymptotic lines (dotted). The actual orbits are hyperbolas (blue, purple). The focal points (black dots), with O being the common focal point of the orbits, lie on the orange circles. The four points of intersection of a circle with the asymptotes form rectangles with dimensions of the transverse axis 2a_j by the conjugate axis 2b_j (Adams & Essex 2021). The impact parameter is the sum b = b₁ + b₂.