Definitions of unit axes used to determine the post-explosion parameters of an eccentric binary. Shown is the binary at the moment of explosion of star 2 with a true anomaly ν_i. The black circle indicates the center of mass of the system. The unit axes ${\widehat{e}}_{\text{x}}$ and ${\widehat{e}}_{\text{y}}$ are defined in terms of the line joining both stars at the moment of explosion, while the unit axes ${\widehat{e}}_{\Vert }$ and ${\widehat{e}}_{\perp }$ are defined in terms of the direction of motion of star 2 at the moment of explosion. These sets of unit vectors are related by a rotation with an angle τ.