where $v_\theta$ is the tangential component of the orbital velocity. The orbital motion and the variation of the primary wind velocity with distance from the primary have an influence on the hyperboloid asymptotic opening angel $\phi_a$. We use the expression given by Eichler & Usov (1993) $$\phi_a \sim 2.1
\left(1-\frac{\eta_w^{{4}/{5}}}{4}\right)\eta_w^{{2}/{3}} ,
\label{eq:phia}$$ where $$\eta_w \equiv \sqrt{\frac{\dot M_2 v_{\rm 2,\infty}}{\dot M_1 v_{\rm wind1}}}
\label{eq:eta}$$ (note that this definition of $\eta_w$ is different from the one used by P09, where $\eta_{P09}=\eta_w^2$). $\phi_a$ has a minimum value of $\sim 58^\circ$ $33$ days before periastron, and reaches maximum of $\sim 72^\circ$ $25$ days after periastron.

\(3) **Hyperboloid rotation.** We take into consideration the rotation of the hyperboloid relatively to the line connecting the two stars. Namely, the winding of the WCR around the secondary star, as the secondary orbits the primary across periastron. This rotation (winding) has a considerable influence close to periastron. We define $\delta \phi$ to be the angle measured from the secondary between the direction to the primary and that to the stagnation point (see Soker 2005 for further details) $$\cos (\delta \phi)=\frac{v_1-v_r}{v_{\rm wind1}}.
\label{eq:deltaphi}$$ We find that the maximum value of $\delta \phi$ is obtained $\sim 6$ days after periastron, 