Kick-orbit distribution
= Kick-orbit distribution
{title2=$f_c(c)=1/(\pi\sqrt{1-c^2})$}
Uniform planar kick angle $\theta$ gives $c=\cos\theta$ with probability density $1/(\pi\sqrt{1-c^2})$. This maps onto a one-dimensional curve in <orbital eccentricity>–<semi-major axis> space. The two radial-kick signs share that curve but have opposite tangential components of the <eccentricity vector>. The resulting density is enhanced near tangential-kick endpoints.