= Pericentre-speed qualification of Kepler orbit classes
{title2=$v_p=k\sqrt{GM/r_p},\quad k\ge1$}
At a genuine <pericentre>, the radial velocity vanishes and the radial acceleration is nonnegative. The radial equation therefore requires $v_p^2\ge GM/r_p$. In terms of the displayed factor k, a circle has k=1, a noncircular ellipse has $1<k<\sqrt2$, a parabola has $k=\sqrt2$ and a hyperbola has $k>\sqrt2$. If $0<k<1$ at a tangential turning point, that point is the apocentre, despite the negative orbital energy. Bound-energy classification alone does not establish which turning point is being specified.
Back to article page
