Safronov number ($\Theta$)

For a planet on a circular stellar orbit, a common convention is $\Theta =\frac{1}{2}(v_{\mathrm{esc}}/v_k{)}^2$. The escape-to-orbital-speed ratio measures the size of a strong gravitational assist relative to the stellar binding energy of a nearby comet. Large values tend to favour ejection over collision; small values favour repeated weak encounters with more collision opportunities. This is a statistical comparison, dependent on the initial orbit and encounter geometry, rather than a universal outcome threshold.