Capture of interstellar objects – I. The capture cross-section

ABSTRACT We study the capture of interstellar objects (ISOs) by a planet–star binary with mass ratio q ≪ 1, semimajor axis ap, orbital speed vc, and eccentricity ep. Very close (slingshot) wide encounters planet are amenable to analytical treatment, while numerically obtained cross-sections σ closely follow results even in intermediate regime. Wide interactions can only generate energy changes $\Delta E\lesssim q{v}_{\mathrm{c}}^2$, when $\sigma \propto v_\infty ^{-2} |\ln \Delta E|^{2/3}$ (with v∞ ISO’s incoming far away from binary), which is slightly enhanced for ep > 0. Energy E\gtrsim on other hand, require ∝ (v∞ΔE)−2 hardly depending Finally, at {v}_{\mathrm{c}}^2$, cross-section drops zero, planet’s radius Rp through Safronov number Θ = qap/Rp. also derive collisions ISOs planets or moons.