Abstract
We study the capture of interstellar objects (ISOs) by a planet-star binary with mass ratio q ≪ 1, semi-major axis ap, orbital speed vc, and eccentricity ep. Very close (slingshot) and wide encounters with the planet are amenable to analytic treatment, while numerically obtained capture cross-sections σ closely follow the analytical results even in the intermediate regime. Wide interactions can only generate energy changes ΔE≲qv2c, when σ∝v−2∞|lnΔE|2/3 (with v∞ the ISO’s incoming speed far away from the binary), which is slightly enhanced for ep > 0. Energy changes ΔE≳qv2c, on the other hand, require close interactions when σ∝(v∞ΔE)−2 hardly depending on ep. Finally, at ΔE≳v2c, the cross-section drops to zero, depending on the planet’s radius Rp through the Safronov number Θ = qap/Rp. We also derive the cross-sections for collisions of ISOs with planets or moons.
Dehnen, Walter