An efficient, low-velocity, resonant mechanism for capture of satellites by a protoplanet

Numerical simulations of the gravitational scattering of planetesimals by a protoplanet reveal that a significant fraction of scattered planetesimals can become trapped as so-called quasi-satellites in heliocentric 1:1 co-orbital resonance with the protoplanet. While trapped, these resonant planetesimals can have deep low-velocity encounters with the protoplanet that result in temporary or permanent capture onto highly eccentric prograde or retrograde circumplanetary orbits. The simulations include solar nebula gas drag and use planetesimals with diameters ranging from ∼1 to ∼ 1000   km . Initial protoplanet eccentricities range from e p = 0 to 0.15 and protoplanet masses range from 300 Earth-masses ( M ⊕ ) down to 0.1 M ⊕ . This mass range effectively covers the final masses of all planets currently thought to be in possession of captured satellites—Jupiter, Saturn, Neptune, Uranus, and Mars. For protoplanets on moderately eccentric orbits ( e p ⩾ 0.1 ) most simulations show from 5–20% of all scattered planetesimals becoming temporarily trapped in the quasi-satellite co-orbital resonance. Typically, 20–30% of the temporarily trapped quasi-satellites of all sizes came within half the Hill radius of the protoplanet while trapped in the resonance. The efficiency of the resonance trapping combined with the subsequent low-velocity circumplanetary capture suggests that this trapped-to-captured transition may be important not only for the origin of captured satellites but also for continued growth of protoplanets.