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A massless particle can be naturally captured by a celestial body with the aid of a third body. In this work, the influence of the mass ratio on ballistic capture is investigated in the planar circular restricted three-body problem (CR3BP) model. Four typical dynamical environments with decreasing mass ratios, i.e., the Pluto–Charon, Earth–Moon, Sun–Jupiter and Saturn–Titan systems, are considered. A generalized method is introduced to derive ballistic capture orbits by starting from a set of initial conditions and integrating backward in time. Particular attention is paid to the backward escape orbits, following which a test particle can be temporarily trapped by a three-body gravity system, although the particle will eventually deviate away from the system. This approach is applied to the four candidate systems with a series of Jacobi constant levels to survey and compare the capture probability (quantitatively) and capture capability (qualitatively) when the mass ratio varies. Capture mechanisms inducing favourable ballistic capture are discussed. Moreover, the possibility and stability of capture by secondary celestial bodies are analysed. The obtained results may be useful in explaining the capture phenomena of minor bodies or in designing mission trajectories for interplanetary probes.
A massless particle can be naturally captured by a celestial body with the aid of a third body. In this work, the influence of the mass ratio on ballistic capture is investigated in the planar circular restricted three-body problem (CR3BP) model. Four typical dynamical environments with decreasing mass ratios, i.e., the Pluto–Charon, Earth–Moon, Sun–Jupiter and Saturn–Titan systems, are considered. A generalized method is introduced to derive ballistic capture orbits by starting from a set of initial conditions and integrating backward in time. Particular attention is paid to the backward escape orbits, following which a test particle can be temporarily trapped by a three-body gravity system, although the particle will eventually deviate away from the system. This approach is applied to the four candidate systems with a series of Jacobi constant levels to survey and compare the capture probability (quantitatively) and capture capability (qualitatively) when the mass ratio varies. Capture mechanisms inducing favourable ballistic capture are discussed. Moreover, the possibility and stability of capture by secondary celestial bodies are analysed. The obtained results may be useful in explaining the capture phenomena of minor bodies or in designing mission trajectories for interplanetary probes.
During 2005-2012, images from Hubble Space Telescope (HST) revealed four moons orbiting Pluto-Charon (Weaver et al. 2006;Showalter et al. 2011Showalter et al. , 2012. Although their orbits and geometric shapes are well-known, the 2σ uncertainties in the masses of the two largest satellites -Nix and Hydra -are comparable to their HST masses (Brozović et al. 2015;Showalter & Hamilton 2015;Weaver et al. 2016). Remarkably, gravitational n-body computer calculations of the long-term system stability on 0.1-1 Gyr time scales place much tighter constraints on the masses of Nix and Hydra, with upper limits ∼ 10% larger than the HST mass. Constraints on the mass density using size measurements from New Horizons suggest Nix and Hydra formed in icier material than Pluto and Charon.Subject headings: planets and satellites: dynamical evolution and stabilityplanets and satellites: individual (Pluto)
We consider a scenario where the small satellites of Pluto and Charon grew within a disk of debris from an impact between Charon and a trans-Neptunian object (TNO). After Charon’s orbital motion boosts the debris into a disk-like structure, rapid orbital damping of meter-sized or smaller objects is essential to prevent the subsequent reaccretion or dynamical ejection by the binary. From analytical estimates and simulations of disk evolution, we estimate an impactor radius of 30–100 km; smaller (larger) radii apply to an oblique (direct) impact. Although collisions between large TNOs and Charon are unlikely today, they were relatively common within the first 0.1–1 Gyr of the solar system. Compared to models where the small satellites agglomerate in the debris left over by the giant impact that produced the Pluto–Charon binary planet, satellite formation from a later impact on Charon avoids the destabilizing resonances that sweep past the satellites during the early orbital expansion of the binary.
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