Planets and satellites orbiting a binary system exist in the solar system and extrasolar planetary systems. Their orbits can be significantly different from Keplerian orbits, if they are close to the binary and the secondary-to-primary mass ratio is high. A proper description of a circumbinary orbit is in terms of the free eccentricity $e_{\rm free}$ at the epicyclic frequency $κ_0$, forced eccentricity $e_{\rm forced}$ at the mean motion $n_0$, and oscillations at higher frequencies forced by the non-axisymmetric components of the binary's potential. We show that accurate numerical values for the amplitudes and frequencies of these terms can be extracted from numerical orbit integrations by applying fast Fourier transformation (FFT) to the cylindrical distance between the circumbinary object and the center of mass of the binary as a function of time. We apply this method to three Kepler circumbinary planets and the satellites of Pluto-Charon. For the satellite Styx of Pluto-Charon, the FFT results for $κ_0$ and $e_{\rm free}$ differ significantly from the first-order analytic value and the value reported by Showalter & Hamilton (2015), respectively. We show that the deviation in $κ_0$ is likely due to the effect of the 3:1 mean-motion resonance and discuss the implications of the lower value for $e_{\rm free}$.
Current theory considers two options for the formation of the Pluto-Charon binary (Canup 2005, 2011; Desch 2015). In the `hit-and-run' model, a lower mass projectile barely hits the more massive Pluto, kicks up some debris, and remains bound to Pluto (see also Asphaug et al. 2006). In a `graze-and-merge' scenario, the projectile ejects substantial debris as it merges with Pluto (see also Canup 2001). To investigate the graze-and-merge idea in more detail, we consider the growth of Charon-mass objects within a circum-Pluto ring of solids. Numerical calculations demonstrate that Charon analogs f…
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-size or smaller objects is essential to prevent the subsequent re-accretion 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…
Using a suite of numerical calculations, we consider the long-term evolution of circumbinary debris from the Pluto-Charon giant impact. Initially, these solids have large eccentricity and pericenters near Charon's orbit. On time scales of 100-1000 yr, dynamical interactions with Pluto and Charon lead to the ejection of most solids from the system. As the dynamics moves particles away from the barycenter, collisional damping reduces the orbital eccentricity of many particles. These solids populate a circumbinary disk in the Pluto-Charon orbital plane; a large fraction of this material lies with…
Pluto's terrains display a diversity of crater retention ages ranging from areas with no identifiable craters to heavily cratered terrains. This variation in crater densities is consistent with geologic activity occurring throughout Pluto's history and also a variety of resurfacing styles, including both exogenic and endogenic processes. Using estimates of impact flux and cratering rates over time, Pluto's heavily cratered terrains appear to be relatively ancient, 4 Ga or older. Charon's smooth plains, informally named Vulcan Planitia, did experience early resurfacing, but there is a relativel…
The Pluto-Charon binary system is the best-studied representative of the binary Kuiper-belt population. Its origins are vital to understanding the formation of other Kupier-belt objects (KBO) and binaries, and the evolution of the outer solar-system. The Pluto-Charon system is believed to form following a giant impact between two massive KBOs at relatively low velocities. However, the likelihood of a random direct collision between two of the most massive KBOs is low, and is further constrained by the requirement of a low-velocity collision, making this a potentially fine-tuned scenario. Here …
During 2005-2012, images from Hubble Space Telescope (HST) revealed four moons orbiting Pluto-Charon (Weaver et al 2006, Showalter et al 2011, 2012). Although their orbits and geometric shapes are well-known, the 2$σ$ uncertainties in the masses of the two largest satellites - Nix and Hydra - are comparable to their HST masses (Brozovic 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 $\sim…
We discuss a new set of $\sim$ 500 numerical n-body calculations designed to constrain the masses and bulk densities of Styx, Nix, Kerberos, and Hydra. Comparisons of different techniques for deriving the semimajor axis and eccentricity of the four satellites favor methods relying on the theory of Lee & Peale (2006), where satellite orbits are derived in the context of the restricted three body problem (Pluto, Charon, and one massless satellite). In each simulation, we adopt the nominal satellite masses derived in Kenyon & Bromley (2019a), multiply the mass of at least one satellite by a numer…
A giant collision is believed to be at the origin of the Pluto-Charon system. As a result, the initial orbit and spins after impact may have substantially differed from those observed today. More precisely, the distance at periapse may have been shorter, subsequently expanding to its current separation by tides raised simultaneously on the two bodies. Here we provide a general 3D model to study the tidal evolution of a binary composed of two triaxial bodies orbiting a central star. We apply this model to the Pluto-Charon binary, and notice some interesting constraints on the initial system. We…
In this paper, the near-optimal capture problem is numerically investigated to locate the optimal capture points around Charon using the Pluto-Charon planar circular restricted three-body problem (PCRTBP). Capture orbits are divided into the pre- and post-maneuver portions. In the pre-maneuver portion, the gravitational capture conditions are discussed by backward numerical integration. In the post-maneuver portion, the smaller alignment index (SALI) is applied to numerically investigate the orbital characters of long-term capture orbits around Charon. The initial conditions corresponding to t…
The flyby of Pluto and Charon by the New Horizons spacecraft provided high-resolution images of cratered surfaces embedded in the Kuiper belt, an extensive region of bodies orbiting beyond Neptune. Impact craters on Pluto and Charon were formed by collisions with other Kuiper belt objects (KBOs) with diameters from ~40 kilometers to ~300 meters, smaller than most KBOs observed directly by telescopes. We find a relative paucity of small craters less than approximately 13 kilometers in diameter, which cannot be explained solely by geological resurfacing. This implies a deficit of small KBOs (les…
Four small moons (Styx, Nix, Kerberos and Hydra) are at present known to orbit around the barycenter of Pluto and Charon, which are themselves considered a binary dwarf-planet due to their relatively high mass ratio. The central, non-axisymmetric potential induces moon orbits inconvenient to be described by Keplerian osculating elements. Here, we report that observed orbital variations, may not be the result of orbital eccentricities or observational uncertainties, but may be due to forced oscillations caused by the central binary. We show, using numerical integration and analytical considerat…
A unique feature of Pluto's large satellite Charon is its dark red northern polar cap. Similar colours on Pluto's surface have been attributed to organic macromolecules produced by energetic radiation processing of hydrocarbons. The polar location of this material on Charon implicates the temperature extremes that result from Charon's high obliquity and long seasons. The escape of Pluto's atmosphere provides a potential feed stock for production of complex chemistry. Gas from Pluto that is transiently cold-trapped and processed at Charon's winter pole was proposed as an explanation on the basi…
Synchronisation of a tidal binary by inward orbital migration. The case of Pluto and Charon
US Naval Observatory（美国海军天文台）；Charles University（查理大学）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；California Institute of Technology（加州理工学院）；ETH Zürich（苏黎世联邦理工学院）
Context. The orbits of the four small moons in the Pluto-Charon system, Styx, Nix, Kerberos and Hydra, are circumbinary, as the former form a binary dwarf planet. Consequently, the orbit of each one of them is characterized by a number of frequencies, arising by the central binary and the mutual gravitational interactions. Aims. In this work, we identify the most prominent of these forced frequencies using Fast Fourier Transformations. Methods. Two methods are implemented, a semi-analytic and a numerical one, and comparisons are being made. Results. The results indicate that as a first approxi…
The formation of Pluto's small satellites - Styx, Nix, Keberos and Hydra - remains a mystery. Their orbits are nearly circular and are near mean-motion resonances and nearly coplanar with Charon's orbit. One scenario suggests that they all formed close to their current locations from a disk of debris that was ejected from the Charon-forming impact before the tidal evolution of Charon. The validity of this scenario is tested by performing $N$-body simulations with the small satellites treated as test particles and Pluto-Charon evolving tidally from an initial orbit at a few Pluto radii with ini…
Using a large suite of n-body simulations, we explore the discovery space for new satellites in the Pluto-Charon system. For the adopted masses and orbits of the known satellites, there are few stable prograde or polar orbits with semimajor axes $a \lesssim 1.1~a_H$, where $a_H$ is the semimajor axis of the outermost moon Hydra. Small moons with radii $r \lesssim$ 2 km and $a \lesssim 1.1~a_H$ are ejected on time scales ranging from several yr to more than 10 Myr. Orbits with $a \gtrsim 1.1~a_H$ are stable on time scales exceeding 100 Myr. Near-IR and mid-IR imaging with JWST and ground-based …
During its departure from Pluto, New Horizons used its LORRI camera to image a portion of Pluto's southern hemisphere that was in a decades-long seasonal winter darkness, but still very faintly illuminated by sunlight reflected by Charon. Recovery of this faint signal was technically challenging. The bright ring of sunlight forward-scattered by haze in the Plutonian atmosphere encircling the nightside hemisphere was severely overexposed, defeating the standard smeared-charge removal required for LORRI images. Reconstruction of the overexposed portions of the raw images, however, allowed adequa…
The Pluto-Charon (PC) pair is usually thought of as a binary in the dual synchronous state, which is the endpoint of its tidal evolution. The discovery of the small circumbinary moons, Styx, Nix, Kerberos, and Hydra, placed close to the mean motions resonances (MMRs) 3/1, 4/1, 5/1, and 6/1 with Charon, respectively, reveals a complex dynamical architecture of the system. Several formation mechanisms for the PC system have been proposed. Our goal is to analyse the past and current orbital dynamics of the satellite system. We study the past and current dynamics of the PC system through a large s…
Existence of subsurface oceans on the satellites of the giant planets and Trans-Neptunian objects has been predicted for some time. Oceans on icy worlds exert a considerable influence on the dynamics of the ice-ocean system and, because of the astrobiological potential, represent an important objective for future missions. The Pluto-Charon system is representative of an icy moon orbiting a dwarf planet formed from the remnants of a giant impact. Evolution of icy moons is primarily controlled by the mode and efficiency of heat transfer through the outer ice shell, which is influenced by the pre…
We describe a fast, approximate method to characterize the orbits of satellites around a central binary in numerical simulations. A goal is to distinguish the free eccentricity -- random motion of a satellite relative to a dynamically cool orbit -- from oscillatory modes driven by the central binary's time-varying gravitational potential. We assess the performance of the method using the Kepler-16, Kepler-47, and Pluto-Charon systems. We then apply the method to a simulation of orbital damping in a circumbinary environment, resolving relative speeds between small bodies that are slow enough to…
Systematic geomorphological mapping and detailed landform analysis using the highest resolution images obtained by the New Horizons spacecraft reveal the presence of a range of differentiable terrains on Charon, the largest moon of Pluto, that were not examined in detail by the early studies. The most important findings of our work include (1) truncation and omission of large craters (diameters > 30-40 km) and their crater rim ridges along the eastern edges of several north-trending, eastward-convex, arcuate ranges in Oz Terra, (2) lobate ridges, lobate knob trains, and lobate aprons resemblin…
Using the Andrade-derived Sundberg-Cooper rheology, we apply several improvements to the secular tidal evolution of TRAPPIST-1e and the early history of Pluto-Charon under the simplifying assumption of homogeneous bodies. By including higher-order eccentricity terms (up to and including $e^{20}$), we find divergences from the traditionally used $e^{2}$ truncation starting around $e=0.1$. Order-of-magnitude differences begin to occur for $e>0.6$. Critically, higher-order eccentricity terms activate additional spin-orbit resonances. Worlds experiencing non-synchronous rotation can fall into and …
The Pluto-Charon system provides a broad variety of constraints on planetary formation, composition, chemistry, and evolution. Pluto was the first body to be discovered in what is now known as the Kuiper belt, its orbit ultimately becoming a major clue that the giant planets underwent substantial orbital migration early in Solar System history. This migration has been linked to an early instability in the orbits of the giant planets and the formation of the Kuiper belt itself, from an ancestral trans-Neptunian planetesimal disk that included Pluto. Pluto-Charon is emblematic of what are now re…
In 2015, the New Horizons spacecraft flew past Pluto and its moon Charon, providing the first clear look at the surface of Charon. New Horizons images revealed an ancient surface, a large, intricate canyon system, and many fractures, among other geologic features. Here, we assess whether tidal stresses played a significant role in the formation of tensile fractures on Charon. Although presently in a circular orbit, most scenarios for the orbital evolution of Charon include an eccentric orbit for some period of time and possibly an internal ocean. Past work has shown that these conditions could…
The discovery of Pluto in 1930 presaged the discoveries of both the Kuiper Belt and ice dwarf planets, which are the third class of planets in our solar system. From the 1970s to the 19990s numerous fascinating attributes of the Pluto system were discovered, including multiple surface volatile species, Pluto's large satellite Charon, and its atmosphere. These attributes, and the 1990s discovery of the Kuiper Belt and Pluto's cohort of small Kuiper Belt planets, motivated the exploration of Pluto. That mission, called New Horizons (NH), revolutionized knowledge of Pluto and its system of satell…
The goal of this chapter is to review hypotheses for the origin of the Pluto system in light of observational constraints that have been considerably refined over the 85-year interval between the discovery of Pluto and its exploration by spacecraft. We focus on the giant impact hypothesis currently understood as the likeliest origin for the Pluto-Charon binary, and devote particular attention to new models of planet formation and migration in the outer solar system. We discuss the origins conundrum posed by the system's four small moons. We also elaborate on the implications of these scenarios…
