Special ArticleDynamical and Observational Constraints on Satellites in the Inner Pluto-Charon System
Abstract
It is not known if Pluto has other satellites besides its massive partner Charon. In the past, searches for additional satellites in the Pluto-Charon system have extended from the Solar-tidal stability boundary (≈90 arcsec from Pluto) inward to about 1 arcsec from Pluto. Here we further explore the inner (i.e., <10 arcsec) region of the Pluto-Charon system to determine where additional satellites might lie. In particular, we report on (i) dynamical simulations to delineate the region where unstable orbits lie around Charon, (ii) dynamical simulations which use the low orbital eccentricity of Charon to constrain the mass of any third body near Pluto, and (iii) analysis of HST archival images to search for satellites in the inner Pluto-Charon system. Although no objects were found, significant new constraints on bodies orbiting in the inner Pluto-Charon system were obtained.
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The sailboat island and the New Horizons trajectory
2015, IcarusCitation Excerpt :These studies could help the New Horizons mission to discover new objects and avoid possible hazards. Stable regions were found for a sample of test particles in orbits around Charon and also around Pluto (for example, Stern et al. (1994) and Nagy et al. (2006)). These stable regions are formed by families of periodic and quasi-periodic orbits explored in detail in Giuliatti Winter et al. (2010) and Giuliatti Winter et al. (2013).
In previous works we have studied the location of stable regions in the Pluto–Charon system. Among the findings, we discovered an island of stability, named sailboat island. One of the main goals of the New Horizons mission, launched in 2006, is to have a flyby close to the Pluto–Charon system in order to explore it. In the present work we analyze the relevance of the sailboat island for the New Horizons mission. Firstly, we identify the location and extent of these stable trajectories in the physical space around Pluto. They go beyond the trajectory of Charon in a way that Charon never crosses such trajectories. We verify that the nominal trajectory of the New Horizons spacecraft passes near the region of the sailboat island trajectories, reaching the closest distance at about 1650 km. Analyzing an alternative trajectory for the spacecraft, known as Deep Inner SHBOT, we found that it is not as safe as the nominal trajectory, because it crosses a region of highly inclined trajectories located at the sailboat island. We also estimate the density of particles from the sailboat island in the physical space around Pluto in comparison with the density of particles from a well-known stable region of near circular trajectories close to Pluto. Finally, we identified the location of the densest regions, which corresponds to the highest probable location of particles of the sailboat island. Such locations can be considered as spots for search and new detections of bodies by the New Horizons cameras along the flyby close to the Pluto–Charon system.
The orbits and masses of satellites of Pluto
2015, IcarusCitation Excerpt :However, the regions interior and exterior to the Charon’s instability strip were not excluded for the existence of small satellites (masses up to 10−4 of the Pluto–Charon GM). Furthermore, Stern et al. (1994) found that at two Pluto–Charon separation distances, it is possible to consider the existence of even more massive satellites (masses up to 10−2 of the Pluto–Charon GM). The discovery of Nix and Hydra in the same orbital plane as Charon and in the proximity of 4:1 and 6:1 mean motion resonances with Pluto–Charon orbital period led to some interesting studies on the stability of their orbits.
We present the numerically integrated orbits of Pluto’s satellites. The orbits have been fit to a data set that includes Earth-based and Hubble Space Telescope (HST) astrometry of Charon, Nix, Hydra, Kerberos, and Styx, as well as the lightcurves from the Pluto–Charon mutual events. We also report new, 2010–2012 HST astrometry of all satellites including recently discovered Styx plus a pre-discovery detection of Kerberos in 2006. Pluto-relative data sets have been corrected for the center-of-light vs. center-of-mass offsets with the Pluto albedo model. The results are summarized in terms of the postfit residuals, state vectors, and mean orbital elements. Orbits of Charon, Styx, Nix, and Kerberos are nearly circular, while Hydra’s shows a small eccentricity. All satellites are in near-resonance conditions, but we did not uncover any resonant arguments. Our model yields 975.5 ± 1.5 km3 s−2, 869.6 ± 1.8 km3 s−2, and 105.9 ± 1.0 km3 s−2 for the system’s, Pluto’s, and Charon’s GM values. The uncertainties reflect both systematic and random measurement errors. The GM values imply a bulk density of 1.89 ± 0.06 g cm−3 for Pluto and 1.72 ± 0.02 g cm−3 for Charon. We also obtain GMNix = 0.0030 ± 0.0027 km3 s−2 GMHydra = 0.0032 ± 0.0028 km3 s−2, GMKerberos = 0.0011 ± 0.0006 km3 s−2, and an upper bound on Styx’s GM of 0.0010 km3 s−2. The 1σ errors are based on the formal covariance from the fit and they reflect only measurement errors. In-orbit (or along the track), radial, and out-of-plane orbital uncertainties at the time of New Horizons encounter are on the order of few tens of km or less for Charon, Nix, and Hydra. Kerberos and Styx have their largest uncertainty component of ∼140 km and ∼500 km respectively in the in-orbit direction.
The Origin of the Natural Satellites
2015, Treatise on Geophysics: Second EditionThis critical review of the current thoughts on the origin of the natural satellites in the solar system includes discussions of the virtues and caveats of numerous theories and points out problems in need of further research. The widely accepted origin of the Moon as resulting from a giant impact of a Mars-sized body on the primitive Earth has been complicated by the need to accommodate several examples of elements with identical isotope ratios in the Earth and Moon. Problems in the dynamic evolution of the Earth–Moon system remain to be resolved in the two modified impact schemes suggested to allow identical compositions of the Moon and Earth's mantle. Mars' satellites formed from a disk of debris, the possible different compositions of the satellites from Mars notwithstanding. The dynamic evolution of the satellites to the present configuration after formation is shown to be consistent with such an origin, although the origin of the disk remains uncertain. A model of Jupiter's satellite formation in a starved accretion disk in the last stages of the formation of Jupiter, where several generations of satellites form that are lost by migration into Jupiter, produces a system within the constraints of observation. But problems remain in the delivery of solids to the disk, justifying the values of the turbulent viscosity parameter α assumed and the treatment of a time-varying opacity during the accretion process. The Saturn system of satellites is the least understood of all the systems. Nearly all the mass of the satellites is within the single large satellite Titan, and the small, generally ice-rich satellites interior to Titan show a nonmonotonic ice to rock ratio as a function of orbital radius. Tethys must be nearly pure ice. A scheme for getting icy satellites close to Saturn where one would have expected rocky satellites involves spawning the satellites from a nearly pure ice particle ring, where the latter would result from the tidal stripping of the outer ice layers from a large, differentiated satellite as the latter spirals toward its destruction in Saturn. But a viable evolution of satellites so created coupled with other satellites still migrating toward Saturn into the current configuration and the deposition of rock into some of these satellites in an uneven distribution leaving a pure ice Tethys has yet to be demonstrated. The origin of the satellites of Uranus is complicated by the apparent necessity of a giant impact to account for Uranus' large obliquity. An existing satellite system would be destroyed during the impact process, but the equatorial disk so formed by the debris can rotate in the same retrograde direction as Uranus' spin only if Uranus already had a significant obliquity before the final impact. In this latter case, a satellite system like that observed could be reassembled. The understanding of the Neptune system configuration is more secure than that for any other satellite system. The capture of the large retrograde satellite Triton by the disruption of a binary asteroid as it passes close to Neptune is dynamically sound and probable. The small prograde satellites interior to Triton's orbit are reaccreted objects after the destruction of the original system during the tidal decay of Triton's initially very eccentric orbit. Like the Moon, Charon, the large satellite of Pluto, was almost certainly the result of a giant impact to account for the large system-specific angular momentum. However, the origin of the four small satellites exterior to Charon's orbit cannot be the result of transport of collisional debris to their current positions locked in mean motion resonances with Charon as the latter's orbit tidally expands to the current state of dual synchronous rotation. The origin of the small Pluto satellites is still a mystery. The distribution of irregular satellites with distant orbits around the four major planets is consistent with their being captured objects from the planetesimal population in the solar nebula, where capture is achieved through several effective mechanisms.
This paper aims to alleviate the confusion between many different ways of defining latitude and longitude on Pluto, as well as to help prevent future Pluto papers from drawing false conclusion due to problems with coordinates. In its 2009 meeting report, the International Astronomical Union Working Group on Cartographic Coordinates and Rotational Elements redefined Pluto coordinates to follow a right-handed system (Archinal, B.A., et al. [2011a]. Celest. Mech. Dynam. Astron. 109, 101–135; Archinal, B.A., et al. [2011b]. Celest. Mech. Dynam. Astron. 110, 401–403). However, before this system was redefined, both the previous system (defining the north pole to be north of the invariable plane), and the “new” system (the right-hand rule system) were commonly used. A summary of major papers on Pluto and the system each paper used is given. Several inconsistencies have been found in the literature. The vast majority of papers and most maps use the right-hand rule, which is now the IAU system and the system recommended here for future papers.
The orbits of Pluto’s four small satellites (Styx, Nix, Kerberos, and Hydra) are nearly circular and coplanar with the orbit of the large satellite Charon, with orbital periods nearly in the ratios 3:1, 4:1, 5:1, and 6:1 with Charon’s orbital period. These properties suggest that the small satellites were created during the same impact event that placed Charon in orbit and had been pushed to their current positions by being locked in mean-motion resonances with Charon as Charon’s orbit was expanded by tidal interactions with Pluto. Using the Pluto–Charon tidal evolution models developed by Cheng et al. (Cheng, W.H., Lee, M.H., Peale, S.J. [2014]. Icarus 233, 242–258), we show that stable capture and transport of a test particle in multiple resonances at the same mean-motion commensurability is possible at the 5:1, 6:1, and 7:1 commensurabilities, if Pluto’s zonal harmonic . However, the test particle has significant orbital eccentricity at the end of the tidal evolution of Pluto–Charon in almost all cases, and there are no stable captures and transports at the 3:1 and 4:1 commensurabilities. Furthermore, a non-zero hydrostatic value of destroys the conditions necessary for multiple resonance migration. Simulations with finite but minimal masses of Nix and Hydra also fail to yield any survivors. We conclude that the placing of the small satellites at their current orbital positions by resonant transport is extremely unlikely.
Two small satellites of Pluto, S/2005 P1 (hereafter P1) and S/2005 P2 (hereafter P2), have recently been discovered outside the orbit of Charon, and their orbits are nearly circular and nearly coplanar with that of Charon. Because the mass ratio of Charon–Pluto is ∼0.1, the orbits of P2 and P1 are significantly non-Keplerian even if P2 and P1 have negligible masses. We present an analytic theory, with P2 and P1 treated as test particles, which shows that the motion can be represented by the superposition of the circular motion of a guiding center, the forced oscillations due to the non-axisymmetric components of the potential rotating at the mean motion of Pluto–Charon, the epicyclic motion, and the vertical motion. The analytic theory shows that the azimuthal periods of P2 and P1 are shorter than the Keplerian orbital periods, and this deviation from Kepler's third law is already detected in the unperturbed Keplerian fit of Buie and coworkers. In this analytic theory, the periapse and ascending node of each of the small satellites precess at nearly equal rates in opposite directions. From direct numerical orbit integrations, we show the increasing influence of the proximity of P2 and P1 to the 3:2 mean-motion commensurability on their orbital motion as their masses increase within the ranges allowed by the albedo uncertainties. If the geometric albedos of P2 and P1 are high and of order of that of Charon, the masses of P2 and P1 are sufficiently low that their orbits are well described by the analytic theory. The variation in the orbital radius of P2 due to the forced oscillations is comparable in magnitude to that due to the best-fit Keplerian eccentricity, and there is at present no evidence that P2 has any significant epicyclic eccentricity. However, the orbit of P1 has a significant epicyclic eccentricity, and the prograde precession of its longitude of periapse with a period of 5300 days should be easily detectable. If the albedos of P2 and P1 are as low as that of comets, the large inferred masses induce significant short-term variations in the epicyclic eccentricities and/or periapse longitudes on the 400–500-day timescales due to the proximity to the 3:2 commensurability. In fact, for the maximum inferred masses, P2 and P1 may be in the 3:2 mean-motion resonance, with the resonance variable involving the periapse longitude of P1 librating. Observations that sample the orbits of P2 and P1 well on the 400–500-day timescales should provide strong constraints on the masses of P2 and P1 in the near future.