# Posts Tagged solar system

## Recent Postings from solar system

### Fast and dynamically reliable symplectic integration for solar system N-body problems

We apply one of the exactly symplectic integrators, that we call HB15, of \cite{HB15} to solve solar system $N$-body problems. We compare the method to Wisdom-Holman methods (WH), MERCURY, and others and find HB15 to have high efficiency. Unlike WH, HB15 solved $N$-body problems exhibiting close encounters with small, acceptable error, although frequent encounters slowed the code. Switching maps like MERCURY change between two methods and are not exactly symplectic. We carry out careful tests on their properties and suggest they must be used with caution. We use different integrators to solve a 3-body problem consisting of a binary planet orbiting a star. For all tested tolerances and time steps, MERCURY unbinds the binary after 0 to 25 years. However, in the solutions of HB15, a time-symmetric Hermite code, and a symplectic Yoshida method, the binary remains bound for $>1000$ years. The methods' solutions are qualitatively different, despite small errors in the first integrals in most cases. Several checks suggest the qualitative binary behavior of HB15's solution is correct. The Bulirsch-Stoer and Radau methods in the MERCURY package also unbind the binary before a time of 50 years.

### Meridional Transport in the Atmospheres of Earth and Mars

As we continue to discover terrestrial exoplanets, many with orbital and planetary characteristics drastically different from anything encountered in our solar system, we are likely to encounter 'exotic' atmospheric transport processes. As an example, we show an analysis of meridional transport from simulations Mars. These simulations provide insight into the differences in meridional transport between Earth and Mars, particularly through the role of a condensation flow. The differences between Earth and Mars are a reminder that there may be a wide variety of meridional transport processes at work across the range of observed terrestrial planets.

### Did the Solar System form in a sequential triggered star formation event?

The presence and abundance of the short-lived radioisotopes (SLRs) $^{26}$Al and $^{60}$Fe during the formation of the Solar System is difficult to explain unless the Sun formed in the vicinity of one or more massive star(s) that exploded as supernovae. Two different scenarios have been proposed to explain the delivery of SLRs to the protosolar nebula: (i) direct pollution of the protosolar disc by supernova ejecta and (ii) the formation of the Sun in a sequential star formation event in which supernovae shockwaves trigger further star formation which is enriched in SLRs. The sequentially triggered model has been suggested as being more astrophysically likely than the direct pollution scenario. In this paper we investigate this claim by analysing a combination of $N$-body and SPH simulations of star formation. We find that sequential star formation would result in large age spreads (or even bi-modal age distributions for spatially coincident events) due to the dynamical relaxation of the first star-formation event(s). Secondly, we discuss the probability of triggering spatially and temporally discrete populations of stars and find this to be only possible in very contrived situations. Taken together, these results suggest that the formation of the Solar System in a triggered star formation event is as improbable, if not more so, than the direct pollution of the protosolar disc by a supernova.

### Fossilized condensation lines in the Solar System protoplanetary disk

The terrestrial planets and the asteroids dominant in the inner asteroid belt are water poor. However, in the protoplanetary disk the temperature should have decreased below water condensation level well before the disk was photoevaporated. Thus, the global water depletion of the inner Solar System is puzling. We show that, even if the inner disk becomes cold, there cannot be direct condensation of water. This is because the snowline moves towards the Sun more slowly than the gas itself. The appearance of ice in a range of heliocentric distances swept by the snowline can only be due to the radial drift of icy particles from the outer disk. However, if a sufficiently massive planet is present, the radial drift of particles is interrupted, because the disk acquires a superKeplerian rotation just outside of the planetary orbit. From this result, we propose that the precursor of Jupiter achieved about 20 Earth masses when the snowline was still around 3 AU. This effectively fossilized the snowline at that location. Although cooling, the disk inside of the Jovian orbit remained ice-depleted because the flow of icy particles from the outer system was intercepted by the planet. This scenario predicts that planetary systems without giant planets should be much more rich in water in their inner regions than our system. We also show that the inner edge of the planetesimal disk at 0.7AU, required in terrestrial planet formation models to explain the small mass of Mercury and the absence of planets inside of its orbit, could be due to the silicate condensation line, fossilized at the end of the phase of streaming instability that generated the planetesimal seeds. Thus, when the disk cooled, silicate particles started to drift inwards of 0.7AU without being sublimated, but they could not be accreted by any pre-existing planetesimals.

### The role of Jupiter in driving Earth's orbital evolution: an update

In the coming decades, the discovery of the first truly Earth-like exoplanets is anticipated. The characterisation of those planets will play a vital role in determining which are chosen as targets for the search for life beyond the Solar system. One of the many variables that will be considered in that characterisation and selection process is the nature of the potential climatic variability of the exoEarths in question. In our own Solar system, the Earth's long-term climate is driven by several factors - including the modifying influence of life on our atmosphere, and the temporal evolution of Solar luminosity. The gravitational influence of the other planets in our Solar system add an extra complication - driving the Milankovitch cycles that are thought to have caused the on-going series of glacial and interglacial periods that have dominated Earth's climate for the past few million years. Here, we present the results of a large suite of dynamical simulations that investigate the influence of the giant planet Jupiter on the Earth's Milankovitch cycles. If Jupiter was located on a different orbit, we find that the long-term variability of Earth's orbit would be significantly different. Our results illustrate how small differences in the architecture of planetary systems can result in marked changes in the potential habitability of the planets therein, and are an important first step in developing a means to characterise the nature of climate variability on planets beyond our Solar system.

### Models of the Eta Corvi debris disk from the Keck Interferometer, Spitzer and Herschel

Debris disks are signposts of analogues to small body populations of the Solar System, often however with much higher masses and dust production rates. The disk associated with the nearby star Eta Corvi is especially striking as it shows strong mid- and far-infrared excesses despite an age of ~1.4 Gyr. We undertake to construct a consistent model of the system able to explain a diverse collection of spatial and spectral data. We analyze Keck Interferometer Nuller measurements and revisit Spitzer and additional spectro-photometric data, as well as resolved Herschel images to determine the dust spatial distribution in the inner exozodi and in the outer belt. We model in detail the two-component disk and the dust properties from the sub-AU scale to the outermost regions by fitting simultaneously all measurements against a large parameter space. The properties of the cold belt are consistent with a collisional cascade in a reservoir of ice-free planetesimals at 133 AU. It shows marginal evidence for asymmetries along the major axis. KIN enables us to establish that the warm dust consists in a ring that peaks between 0.2 and 0.8 AU. To reconcile this location with the ~400 K dust temperature, very high albedo dust must be invoked and a distribution of forsterite grains starting from micron sizes satisfies this criterion while providing an excellent fit to the spectrum. We discuss additional constraints from the LBTI and near-infrared spectra, and we present predictions of what JWST can unveil about this unusual object and whether it can detect unseen planets.

### Ethyl alcohol and sugar in comet C/2014Q2 (Lovejoy)

The presence of numerous complex organic molecules (COMs; defined as those containing six or more atoms) around protostars shows that star formation is accompanied by an increase of molecular complexity. These COMs may be part of the material from which planetesimals and, ultimately, planets formed. Comets represent some of the oldest and most primitive material in the solar system, including ices, and are thus our best window into the volatile composition of the solar protoplanetary disk. Molecules identified to be present in cometary ices include water, simple hydrocarbons, oxygen, sulfur, and nitrogen-bearing species, as well as a few COMs, such as ethylene glycol and glycine. We report the detection of 21 molecules in comet C/2014 Q2 (Lovejoy), including the first identification of ethyl alcohol (ethanol, C2H5OH) and the simplest monosaccharide sugar glycolaldehyde (CH2OHCHO) in a comet. The abundances of ethanol and glycolaldehyde, respectively 5 and 0.8% relative to methanol (0.12 and 0.02% relative to water), are somewhat higher than the values measured in solar- type protostars. Overall, the high abundance of COMs in cometary ices supports the formation through grain-surface reactions in the solar system protoplanetary disk.

### Water On -and In- Terrestrial Planets

Earth has a unique surface character among Solar System worlds. Not only does it harbor liquid water, but also large continents. An exoplanet with a similar appearance would remind us of home, but it is not obvious whether such a planet is more likely to bear life than an entirely ocean-covered waterworld---after all, surface liquid water defines the canonical habitable zone. In this proceeding, I argue that 1) Earth's bimodal surface character is critical to its long-term climate stability and hence is a signpost of habitability, and 2) we will be able to constrain the surface character of terrestrial exoplanets with next-generation space missions.

### Observing Outer Planet Satellites (except Titan) with JWST: Science Justification and Observational Requirements

The James Webb Space Telescope (JWST) will allow observations with a unique combination of spectral, spatial, and temporal resolution for the study of outer planet satellites within our Solar System. We highlight the infrared spectroscopy of icy moons and temporal changes on geologically active satellites as two particularly valuable avenues of scientific inquiry. While some care must be taken to avoid saturation issues, JWST has observation modes that should provide excellent infrared data for such studies.

### Chondrule Formation via Impact Jetting Triggered by Planetary Accretion

Chondrules are one of the most primitive elements that can serve as a fundamental clue as to the origin of our Solar system. We investigate a formation scenario of chondrules that involves planetesimal collisions and the resultant impact jetting. Planetesimal collisions are the main agent to regulate planetary accretion that corresponds to the formation of terrestrial planets and cores of gas giants. The key component of this scenario is that ejected materials can melt when the impact velocity between colliding planetesimals exceeds about 2.5 km s$^{-1}$. The previous simulations show that the process is efficient enough to reproduce the primordial abundance of chondrules. We examine this scenario carefully by performing semi-analytical calculations that are developed based on the results of direct $N$-body simulations. As found by the previous work, we confirm that planetesimal collisions that occur during planetary accretion can play an important role in forming chondrules. This arises because protoplanet-planetesimal collisions can achieve the impact velocity of about 2.5 km s$^{-1}$ or higher, as protoplanets approach the isolation mass ($M_{p,iso}$). Assuming that the ejected mass is a fraction ($F_{ch}$) of colliding planetesimals' mass, we show that the resultant abundance of chondrules is formulated well by $F_{ch}M_{p,iso}$, as long as the formation of protoplanets is completed within a given disk lifetime. We perform a parameter study and examine how the abundance of chondrules and their formation timing change. We find that the impact jetting scenario generally works reasonably well for a certain range of parameters, while more dedicated work would be needed to include other physical processes that are neglected in this work and to examine their effects on chondrule formation.

### The Outer Solar System Origins Survey: I. Design and First-Quarter Discoveries

We report 85 trans-Neptunian objects (TNOs) from the first 42 deg$^{2}$ of the Outer Solar System Origins Survey (OSSOS), an ongoing $r$-band survey with the 0.9 deg$^{2}$ field-of-view MegaPrime camera on the 3.6 m Canada-France-Hawaii Telescope. A dense observing cadence and our innovative astrometric technique produced survey-measured orbital elements for these TNOs precise to a fractional semi-major axis uncertainty $<0.1\%$ in two sequential years, instead of the 3-5 years needed with sparser observing strategies. These discoveries are free of ephemeris bias, a first for large Kuiper belt surveys. The survey's simulator provides full characterization, including calibrated detection efficiency functions, for debiasing the discovery sample. We confirm the existence of a cold "kernel" of objects within the main cold classical Kuiper belt, and imply the existence of an extension of the "stirred" cold classical Kuiper belt to at least several AU beyond the 2:1 mean motion resonance with Neptune. The population model of Petit et al. (2011) remains a plausible interpretation of the Kuiper belt. The full survey will provide an exquisitely characterized sample of important resonant TNO populations, ideal for testing models of giant planet migration during the early history of the Solar System.

### The Galactic One-Way Shapiro Delay to PSR B1937+21

The time delay experienced by a light ray as it passes through a changing gravitational potential by a non-zero mass distribution along the line of sight is usually referred to as Shapiro delay. Shapiro delay has been extensively measured in the Solar system and in binary pulsars, enabling stringent tests of general relativity as well as measurement of neutron star masses . However, Shapiro delay is ubiquitous and experienced by all astrophysical messengers on their way from the source to the Earth. We calculate the "one-way" static Shapiro delay for the first discovered millisecond pulsar PSR~B1937+21, by including the contributions from both the dark matter and baryonic matter between this pulsar and the Earth. We find a value of approximately 5 days (of which 4.74 days is from the dark matter and 0.22 days from the baryonic matter). We also calculate the modulation of Shapiro delay from the motion of a single dark matter halo, and also evaluate the cumulative effects of the motion of matter distribution on the change in pulsar's period and its derivative. The time-dependent effects are too small to be detected with the current timing noise observed for this pulsar. Finally, we would like to emphasize that although the one-way Shapiro delay is mostly of academic interest for electromagnetic astronomy, its ubiquity should not be forgotten in the era of multi-messenger astronomy.

### Rotation periods and astrometric motions of the Luhman 16AB brown dwarfs by high-resolution lucky-imaging monitoring

Context. Photometric monitoring of the variability of brown dwarfs can provide useful information about the structure of clouds in their cold atmospheres. The brown-dwarf binary system Luhman 16AB is an interesting target for such a study, as its components stand at the L/T transition and show high levels of variability. Luhman 16AB is also the third closest system to the Solar system, allowing precise astrometric investigations with ground-based facilities. Aims. The aim of the work is to estimate the rotation period and study the astrometric motion of both components. Methods. We have monitored Luhman 16AB over a period of two years with the lucky-imaging camera mounted on the Danish 1.54m telescope at La Silla, through a special i+z long-pass filter, which allowed us to clearly resolve the two brown dwarfs into single objects. An intense monitoring of the target was also performed over 16 nights, in which we observed a peak-to-peak variability of 0.20 \pm 0.02 mag and 0.34 \pm 0.02 mag for Luhman 16A and 16B, respectively. Results. We used the 16-night time-series data to estimate the rotation period of the two components. We found that Luhman 16B rotates with a period of 5.1 \pm 0.1 hr, in very good agreement with previous measurements. For Luhman 16A, we report that it rotates slower than its companion and, even though we were not able to get a robust determination, our data indicate a rotation period of roughly 8 hr. This implies that the rotation axes of the two components are well aligned and suggests a scenario in which the two objects underwent the same accretion process. The 2-year complete dataset was used to study the astrometric motion of Luhman 16AB. We predict a motion of the system that is not consistent with a previous estimate based on two months of monitoring, but cannot confirm or refute the presence of additional planetary-mass bodies in the system.

### CMB Anomalies after Planck

Several unexpected features have been observed in the microwave sky at large angular scales, both by WMAP an by Planck. Among those features is a lack of both variance and correlation on the largest angular scales, alignment of the lowest multipole moments with one another and with the motion and geometry of the Solar System, a hemispherical power asymmetry or dipolar power modulation, a preference for odd parity modes and an unexpectedly large cold spot in the Southern hemisphere. The individual p-values of the significance of these features are in the per mille to per cent level, when compared to the expectations of the best-fit inflationary $\Lambda$CDM model. Some pairs of those features are demonstrably uncorrelated, increasing their combined statistical significance and indicating a significant detection of CMB features at angular scales larger than a few degrees on top of the standard model. Despite numerous detailed investigations, we still lack a clear understanding of these large-scale features, which seem to imply a violation of statistical isotropy and scale invariance of inflationary perturbations. In this contribution we present a critical analysis of our current understanding and discuss several ideas of how to make further progress.

### Methane clathrates in the Solar System

We review the reservoirs of methane clathrates that may exist in the different bodies of the Solar System. Methane was formed in the interstellar medium prior to having been embedded in the protosolar nebula gas phase. This molecule was subsequently trapped in clathrates that formed from crystalline water ice during the cooling of the disk and incorporated in this form in the building blocks of comets, icy bodies, and giant planets. Methane clathrates may play an important role in the evolution of planetary atmospheres. On Earth, the production of methane in clathrates is essentially biological, and these compounds are mostly found in permafrost regions or in the sediments of continental shelves. On Mars, methane would more likely derive from hydrothermal reactions with olivine-rich material. If they do exist, martian methane clathrates would be stable only at depth in the cryosphere and sporadically release some methane into the atmosphere via mechanisms that remain to be determined.

### New and updated convex shape models of asteroids based on optical data from a large collaboration network

Asteroid modeling efforts in the last decade resulted in a comprehensive dataset of almost 400 convex shape models and their rotation states. This amount already provided a deep insight into physical properties of main-belt asteroids or large collisional families. We aim to increase the number of asteroid shape models and rotation states. Such results are an important input for various further studies such as analysis of asteroid physical properties in different populations, including smaller collisional families, thermophysical modeling, and scaling shape models by disk-resolved images, or stellar occultation data. This provides, in combination with known masses, bulk density estimates, but constrains also theoretical collisional and evolutional models of the Solar System. We use all available disk-integrated optical data (i.e., classical dense-in-time photometry obtained from public databases and through a large collaboration network as well as sparse-in-time individual measurements from a few sky surveys) as an input for the convex inversion method, and derive 3D shape models of asteroids, together with their rotation periods and orientations of rotation axes. The key ingredient is the support of more that one hundred observers who submit their optical data to publicly available databases. We present updated shape models for 36 asteroids, for which mass estimates are currently available in the literature or their masses will be most likely determined from their gravitational influence on smaller bodies, which orbital deflection will be observed by the ESA Gaia astrometric mission. This was achieved by using additional optical data from recent apparitions for the shape optimization. Moreover, we also present new shape model determinations for 250 asteroids, including 13 Hungarias and 3 near-Earth asteroids.

### A disintegrating minor planet transiting a white dwarf

White dwarfs are the end state of most stars, including the Sun, after they exhaust their nuclear fuel. Between 1/4 and 1/2 of white dwarfs have elements heavier than helium in their atmospheres, even though these elements should rapidly settle into the stellar interiors unless they are occasionally replenished. The abundance ratios of heavy elements in white dwarf atmospheres are similar to rocky bodies in the Solar system. This and the existence of warm dusty debris disks around about 4% of white dwarfs suggest that rocky debris from white dwarf progenitors' planetary systems occasionally pollute the stars' atmospheres. The total accreted mass can be comparable to that of large asteroids in the solar system. However, the process of disrupting planetary material has not yet been observed. Here, we report observations of a white dwarf being transited by at least one and likely multiple disintegrating planetesimals with periods ranging from 4.5 hours to 4.9 hours. The strongest transit signals occur every 4.5 hours and exhibit varying depths up to 40% and asymmetric profiles, indicative of a small object with a cometary tail of dusty effluent material. The star hosts a dusty debris disk and the star's spectrum shows prominent lines from heavy elements like magnesium, aluminium, silicon, calcium, iron, and nickel. This system provides evidence that heavy element pollution of white dwarfs can originate from disrupted rocky bodies such as asteroids and minor planets.

### Detection and Characterization of Micrometeoroids with LISA Pathfinder

The Solar System contains a population of dust and small particles originating from asteroids, comets, and other bodies. These particles have been studied using a number of techniques ranging from in-situ satellite detectors to analysis of lunar microcraters to ground-based observations of zodiacal light. In this paper, we describe an approach for using the LISA Pathfinder (LPF) mission as an instrument to detect and characterize the dynamics of dust particles in the vicinity of Earth-Sun L1. Launching in late 2015, LPF is a dedicated technology demonstrator mission that will validate several key technologies for a future space-based gravitational-wave observatory. The primary science instrument aboard LPF is a precision accelerometer which we show will be capable of sensing discrete momentum impulses as small as $4\times 10^{-8}\,\textrm{N}\cdot\textrm{s}$. We then estimate the rate of such impulses resulting from impacts of micrometeoroids based on standard models of the micrometeoroid environment in the inner solar system. We find that LPF may detect dozens to hundreds of individual events corresponding to impacts of particles with masses $> 10^{-9}\,$g during LPF's roughly six-month science operations phase in a $5\times 10^5\,\textrm{km}$ by $8\times 10^5\,\textrm{km}$ Lissajous orbit around L1. In addition, we estimate the ability of LPF to characterize individual impacts by measuring quantities such as total momentum transferred, direction of impact, and location of impact on the spacecraft. Information on flux and direction provided by LPF may provide insight as to the nature and origin of the individual impact and help constrain models of the interplanetary dust complex in general. Additionally, this direct in-situ measurement of micrometeoroid impacts will be valuable to designers of future spacecraft targeting the environment around L1.

### Detection and Characterization of Micrometeoroids with LISA Pathfinder [Replacement]

The Solar System contains a population of dust and small particles originating from asteroids, comets, and other bodies. These particles have been studied using a number of techniques ranging from in-situ satellite detectors to analysis of lunar microcraters to ground-based observations of zodiacal light. In this paper, we describe an approach for using the LISA Pathfinder (LPF) mission as an instrument to detect and characterize the dynamics of dust particles in the vicinity of Earth-Sun L1. Launching in late 2015, LPF is a dedicated technology demonstrator mission that will validate several key technologies for a future space-based gravitational-wave observatory. The primary science instrument aboard LPF is a precision accelerometer which we show will be capable of sensing discrete momentum impulses as small as $4\times 10^{-8}\,\textrm{N}\cdot\textrm{s}$. We then estimate the rate of such impulses resulting from impacts of micrometeoroids based on standard models of the micrometeoroid environment in the inner solar system. We find that LPF may detect dozens to hundreds of individual events corresponding to impacts of particles with masses $> 10^{-9}\,$g during LPF's roughly six-month science operations phase in a $5\times 10^5\,\textrm{km}$ by $8\times 10^5\,\textrm{km}$ Lissajous orbit around L1. In addition, we estimate the ability of LPF to characterize individual impacts by measuring quantities such as total momentum transferred, direction of impact, and location of impact on the spacecraft. Information on flux and direction provided by LPF may provide insight as to the nature and origin of the individual impact and help constrain models of the interplanetary dust complex in general. Additionally, this direct in-situ measurement of micrometeoroid impacts will be valuable to designers of future spacecraft targeting the environment around L1.

### Detection and Characterization of Micrometeoroids with LISA Pathfinder [Replacement]

The Solar System contains a population of dust and small particles originating from asteroids, comets, and other bodies. These particles have been studied using a number of techniques ranging from in-situ satellite detectors to analysis of lunar microcraters to ground-based observations of zodiacal light. In this paper, we describe an approach for using the LISA Pathfinder (LPF) mission as an instrument to detect and characterize the dynamics of dust particles in the vicinity of Earth-Sun L1. Launching in late 2015, LPF is a dedicated technology demonstrator mission that will validate several key technologies for a future space-based gravitational-wave observatory. The primary science instrument aboard LPF is a precision accelerometer which we show will be capable of sensing discrete momentum impulses as small as $4\times 10^{-8}\,\textrm{N}\cdot\textrm{s}$. We then estimate the rate of such impulses resulting from impacts of micrometeoroids based on standard models of the micrometeoroid environment in the inner solar system. We find that LPF may detect dozens to hundreds of individual events corresponding to impacts of particles with masses $> 10^{-9}\,$g during LPF's roughly six-month science operations phase in a $5\times 10^5\,\textrm{km}$ by $8\times 10^5\,\textrm{km}$ Lissajous orbit around L1. In addition, we estimate the ability of LPF to characterize individual impacts by measuring quantities such as total momentum transferred, direction of impact, and location of impact on the spacecraft. Information on flux and direction provided by LPF may provide insight as to the nature and origin of the individual impact and help constrain models of the interplanetary dust complex in general. Additionally, this direct in-situ measurement of micrometeoroid impacts will be valuable to designers of future spacecraft targeting the environment around L1.

### 16 Years of Ulysses Interstellar Dust Measurements in the Solar System: I. Mass Distribution and Gas-to-Dust Mass Ratio

In the early 1990s, contemporary interstellar dust (ISD) penetrating deep into the heliosphere was identified with the in-situ dust detector on board the Ulysses spacecraft. Between 1992 and the end of 2007 Ulysses monitored the ISD stream. The interstellar grains act as tracers of the physical conditions in the local interstellar medium surrounding our solar system. Earlier analyses of the Ulysses ISD data measured between 1992 and 1998 implied the existence of 'big' ISD grains [up to 10^-13kg]. The derived gas-to-dust-mass ratio was smaller than the one derived from astronomical observations, implying a concentration of ISD in the very local interstellar medium. We analyse the entire data set from 16 yr of Ulysses ISD measurements in interplanetary space. This paper concentrates on the overall mass distribution of ISD. An accompanying paper investigates time-variable phenomena in the Ulysses ISD data, and in a third paper we present the results from dynamical modelling of the ISD flow applied to Ulysses. We use the latest values for the interstellar hydrogen and helium densities, the interstellar helium flow speed of v_ISM,inf=23.2km/s, and the ratio of radiation pressure to gravity, beta, calculated for astronomical silicates. We find a gas-to-dust-mass ratio in the local interstellar cloud of R_g/d=193^+85_-57, and a dust density of 2.1+/-0.6x10^-24kg/m^3. For a higher inflow speed of 26km/s, the gas-to-dust-mass ratio is 20% higher, and, accordingly, the dust density is lower by the same amount. The gas-to-dust mass ratio derived from our new analysis is compatible with the value most recently determined from astronomical observations. We confirm earlier results that the very local interstellar medium contains 'big' (i.e. 1 um-sized) ISD grains. We find a dust density in the local interstellar medium that is a factor of three lower than values implied by earlier analyses.

### Cometary Science with the James Webb Space Telescope

The James Webb Space Telescope (JWST), as the largest space-based astronomical observatory with near- and mid-infrared instrumentation, will elucidate many mysterious aspects of comets. We summarize four cometary science themes especially suited for this telescope and its instrumentation: the drivers of cometary activity, comet nucleus heterogeneity, water ice in comae and on surfaces, and activity in faint comets and main-belt asteroids. With JWST, we can expect the most distant detections of gas, especially CO2, in what we now consider to be only moderately bright comets. For nearby comets, coma dust properties can be studied with their driving gases, measured simultaneously with the same instrument or contemporaneously with another. Studies of water ice and gas in the distant Solar System will help us test our understanding of cometary interiors and coma evolution. The question of cometary activity in main-belt comets will be further explored with the possibility of a direct detection of coma gas. We explore the technical approaches to these science cases and provide simple tools for estimating comet dust and gas brightness. Finally, we consider the effects of the observatory's non-sidereal tracking limits, and provide a list of potential comet targets during the first 5 years of the mission.

### The James Webb Space Telescopes plan for operations and instrument capabilities for observations in the Solar System

The James Webb Space Telescope (JWST) is optimized for observations in the near and mid infrared and will provide essential observations for targets that cannot be conducted from the ground or other missions during its lifetime. The state of the art science instruments, along with the telescopes moving target tracking, will enable the infrared study, with unprecedented detail, for nearly every object, Mars and beyond, in the solar system. The goals of this special issue are to stimulate discussion and encourage participation in JWST planning among members of the planetary science community. Key science goals for various targets, observing for JWST, and highlights for the complementary nature with other missions and observatories are described in this paper.

### Growing the terrestrial planets from the gradual accumulation of sub-meter sized objects

Building the terrestrial planets has been a challenge for planet formation models. In particular, classical theories have been unable to reproduce the small mass of Mars and instead predict that a planet near 1.5 AU should roughly be the same mass as the Earth. Recently, a new model called Viscous Stirred Pebble Accretion (VSPA) has been developed that can explain the formation of the gas giants. This model envisions that the cores of the giant planets formed from 100 to 1000 km bodies that directly accreted a population of pebbles --- sub-meter sized objects that slowly grew in the protoplanetary disk. Here we apply this model to the terrestrial planet region and find that it can reproduce the basic structure of the inner Solar System, including a small Mars and a low-mass asteroid belt. Our models show that for an initial population of planetesimals with sizes similar to those of the main belt asteroids, VSPA becomes inefficient beyond $\sim\!$1.5 AU. As a result, Mars's growth is stunted and nothing large in the asteroid belt can accumulate.

### Stealing the Gas: Giant Impacts and the Large Diversity in Exoplanet Densities

Although current sensitivity limits are such that true Solar System analogs remain challenging to detect, numerous planetary systems have been discovered that are very different from our own Solar System. The majority of systems harbor a new class of planets, bodies that are typically several times more massive than the Earth but that orbit their host stars well inside the orbit of Mercury. These planets frequently show evidence for large Hydrogen and Helium envelopes containing several percent of the planet's mass and display a large diversity in mean densities. Here we show that this wide range can be achieved by one or two late giant impacts, which are frequently needed to achieve long-term orbital stability in multiple planet systems once the gas disk has disappeared. We demonstrate using hydrodynamical simulations that a single collision between similarly sized exoplanets can easily reduce the envelope-to-core-mass ratio by a factor of two and show that this leads to a corresponding increase in the observed mean density by factors of 2-3. In addition we investigate how envelope-mass-loss depends on envelope mass, planet radius, semi-major axis, and the mass distribution inside the envelope. We propose that a small number of giant impacts may be responsible for the large observed spread in mean densities, especially for multiple-planet systems containing planets with very different densities and which have not been significantly sculpted by photo evaporation.

### A New Analysis of the Exoplanet Hosting System HD 6434

The current goal of exoplanetary science is not only focused on detecting but characterizing planetary systems in hopes of understanding how they formed, evolved, and relate to the Solar System. The Transit Ephemeris Refinement and Monitoring Survey (TERMS) combines both radial velocity (RV) and photometric data in order to achieve unprecedented ground-based precision in the fundamental properties of nearby, bright, exoplanet-hosting systems. Here we discuss HD 6434 and its planet, HD 6434b, which has a M_p*sin(i) = 0.44 M_J mass and orbits every 22.0170 days with an eccentricity of 0.146. We have combined previously published RV data with new measurements to derive a predicted transit duration of ~6 hrs, or 0.25 days, and a transit probability of 4%. Additionally, we have photometrically observed the planetary system using both the 0.9m and 1.0m telescopes at the Cerro Tololo Inter-American Observatory, covering 75.4% of the predicted transit window. We reduced the data using the automated TERMS Photometry Pipeline, developed to ensure consistent and accurate results. We determine a dispositive null result for the transit of HD 6434b, excluding the full transit to a depth of 0.9% and grazing transit due to impact parameter limitations to a depth of 1.6%

### Combined Solar System and rotation curve constraints on MOND

The Modified Newtonian Dynamics (MOND) paradigm generically predicts that the external gravitational field in which a system is embedded can produce effects on its internal dynamics. In this communication, we first show that this External Field Effect can significantly improve some galactic rotation curves fits by decreasing the predicted velocities of the external part of the rotation curves. In modified gravity versions of MOND, this External Field Effect also appears in the Solar System and leads to a very good way to constrain the transition function of the theory. A combined analysis of the galactic rotation curves and Solar System constraints (provided by the Cassini spacecraft) rules out several classes of popular MOND transition functions, but leaves others viable. Moreover, we show that LISA Pathfinder will not be able to improve the current constraints on these still viable transition functions.

### Forming the Cold Classical Kuiper Belt in a light Disk

Large Kuiper Belt Objects are conventionally thought to have formed out of a massive planetesimal belt that is a few thousand times its current mass. Such a picture, however, is incompatible with multiple lines of evidence. Here, we present a new model for the conglomeration of Cold Classical Kuiper belt objects, out of a solid belt only a few times its current mass, or a few percent of the solid density in a Minimum Mass Solar Nebula. This is made possible by depositing most of the primordial mass in grains of size centimetre or smaller. These grains collide frequently and maintain a dynamically cold belt out of which large bodies grow efficiently: an order-unity fraction of the solid mass can be converted into large bodies, in contrast to the ~0.1% efficiency in conventional models. Such a light belt may represent the true outer edge of the Solar system, and it may have effectively halted the outward migration of Neptune. In addition to the high efficiency, our model can also produce a mass spectrum that peaks at an intermediate size, similar to the observed Cold Classicals, if one includes the effect of cratering collisions. In particular, the observed power-law break observed at ~30 km for Cold Classicals, one that has been interpreted as a result of collisional erosion, may be primordial in origin.

### A new inclination instability reshapes Keplerian disks into cones: application to the outer Solar System

Disks of bodies orbiting a much more massive central object are extremely common in astrophysics. When the orbits comprising such disks are eccentric, we show they are susceptible to a new dynamical instability. Gravitational forces between bodies in the disk drive exponential growth of their orbital inclinations and clustering in their angles of pericenter, expanding an initially thin disk into a conical shape by giving each orbit an identical 'tilt' with respect to the disk plane. This new instability dynamically produces the unusual distribution of orbits observed for minor planets beyond Neptune, suggesting that the instability has shaped the outer Solar System. It also implies a large initial disk mass (1-10 Earth masses) of scattered bodies at hundreds of AU; we predict increasing numbers of detections of minor planets clustered in their angles of pericenter with high inclinations.

### Light propagation in the gravitational field of N arbitrarily moving bodies in 1PN approximation for high-precision astrometry

The light-trajectory in the gravitational field of N extended bodies in arbitrary motion is determined in the first post-Newtonian approximation. According to the theory of reference systems, the gravitational fields of these massive bodies are expressed in terms of their intrinsic multipoles, allowing for arbitrary shape and inner structure of these bodies. The results of this investigation aim towards a consistent general-relativistic theory of light propagation in the Solar system for high-precision astrometry at sub-micro-arcsecond level of accuracy.

### Tilting Saturn without tilting Jupiter: Constraints on giant planet migration

The migration and encounter histories of the giant planets in our Solar System can be constrained by the obliquities of Jupiter and Saturn. We have performed secular simulations with imposed migration and N-body simulations with planetesimals to study the expected obliquity distribution of migrating planets with initial conditions resembling those of the smooth migration model, the resonant Nice model and two models with five giant planets initially in resonance (one compact and one loose configuration). For smooth migration, the secular spin-orbit resonance mechanism can tilt Saturn's spin axis to the current obliquity if the product of the migration time scale and the orbital inclinations is sufficiently large (exceeding 30 Myr deg). For the resonant Nice model with imposed migration, it is difficult to reproduce today's obliquity values, because the compactness of the initial system raises the frequency that tilts Saturn above the spin precession frequency of Jupiter, causing a Jupiter spin-orbit resonance crossing. Migration time scales sufficiently long to tilt Saturn generally suffice to tilt Jupiter more than is observed. The full N-body simulations tell a somewhat different story, with Jupiter generally being tilted as often as Saturn, but on average having a higher obliquity. The main obstacle is the final orbital spacing of the giant planets, coupled with the tail of Neptune's migration. The resonant Nice case is barely able to simultaneously reproduce the {orbital and spin} properties of the giant planets, with a probability ~0.15%. The loose five planet model is unable to match all our constraints (probability <0.08%). The compact five planet model has the highest chance of matching the orbital and obliquity constraints simultaneously (probability ~0.3%).

### Surface ages of mid-size Saturnian satellites

The observations of the surfaces of the mid sized Saturnian satellites made by Cassini Huygens mission have shown a variety of features that allows study of the processes that took place and are taking place on those worlds. Research of the Saturnian satellite surfaces has clear implications for Saturn history and surroundings. In a recent paper, the production of craters on the mid sized Saturnian satellites by Centaur objects was calculated considering the current Solar System. We have compared our results with crater counts from Cassini images and we have noted that the number of observed small craters is less than our calculated number. In this paper we estimate the age of the surface for each observed terrain on each mid sized satellite of Saturn. We have noticed that since there are less observed small craters than calculated (except on Iapetus), this results in younger ages. This could be the result of efficient endogenous or exogenous process(es) for erasing small craters and or crater saturation at those sizes. The size limit from which the observed number of smaller craters is less than the calculated is different for each satellite, possibly indicating processes that are unique to each, but other potential common explanations would be crater saturation and or deposition of E ring particles. These processes are also suggested by the findings that the smaller craters are being preferentially removed, and the erasure process is gradual. On Enceladus, only mid and high latitude plains have remnants of old terrains; the other regions could be young; the regions near the South Polar Terrain could be as young as 50 Myr old. On the contrary for Iapetus, all the surface is old and it notably registers a primordial source of craters. As the crater size is decreased, it would be perceived to approach saturation until D less than 2 km craters, where saturation is complete.

### The Formation of Striae within Cometary Dust Tails by a Sublimation-Driven YORP-like Effect

Sublimating gas molecules scatter off of the surface of an icy body in the same manner as photons. This means that for every photon-driven body force, there should be a sublimation-driven analogue that affects icy bodies. Thermal photons emitted from the surfaces of asymmetrically shaped bodies in the Solar System generate net torques that change the spin rates of these bodies over time. The long-term averaging of this torque is called the YORP effect. Here we propose a sublimation-driven analogue to the YORP effect (SYORP), in which sublimating gas molecules emitted from the surfaces of icy bodies also generate net torques on the bodies. However, sublimating molecules carry momentum away from the body at a rate ~10^4-10^5 greater than thermal photons, resulting in much greater body torques. While previous studies of sublimative torques focused on emissions from highly localized sources on the surfaces of Jupiter Family Comet nuclei, SYORP applies to non-localized emissions across the entire body, which likely dominates sublimation-drive torques on small icy chunks and Dynamically Young Comets, and can therefore be applied without high-resolution spacecraft observations of their surfaces. Instead, we repurpose the equations of the YORP effect to account for sublimation-driven torques. We show how an SYORP-driven mechanism best matches observations of the Sun-oriented lineaments (striae) of comet tails, whose formation mechanism has remained enigmatic for decades. The SYORP effect explains why striae are observed between near-perihelion and ~1 AU from the Sun for comets with perihelia less than 0.6 AU, and solves longstanding problems with moving enough material into the cometary tail to form visible striae. We show that SYORP can form striae that match those of Comet West, and produce a power-law size frequency distribution of their parent chunks with an index of -1.4 (-1.1- 2).

### Detectability of quasi-circular co-orbital planets. Application to the radial velocity technique

Several celestial bodies in co-orbital configurations exist in the solar system. However, co-orbital exoplanets have not yet been discovered. This lack may result from a degeneracy between the signal induced by co-orbital planets and other orbital configurations. Here we determine a criterion for the detectability of quasi-circular co-orbital planets and develop a demodulation method to bring out their signature from the observational data. We show that the precision required to identify a pair of co-orbital planets depends only on the libration amplitude and on the planet's mass ratio. We apply our method to synthetic radial velocity data, and show that for tadpole orbits we are able to determine the inclination of the system to the line of sight. Our method is also valid for planets detected through the transit and astrometry techniques.

### Maps and Masses of Transiting Exoplanets: Towards New Insights into Atmospheric and Interior Properties of Planets

With over 1800 planets discovered outside of the Solar System in the past two decades, the field of exoplanetology has broadened our perspective on planetary systems. Research priorities are now moving from planet detection to planet characterization. In this context, transiting exoplanets are of special interest due to the wealth of data made available by their orbital configuration. Here, I introduce two methods to gain new insights into the atmospheric and interior properties of exoplanets. The first method aims to map an exoplanet's atmosphere based on the scanning obtained while it is occulted by its host star. I introduce the basics of eclipse mapping, its caveats, and a framework to mitigate their effects via global analyses including transits, phase curves, and radial velocity measurements. I use this method to create the first 2D map and the first cloud map of an exoplanet for the hot-Jupiters HD189733b and Kepler-7b, respectively. Ultimately temperature, composition, and circulation patterns could be constrained in 3D, a significant asset for informing atmospheric models. The second method, MassSpec, aims to determine transiting planet masses and atmospheric properties solely from transmission spectra. Determination of an exoplanet's mass is key to understanding its basic properties, including its potential for supporting life. To date, mass constraints for exoplanets are mainly based on radial velocity measurements, which are not suited for planets with low masses, large semi-major axes, or those orbiting faint or active stars. I demonstrate that a planet's mass has to be accounted for by atmospheric retrieval methods to avoid biases and that JWST could determine the mass and atmospheric properties of half a dozen Earth-sized planets in their host's habitable zones over its lifetime, which could lead to the first identification of a habitable exoplanet.

### Stimulated Radiative Molecular Association in the Early Solar System. II. Orbital Radii of the Planets and Other Satellites of the Sun

In a previous investigation, the orbital radii of regular satellites of Uranus, Jupiter, Neptune, and Saturn are shown to be directly related to photon energies in the spectra of atomic and molecular hydrogen. To explain these observations a model was developed involving stimulated radiative molecular association (SRMA) reactions among photons and atoms in the protosatellite disks of the planets. In the present investigation, the previously developed model is applied to the planets and important satellites of the Sun. A key component of the model involves resonance associated with SRMA. Through this resonance, thermal energy is extracted from the protosun's protoplanetary disk at specific distances from the protosun wherever there is a match between the local thermal energy of the disk and the energy of photons impinging on the disk. Orbital radii of the planets and satellites are related to photon energies ($E_P$ values) in the spectrum of atomic hydrogen. An expression determined previously is used to relate $E_P$ values to temperatures in the disk. Results indicate the surface temperature of the protosun at the time when the evolution of the planets begins is higher than the surface temperature of a typical T Tauri star. The present investigation offers an explanation for the existence of the asteroid and classical Kuiper belts and predicts that a primordial belt once existed in the vicinity of Neptune. It also indicates that Uranus is formed from two protoplanets and is thus consistent with the theory that the large tilt of Uranus's axis of rotation was created by the collision of two bodies.

### Testing long-distance modifications of gravity to 100 astronomical units [Replacement]

There are very few direct experimental tests of the inverse square law of gravity at distances comparable to the scale of the Solar System and beyond. Here we describe a possible space mission optimized to test the inverse square law at a scale of up to 100 AU. For example, sensitivity to a Yukawa correction with a strength of $10^{-7}$ times gravity and length scale of 100 AU is within reach, improving the current state of the art by over two orders of magnitude. This experiment would extend our understanding of gravity to the largest scale that can be reached with a direct probe using known technology. This would provide a powerful test of long-distance modifications of gravity including many theories motivated by dark matter or dark energy.

### Testing long-distance modifications of gravity to 100 astronomical units [Cross-Listing]

There are very few direct experimental tests of the inverse square law of gravity at distances comparable to the scale of the Solar System and beyond. Here we describe a possible space mission optimized to test the inverse square law at a scale of up to 100 AU. For example, sensitivity to a Yukawa correction with a strength of $10^{-7}$ times gravity and length scale of 100 AU is within reach, improving the current state of the art by over two orders of magnitude. This experiment would extend our understanding of gravity to the largest scale that can be reached with a direct probe using known technology. This would provide a powerful test of long-distance modifications of gravity including many theories motivated by dark matter or dark energy.

### Testing long-distance modifications of gravity to 100 astronomical units [Replacement]

There are very few direct experimental tests of the inverse square law of gravity at distances comparable to the scale of the Solar System and beyond. Here we describe a possible space mission optimized to test the inverse square law at a scale of up to 100 AU. For example, sensitivity to a Yukawa correction with a strength of $10^{-7}$ times gravity and length scale of 100 AU is within reach, improving the current state of the art by over two orders of magnitude. This experiment would extend our understanding of gravity to the largest scale that can be reached with a direct probe using known technology. This would provide a powerful test of long-distance modifications of gravity including many theories motivated by dark matter or dark energy.

### Testing long-distance modifications of gravity to 100 astronomical units [Cross-Listing]

There are very few direct experimental tests of the inverse square law of gravity at distances comparable to the scale of the Solar System and beyond. Here we describe a possible space mission optimized to test the inverse square law at a scale of up to 100 AU. For example, sensitivity to a Yukawa correction with a strength of $10^{-7}$ times gravity and length scale of 100 AU is within reach, improving the current state of the art by over two orders of magnitude. This experiment would extend our understanding of gravity to the largest scale that can be reached with a direct probe using known technology. This would provide a powerful test of long-distance modifications of gravity including many theories motivated by dark matter or dark energy.

### Testing long-distance modifications of gravity to 100 astronomical units [Replacement]

There are very few direct experimental tests of the inverse square law of gravity at distances comparable to the scale of the Solar System and beyond. Here we describe a possible space mission optimized to test the inverse square law at a scale of up to 100 AU. For example, sensitivity to a Yukawa correction with a strength of $10^{-7}$ times gravity and length scale of 100 AU is within reach, improving the current state of the art by over two orders of magnitude. This experiment would extend our understanding of gravity to the largest scale that can be reached with a direct probe using known technology. This would provide a powerful test of long-distance modifications of gravity including many theories motivated by dark matter or dark energy.

### Testing long-distance modifications of gravity to 100 astronomical units [Cross-Listing]

There are very few direct experimental tests of the inverse square law of gravity at distances comparable to the scale of the Solar System and beyond. Here we describe a possible space mission optimized to test the inverse square law at a scale of up to 100 AU. For example, sensitivity to a Yukawa correction with a strength of $10^{-7}$ times gravity and length scale of 100 AU is within reach, improving the current state of the art by over two orders of magnitude. This experiment would extend our understanding of gravity to the largest scale that can be reached with a direct probe using known technology. This would provide a powerful test of long-distance modifications of gravity including many theories motivated by dark matter or dark energy.

### Testing long-distance modifications of gravity to 100 astronomical units [Replacement]

There are very few direct experimental tests of the inverse square law of gravity at distances comparable to the scale of the Solar System and beyond. Here we describe a possible space mission optimized to test the inverse square law at a scale of up to 100 AU. For example, sensitivity to a Yukawa correction with a strength of $10^{-7}$ times gravity and length scale of 100 AU is within reach, improving the current state of the art by over two orders of magnitude. This experiment would extend our understanding of gravity to the largest scale that can be reached with a direct probe using known technology. This would provide a powerful test of long-distance modifications of gravity including many theories motivated by dark matter or dark energy.

### Testing long-distance modifications of gravity to 100 astronomical units [Cross-Listing]

There are very few direct experimental tests of the inverse square law of gravity at distances comparable to the scale of the Solar System and beyond. Here we describe a possible space mission optimized to test the inverse square law at a scale of up to 100 AU. For example, sensitivity to a Yukawa correction with a strength of $10^{-7}$ times gravity and length scale of 100 AU is within reach, improving the current state of the art by over two orders of magnitude. This experiment would extend our understanding of gravity to the largest scale that can be reached with a direct probe using known technology. This would provide a powerful test of long-distance modifications of gravity including many theories motivated by dark matter or dark energy.

### Testing long-distance modifications of gravity to 100 astronomical units [Replacement]

There are very few direct experimental tests of the inverse square law of gravity at distances comparable to the scale of the Solar System and beyond. Here we describe a possible space mission optimized to test the inverse square law at a scale of up to 100 AU. For example, sensitivity to a Yukawa correction with a strength of $10^{-7}$ times gravity and length scale of 100 AU is within reach, improving the current state of the art by over two orders of magnitude. This experiment would extend our understanding of gravity to the largest scale that can be reached with a direct probe using known technology. This would provide a powerful test of long-distance modifications of gravity including many theories motivated by dark matter or dark energy.

### Testing long-distance modifications of gravity to 100 astronomical units [Replacement]

There are very few direct experimental tests of the inverse square law of gravity at distances comparable to the scale of the Solar System and beyond. Here we describe a possible space mission optimized to test the inverse square law at a scale of up to 100 AU. For example, sensitivity to a Yukawa correction with a strength of $10^{-7}$ times gravity and length scale of 100 AU is within reach, improving the current state of the art by over two orders of magnitude. This experiment would extend our understanding of gravity to the largest scale that can be reached with a direct probe using known technology. This would provide a powerful test of long-distance modifications of gravity including many theories motivated by dark matter or dark energy.

### Testing long-distance modifications of gravity to 100 astronomical units [Replacement]

There are very few direct experimental tests of the inverse square law of gravity at distances comparable to the scale of the Solar System and beyond. Here we describe a possible space mission optimized to test the inverse square law at a scale of up to 100 AU. For example, sensitivity to a Yukawa correction with a strength of $10^{-7}$ times gravity and length scale of 100 AU is within reach, improving the current state of the art by over two orders of magnitude. This experiment would extend our understanding of gravity to the largest scale that can be reached with a direct probe using known technology. This would provide a powerful test of long-distance modifications of gravity including many theories motivated by dark matter or dark energy.

### Testing long-distance modifications of gravity to 100 astronomical units [Replacement]

There are very few direct experimental tests of the inverse square law of gravity at distances comparable to the scale of the Solar System and beyond. Here we describe a possible space mission optimized to test the inverse square law at a scale of up to 100 AU. For example, sensitivity to a Yukawa correction with a strength of $10^{-7}$ times gravity and length scale of 100 AU is within reach, improving the current state of the art by over two orders of magnitude. This experiment would extend our understanding of gravity to the largest scale that can be reached with a direct probe using known technology. This would provide a powerful test of long-distance modifications of gravity including many theories motivated by dark matter or dark energy.

### Highly stable evolution of Earth's future orbit despite chaotic behavior of the Solar System

Due to the chaotic nature of the Solar System, the question of its dynamic long-term stability can only be answered in a statistical sense, e.g. based on numerical ensemble integrations of nearby orbits. Destabilization, including catastrophic encounters and/or collisions involving the Earth, has been suggested to be initiated through a large increase in Mercury's eccentricity (eM), with an estimated probability of ~1%. However, it has recently been shown that the statistics of numerical Solar System integrations are sensitive to the accuracy and type of numerical algorithm. Here I report results from computationally demanding ensemble integrations (N=1,600 with slightly different initial conditions) at unprecedented accuracy based on the full equations of motion of the eight planets and Pluto over 5Gyr, including contributions from general relativity. The standard symplectic algorithm produced spurious results for highly eccentric orbits and during close encounters, which were hence integrated with a suitable Bulirsch-Stoer algorithm, specifically designed for these situations. The present study yields odds for a large increase in Mercury's eccentricity that are less than previous estimates. Strikingly, in two solutions Mercury continued on highly eccentric orbits (after reaching eM values >0.93) for 80-100Myr before colliding with Venus or the Sun. Most importantly, none of the 1,600 solutions led to a close encounter involving the Earth or a destabilization of Earth's orbit in the future. I conclude that Earth's orbit is dynamically highly stable for billions of years, despite the chaotic behavior of the Solar System.

### Detection of N$_2$D$^+$ in a protoplanetary disk

Observations of deuterium fractionation in the solar system, and in interstellar and circumstellar material, are commonly used to constrain the formation environment of volatiles. Toward protoplanetary disks, this approach has been limited by the small number of detected deuterated molecules, i.e. DCO$^+$ and DCN. Based on ALMA Cycle 2 observations toward the disk around the T Tauri star AS 209, we report the first detection of N$_2$D$^+$ (J=3-2) in a protoplanetary disk. These data are used together with previous Submillimeter Array observations of N$_2$H$^+$ (J=3-2) to estimate a disk-averaged D/H ratio of 0.3--0.5, an order of magnitude higher than disk-averaged ratios previously derived for DCN/HCN and DCO$^+$/HCO$^+$ around other young stars. The high fractionation in N$_2$H$^+$ is consistent with model predictions. The presence of abundant N$_2$D$^+$ toward AS 209 also suggests that N$_2$D$^+$ and the N$_2$D$^+$/N$_2$H$^+$ ratio can be developed into effective probes of deuterium chemistry, kinematics, and ionization processes outside the CO snowline of disks.