# Posts Tagged solar system

## Recent Postings from solar system

### Photometry of Centaurs and trans-Neptunian objects: 2060 Chiron (1977 UB), 10199 Chariklo (1997 CU26), 38628 Huya (2000 EB173), 28978 Ixion (2001 KX76), and 90482 Orcus (2004 DW)

Both Centaurs and trans-Neptunian objects (TNOs) are minor bodies found in the outer Solar System. Centaurs are a transient population that moves between the orbits of Jupiter and Neptune, and they probably diffused out of the TNOs. TNOs move mainly beyond Neptune. Some of these objects display episodic cometary behaviour; a few percent of them are known to host binary companions. Here, we study the light-curves of two Centaurs -2060 Chiron (1977 UB) and 10199 Chariklo (1997 CU26)- and three TNOs -38628 Huya (2000 EB173), 28978 Ixion (2001 KX76), and 90482 Orcus (2004 DW)- and the colours of the Centaurs and Huya. Precise, ~1%, R-band absolute CCD photometry of these minor bodies acquired between 2006 and 2011 is presented; the new data are used to investigate the rotation rate of these objects. The colours of the Centaurs and Huya are determined using BVRI photometry. The point spread function of the five minor bodies is analysed, searching for signs of a coma or close companions. Astrometry is also discussed. A periodogram analysis of the light-curves of these objects gives the following rotational periods: 5.5+-0.4 h for Chiron, 7.0+-0.6 h for Chariklo, 4.45+-0.07 h for Huya, 12.4+-0.3 h for Ixion, and 11.9+-0.5 h for Orcus. The colour indices of Chiron are found to be B-V=0.53+-0.05, V-R=0.37+-0.08, and R-I=0.36+-0.15. The values computed for Chariklo are V-R=0.62+-0.07 and R-I=0.61+-0.07. For Huya, we find V-R=0.58+-0.09 and R-I=0.64+-0.20. We find very low levels of cometary activity (if any) and no sign of close or wide binary companions for these minor bodies.

### Constraining the Nordtvedt parameter with the BepiColombo Radioscience experiment

BepiColombo is a joint ESA/JAXA mission to Mercury with challenging objectives regarding geophysics, geodesy and fundamental physics. The Mercury Orbiter Radioscience Experiment (MORE) is one of the on-board experiments, including three different but linked experiments: gravimetry, rotation and relativity. The aim of the relativity experiment is the measurement of the post-Newtonian parameters. Thanks to accurate tracking between Earth and spacecraft, the results are expected to be very precise. However, the outcomes of the experiment strictly depends on our "knowledge" about solar system: ephemerides, number of bodies (planets, satellites and asteroids) and their masses. In this paper we describe a semi-analytic model used to perform a covariance analysis to quantify the effects, on the relativity experiment, due to the uncertainties of solar system bodies parameters. In particular, our attention is focused on the Nordtvedt parameter $\eta$ used to parametrize the strong equivalence principle violation. After our analysis we estimated $\sigma[\eta]\lessapprox 4.5\times 10^{-5}$ which is about 1~order of magnitude larger than the "ideal" case where masses of planets and asteroids have no errors. The current value, obtained from ground based experiments and lunar laser ranging measurements, is $\sigma[\eta]\approx 4.4\times 10^{-4}$. Therefore, we conclude that, even in presence of uncertainties on solar system parameters, the measurement of $\eta$ by MORE can improve the current precision of about 1~order of magnitude.

### Bayes' theorem and early solar short-lived radionuclides: the case for an unexceptional origin for the solar system

The presence of excesses of short-lived radionuclides in the early solar system evidenced in meteorites has been taken as testament to close encounters with exotic nucleosynthetic sources, including supernovae or AGB stars. An analysis of the likelihoods associated with different sources of these extinct nuclides in the early solar system indicates that rather than being exotic, their abundances were typical of star-forming regions like those observed today in the Galaxy. The radiochemistry of the early solar system is therefore unexceptional, being the consequence of extensive averaging of molecular cloud solids.

### A Ninth Planet Would Produce a Distinctly Different Distant Kuiper Belt

The orbital element distribution of trans-Neptunian objects (TNOs) with large pericenters has been suggested to be influenced by the presence of an undetected, large planet at 200 or more AU from the Sun. We perform 4 Gyr N-body simulations with the currently known Solar System planetary architecture, plus a 10 Earth mass planet with similar orbital parameters to those suggested by Batygin and Brown (2016) or Trujillo and Sheppard (2014), and a hundred thousand test particles in an initial planetesimal disk. We find that including a distant superearth-mass ninth planet produces a substantially different orbital distribution for the scattering and detached TNOs, raising the pericenters and inclinations of moderate semimajor axis (50 < a < 500 AU) objects. We test whether this signature is detectable via a simulator with the observational characteristics of four precisely characterized TNO surveys. We find that the qualitatively very distinct Solar System models that include a ninth planet are essentially observationally indistinguishable from an outer Solar System produced solely by the four giant planets. We also find that the mass of the Kuiper Belt's current scattering and detached populations is required be 3-10 times larger in the presence of an additional planet. Wide-field, deep surveys targeting inclined high-pericenter objects will be required to distinguish between these different scenarios.

### Interpreting the librations of a synchronous satellite

Most of the main planetary satellites of our Solar System are expected to be in synchronous rotation, the departures from the strict synchronicity being a signature of the interior. Librations have been measured for the Moon, Phobos, and some satellites of Saturn. I here revisit the theory of the longitudinal librations in considering that part of the interior is not hydrostatic, i.e. has not been shaped by the rotational and tidal deformations, but is fossil. This consideration affects the rotational behavior. For that, I derive the tensor of inertia of the satellite in splitting these two parts, before proposing an analytical solution that I validate with numerical simulations. I apply this new theory on Mimas and Epimetheus, for which librations have been measured from Cassini data. I show that the large measured amplitudes of these bodies can be explained by an excess of triaxiality that would not result from the hydrostatic theory. However, explaining the phase shift observed for Mimas with this theory requires a Maxwell time of a few seconds, which is very much smaller than expected. Finally, this theory does not predict any supersynchronous rotation.

### Chemical Complementarity between the Gas Phase of the Interstellar Medium and the Rocky Material of Our Planetary System

We compare the elemental depletions in the gas phase of the interstellar medium (ISM) with the elemental depletions in the rocky material of our Solar System. Our analysis finds a high degree of chemical complementarity: elements depleted in the gas phase of the ISM are enriched in the rocky material of our Solar System, and vice versa. This chemical complementarity reveals the generic connections between interstellar dust and rocky planetary material. We use an inheritance model to explain the formation of primordial grains in the solar nebula. The primary dust grains inherited from the ISM, in combination with the secondary ones condensed from the solar nebula, constitute the primordial rocky material of our planetary system, from which terrestrial planets are formed through the effects of the progressive accretion and sublimation. The semi-major-axis-dependence of the chemical composition of rocky planetary material is also observed by comparing elemental depletions in the Earth, CI chondrites and other types of carbonaceous chondrites.

### The First Spectrum of the Coldest Brown Dwarf

The recently discovered brown dwarf WISE 0855 presents our first opportunity to directly study an object outside the Solar System that is nearly as cold as our own gas giant planets. However the traditional methodology for characterizing brown dwarfs---near infrared spectroscopy---is not currently feasible as WISE 0855 is too cold and faint. To characterize this frozen extrasolar world we obtained a 4.5-5.2 $\mu$m spectrum, the same bandpass long used to study Jupiter's deep thermal emission. Our spectrum reveals the presence of atmospheric water vapor and clouds, with an absorption profile that is strikingly similar to Jupiter. The spectrum is high enough quality to allow the investigation of dynamical and chemical processes that have long been studied in Jupiter's atmosphere, but now on an extrasolar world.

### The production of proton-rich isotopes beyond iron: The $\gamma$ process in stars

Beyond iron, a small fraction of the total abundances in the Solar System is made of proton-rich isotopes, the p nuclei. The clear understanding of their production is a fundamental challenge for nuclear astrophysics. The p nuclei constrain the nucleosynthesis in core-collapse and thermonuclear supernovae. The $\gamma$ process is the most established scenario for the production of the p nuclei, which are produced via different photodisintegration paths starting on heavier nuclei. A large effort from nuclear physics is needed to access the relevant nuclear reaction rates far from the valley of stability. This review describes the production of the heavy proton-rich isotopes by the $\gamma$ process in stars, and explores the state of the art of experimental nuclear physics to provide nuclear data for stellar nucleosynthesis.

### Orbital clustering of distant Kuiper Belt Objects by hypothetical Planet 9. Secular or resonant ?

Statistical analysis of the orbits of distant Kuiper Belt Objects (KBOs) have led to suggest that an additional planet should reside in the Solar System. According to recent models, the secular action of this body should cause orbital alignment of the KBOs. It was recently claimed that the KBOs concerned by this dynamics are presumably trapped in mean motion resonances with the suspected planet. I reinvestigate here the secular model underlying this idea. The original analysis was done expanding and truncating the secular Hamiltonian. I show that this is inappropriate here, as the series expansion is not convergent. I present a study based on numerical computation of the Hamiltonian with no expansion. I show in phase-space diagrams the existence of apsidally anti-aligned, high eccentricity libration islands that were not present in the original modelling, but that match numerical simulations. These island were claimed to correspond to bodies trapped in mean-motion resonances with the hypothetical planet, and match the characteristics of the distant KBOs observed. My main result is that regular secular dynamics can account for the anti-aligned particles itself as well as mean-motion resonances. I also perform a semi-analytical study of resonant motion and show that some resonance are actually capable of producing the same libration islands. I discuss then the relative importance of both mechanisms.

### Low-Frequency Radio Bursts and Space Weather

Low-frequency radio phenomena are due to the presence of nonthermal electrons in the interplanetary (IP) medium. Understanding these phenomena is important in characterizing the space environment near Earth and other destinations in the solar system. Substantial progress has been made in the past two decades, because of the continuous and uniform data sets available from space-based radio and white-light instrumentation. This paper highlights some recent results obtained on IP radio phenomena. In particular, the source of type IV radio bursts, the behavior of type III storms, shock propagation in the IP medium, and the solar-cycle variation of type II radio bursts are considered. All these phenomena are closely related to solar eruptions and active region evolution. The results presented were obtained by combining data from the Wind and SOHO missions.

### Why is there no von Neumann probe on Ceres? Error catastrophe can explain the Fermi-Hart Paradox [Cross-Listing]

It has been argued that self-replicating robotic probes could spread to all stars of our galaxy within a timespan that is tiny on cosmological scales, even if they travel well below the speed of light. The apparent absence of such von Neumann probes in our own solar system then needs an explanation that holds for all possible extraterrestrial civilisations. Here I propose such a solution, which is based on a runaway error propagation that can occur in any self-replicating system with finite accuracy of its components. Under universally applicable assumptions (finite resources and finite lifespans) it follows that an optimal probe design always leads to an error catastrophe and breakdown of the probes. Thus, there might be many advanced civilizations in our galaxy, each surrounded by their own small sphere of self-replicating probes. But unless our own solar system has the extraordinary luck to be close enough to one of these civilizations, none of these probes will ever reach us.

### Maps of Evolving Cloud Structures in Luhman 16AB from HST Time-Resolved Spectroscopy

WISE J104915.57-531906.1 is the nearest brown dwarf binary to our Solar system, consisting of two brown dwarfs in the L/T transition: Luhman 16A & B. In this paper we present the first map of Luhman 16A, and maps of Luhman 16B for two epochs. Our maps were created by applying Aeolus, a Markov-Chain Monte Carlo code that maps the top-of-the-atmosphere structure of brown dwarf and other ultracool atmospheres, to light curves of Luhman 16A & B using the Hubble Space Telescope's G141 and G102 grisms. Aeolus retrieved three or four spots in the top-of-the-atmosphere of Luhman 16A & B, with a surface coverage of 19%-32% (depending on an assumed rotational period of 5 hr or 8 hr) or 21%-38.5% (depending on the observational epoch) respectively. The brightness temperature of the spots of the best-fit models was ~200 K hotter than the background top-of-the-atmosphere. We compared our Luhman 16B map with the only previously published map. Interestingly, our map contained a large, cooler (DT~51 K) than the background top-of-the-atmosphere spot that lay at low latitudes, in agreement with the previous Luhman 16B map. Finally, we report the detection of a feature reappearing in Luhman 16B light curves that are separated by tens of hundreds of rotations from each other. We speculate this feature is related to top-of-the-atmosphere structures of Luhman 16B.

### A new distance law of planets and satellites in the solar system

In the 1960s, it has been substantiated that an equation of Schrodinger type could describe the diffusion phenomena, and the main consequence from this finding has been that there would be wave property in the diffusion processes as well. This theory has been immediately proved through laboratorial experiments. Afterwards the theory was applied to the primordial nebula which was thought to surround the protosun, and has found the consistency of the prediction of the theory with current distance distribution of the planets to be excellent. At the end of 20th century new satellites of planets were discovered. On the basis of the new data, the theory is tested thoroughly and the result allows us to come to the conclusion that the basic process for the distances of the planets from the protosun to be determined has been the diffusion of the primordial nebula consisting of mainly molecular gas.

### Giga-Year Evolution of Jupiter Trojans and the Asymmetry Problem

We present a series of numerical integrations of observed and fictitious Jupiter Trojan asteroids, under the gravitational effects of the four outer planets, for time-spans comparable with the age of the Solar System. From these results we calculate the escape rate from each Lagrange point, and construct dynamical maps of "permanence" time in different regions of the phase space. Fictitious asteroids in L4 and L5 show no significant difference, showing almost identical dynamical maps and escape rates. For real Trojans, however, we found that approximately 23% o f the members of the leading swarm escaped after 4.5 Gyrs, while this number increased to 28.3% for L5. This implies that the asymmetry between the two populations increases with time, indicating that it may have been smaller at the time of formation/capture of these asteroids. Nevertheless, the difference in chaotic diffusion cannot, in itself, account for the current observed asymmetry (~40%), and must be primarily primordial and characteristic of the capture mechanism of the Trojans. Finally, we calculate new proper elements for all the numbered Trojans using the semi-analytical approach of Beaug\'e and Roig (2001), and compare the results with the numerical estimations by Bro\v{z} and Rosehnal (2011). For asteroids that were already numbered in 2011, both methods yield very similar results, while significant differences were found for those bodies that became numbered after 2011.

### Quantification of tidal parameters from Solar system data

Tidal dissipation is the main driver of orbital evolution of natural satellites and a key point to understand the exoplanetary system configurations. Despite its importance, its quantification from observations still remains difficult for most objects of our own Solar system. In this work, we overview the method that has been used to determine, directly from observations, the tidal parameters, with emphasis on the Love number k2 and the tidal quality factor Q. Up-to-date values of these tidal parameters are summarized. Last, an assessment on the possible determination of the tidal ratio k2/Q of Uranus and Neptune is done. This may be particularly relevant for coming astrometric campaigns and future space missions focused on these systems.

### Observational Constraints on Planet Nine: Cassini Range Observations

We significantly constrain the sky position, distance, and mass of a possible additional, distant planet in the solar system by examining its influence on the distance between Earth and the Cassini Spacecraft. Our preferred region is approximately centered on (RA, Dec) = ($40\arcdeg$, $-15\arcdeg$), extending approximately 20 degrees in all directions.

### The collisional evolution of undifferentiated asteroids and the formation of chondritic meteoroids

Most meteorites are fragments from recent collisions experienced in the asteroid belt. In such a hyper-velocity collision, the smaller collision partner is destroyed, whereas a crater on the asteroid is formed or it is entirely disrupted, too. The present size distribution of the asteroid belt suggests that an asteroid with 100 km radius is encountered $10^{14}$ times during the lifetime of the Solar System by objects larger than 10 cm in radius; the formed craters cover the surface of the asteroid about 100 times. We present a Monte Carlo code that takes into account the statistical bombardment of individual infinitesimally small surface elements, the subsequent compaction of the underlying material, the formation of a crater and a regolith layer. For the entire asteroid, 10,000 individual surface elements are calculated. We compare the ejected material from the calculated craters with the shock stage of meteorites with low petrologic type and find that these most likely stem from smaller parent bodies that do not possess a significant regolith layer. For larger objects, which accrete a regolith layer, a prediction of the thickness depending on the largest visible crater can be made. Additionally, we compare the crater distribution of an object initially 100 km in radius with the shape model of the asteroid (21) Lutetia, assuming it to be initially formed spherical with a radius that is equal to its longest present ellipsoid length. Here, we find the shapes of both objects to show resemblance to each other.

### Solar system tests for linear massive conformal gravity

We first find the linearized gravitational field of a static spherically symmetric mass distribution in massive conformal gravity. Then we test this field with two solar system experiments: deflection of light by the sun and radar echo delay. The result is that the linear massive conformal gravity agrees with the linear general relativistic observations in the solar system. However, besides the standard general relativistic deflection of light, the theory gives an extra deflection at galactic scales. It is likely that this additional deflection replaces the effects of dark matter in general relativity.

### How to form asteroids from mm-sized grains

The size distribution of asteroids in the solar system suggests that they formed top-down, with 100-1000 km bodies forming from the gravitational collapse of dense clumps of small solid particles. We investigate the conditions under which solid particles can form dense clumps in a protoplanetary disc. We used a hydrodynamic code to model the solid-gas interaction in disc. We found that particles down to millimeter size can form dense clumps, but only in regions where solids make $\sim$ 8% of the local surface density. More generally, we mapped the range of particle sizes and concentrations that is consistent with the formation of particle clumps.

### CD-HPF: New Habitability Score Via Data Analytic Modeling

The search for life on the planets outside the Solar System can be broadly classified into the following: looking for Earth-like conditions or the planets similar to the Earth (Earth similarity), and looking for the possibility of life in a form known or unknown to us (habitability). The two frequently used indices, ESI and PHI, describe heuristic methods to score similarity/habitability in the efforts to categorize different exoplanets or exomoons. ESI, in particular, considers Earth as the reference frame for habitability and is a quick screening tool to categorize and measure physical similarity of any planetary body with the Earth. The PHI assesses the probability that life in some form may exist on any given world, and is based on the essential requirements of known life: a stable and protected substrate, energy, appropriate chemistry and a liquid medium. We propose here a different metric, a Cobb-Douglas Habitability Score (CDHS), based on Cobb-Douglas habitability production function (CD-HPF), which computes the habitability score by using measured and calculated planetary input parameters. The proposed metric, with exponents accounting for metric elasticity, is endowed with verifiable analytical properties that ensure global optima, and is scalable to accommodate finitely many input parameters. The model is elastic, does not suffer from curvature violations and, as we discovered, the standard PHI is a special case of CDHS. Computed CDHS scores are fed to K-NN (K-Nearest Neighbour) classification algorithm with probabilistic herding that facilitates the assignment of exoplanets to appropriate classes via supervised feature learning methods, producing granular clusters of habitability. The proposed work describes a decision-theoretical model using the power of convex optimization and algorithmic machine learning.

### A Roadmap to Interstellar Flight

In the nearly 60 years of spaceflight we have accomplished wonderful feats of exploration that have shown the incredible spirit of the human drive to explore and understand our universe. Yet in those 60 years we have barely left our solar system with the Voyager 1 spacecraft launched in 1977 finally leaving the solar system after 37 years of flight at a speed of 17 km/s or less than 0.006% the speed of light. As remarkable as this is we will never reach even the nearest stars with our current propulsion technology in even 10 millennium. We have to radically rethink our strategy or give up our dreams of reaching the stars, or wait for technology that does not currently exist. While we all dream of human spaceflight to the stars in a way romanticized in books and movies, it is not within our power to do so, nor it is clear that this is the path we should choose. We posit a technological path forward, that while not simple, it is within our technological reach. We propose a roadmap to a program that will lead to sending relativistic probes to the nearest stars and will open up a vast array of possibilities of flight both within our solar system and far beyond. Spacecraft from gram level complete spacecraft on a wafer ("wafersats") that reach more than 1/4 c and reach the nearest star in 20 years to spacecraft with masses more than 10^5 kg (100 tons) that can reach speeds of greater than 1000 km/s. These systems can be propelled to speeds currently unimaginable with existing propulsion technologies. To do so requires a fundamental change in our thinking of both propulsion and in many cases what a spacecraft is. In addition to larger spacecraft, some capable of transporting humans, we consider functional spacecraft on a wafer, including integrated optical communications, imaging systems, photon thrusters, power and sensors combined with directed energy propulsion.

### A Roadmap to Interstellar Flight [Replacement]

In the nearly 60 years of spaceflight we have accomplished wonderful feats of exploration that have shown the incredible spirit of the human drive to explore and understand our universe. Yet in those 60 years we have barely left our solar system with the Voyager 1 spacecraft launched in 1977 finally leaving the solar system after 37 years of flight at a speed of 17 km/s or less than 0.006% the speed of light. As remarkable as this is we will never reach even the nearest stars with our current propulsion technology in even 10 millennium. We have to radically rethink our strategy or give up our dreams of reaching the stars, or wait for technology that does not currently exist. While we all dream of human spaceflight to the stars in a way romanticized in books and movies, it is not within our power to do so, nor it is clear that this is the path we should choose. We posit a technological path forward, that while not simple, it is within our technological reach. We propose a roadmap to a program that will lead to sending relativistic probes to the nearest stars and will open up a vast array of possibilities of flight both within our solar system and far beyond. Spacecraft from gram level complete spacecraft on a wafer ("wafersats") that reach more than 1/4 c and reach the nearest star in 20 years to spacecraft with masses more than 10^5 kg (100 tons) that can reach speeds of greater than 1000 km/s. These systems can be propelled to speeds currently unimaginable with existing propulsion technologies. To do so requires a fundamental change in our thinking of both propulsion and in many cases what a spacecraft is. In addition to larger spacecraft, some capable of transporting humans, we consider functional spacecraft on a wafer, including integrated optical communications, imaging systems, photon thrusters, power and sensors combined with directed energy propulsion.

### A Roadmap to Interstellar Flight [Replacement]

In the nearly 60 years of spaceflight we have accomplished wonderful feats of exploration that have shown the incredible spirit of the human drive to explore and understand our universe. Yet in those 60 years we have barely left our solar system with the Voyager 1 spacecraft launched in 1977 finally leaving the solar system after 37 years of flight at a speed of 17 km/s or less than 0.006% the speed of light. As remarkable as this is we will never reach even the nearest stars with our current propulsion technology in even 10 millennium. We have to radically rethink our strategy or give up our dreams of reaching the stars, or wait for technology that does not currently exist. While we all dream of human spaceflight to the stars in a way romanticized in books and movies, it is not within our power to do so, nor it is clear that this is the path we should choose. We posit a technological path forward, that while not simple, it is within our technological reach. We propose a roadmap to a program that will lead to sending relativistic probes to the nearest stars and will open up a vast array of possibilities of flight both within our solar system and far beyond. Spacecraft from gram level complete spacecraft on a wafer ("wafersats") that reach more than 1/4 c and reach the nearest star in 20 years to spacecraft with masses more than 10^5 kg (100 tons) that can reach speeds of greater than 1000 km/s. These systems can be propelled to speeds currently unimaginable with existing propulsion technologies. To do so requires a fundamental change in our thinking of both propulsion and in many cases what a spacecraft is. In addition to larger spacecraft, some capable of transporting humans, we consider functional spacecraft on a wafer, including integrated optical communications, imaging systems, photon thrusters, power and sensors combined with directed energy propulsion.

### Testing General Free Functions in Preferred Scale Theories

Building on previous work, we explore the parameter space of general free functions in non-relativistic modified gravity theories motivated by k-essence and other scalar-tensor theories. Using a few proposed tests, we aim to update Solar System based constraints on these ideas in line with previous theories and suggest their utility in constraining modification to GR, potentially even being able to test k-essence type theories.

### First detection of gas-phase ammonia in a planet-forming disk

Nitrogen chemistry in protoplanetary disks and the freeze-out on dust particles is key to understand the formation of nitrogen bearing species in early solar system analogs. So far, ammonia has not been detected beyond the snowline in protoplanetary disks. We aim to find gas-phase ammonia in a protoplanetary disk and characterize its abundance with respect to water vapor. Using HIFI on the Herschel Space Observatory we detect, for the first time, the ground-state rotational emission of ortho-NH$_3$ in a protoplanetary disk, around TW Hya. We use detailed models of the disk's physical structure and the chemistry of ammonia and water to infer the amounts of gas-phase molecules of these species. We explore two radial distributions ( confined to $<$60 au like the millimeter-sized grains) and two vertical distributions (near the midplane where water is expected to photodesorb off icy grains) to describe the (unknown) location of the molecules. These distributions capture the effects of radial drift and vertical settling of ice-covered grains. We use physical-chemical models to reproduce the fluxes with assuming that water and ammonia are co-spatial. We infer ammonia gas-phase masses of 0.7-11.0 $\times$10$^{21}$ g. For water, we infer gas-phase masses of 0.2-16.0 $\times$10$^{22}$ g. This corresponds to NH$_3$/H$_2$O abundance ratios of 7\%-84\%, assuming that water and ammonia are co-located. Only in the most compact and settled adopted configuration is the inferred NH$_3$/H$_2$O consistent with interstellar ices and solar system bodies of $\sim$ 5\%-10\%. Volatile release in the midplane may occur via collisions between icy bodies if the available surface for subsequent freeze-out is significantly reduced, e.g., through growth of small grains into pebbles or larger.

### Impact-induced melting during accretion of the Earth

Because of the high energies involved, giant impacts that occur during planetary accretion cause large degrees of melting. The depth of melting in the target body after each collision determines the pressure and temperature conditions of metal-silicate equilibration and thus geochemical fractionation that results from core-mantle differentiation. The accretional collisions involved in forming the terrestrial planets of the inner Solar System have been calculated by previous studies using N-body accretion simulations. Here we use the output from such simulations to determine the volumes of melt produced and thus the pressure and temperature conditions of metal-silicate equilibration, after each impact, as Earth-like planets accrete. For these calculations a parametrised melting model is used that takes impact velocity, impact angle and the respective masses of the impacting bodies into account. The evolution of metal-silicate equilibration pressures (as defined by evolving magma ocean depths) during Earth's accretion depends strongly on the lifetime of impact-generated magma oceans compared to the time interval between large impacts. In addition, such results depend on starting parameters in the N-body simulations, such as the number and initial mass of embryos. Thus, there is the potential for combining the results, such as those presented here, with multistage core formation models to better constrain the accretional history of the Earth.

### On the Formation of Super-Earths with Implications for the Solar System

We first consider how the level of turbulence in a protoplanetary disk affects the formation locations for the observed close-in super-Earths in exosolar systems. We find that a protoplanetary disk that includes a dead zone (a region of low turbulence) has substantially more material in the inner parts of the disk, possibly allowing for in situ formation. For the dead zone to last the entire lifetime of the disk requires the active layer surface density to be sufficiently small, <100 g/cm^2. Migration through a dead zone may be very slow and thus super-Earth formation followed by migration towards the star through the dead zone is less likely. For fully turbulent disks, there is not enough material for in situ formation. However, in this case, super-Earths can form farther out in the disk and migrate inwards on a reasonable timescale. We suggest that both of these formation mechanisms operate in different planetary systems. This can help to explain the observed large range in densities of super-Earths because the formation location determines the composition. Furthermore, we speculate that super-Earths could have formed in the inner parts of our solar system and cleared the material in the region inside of Mercury's orbit. The super-Earths could migrate through the gas disk and fall into the Sun if the disk was sufficiently cool during the final gas disk accretion process. While it is definitely possible to meet all of these requirements, we don't expect them to occur in all systems, which may explain why the solar system is somewhat special in its lack of super-Earths.

### Making Planet Nine: Pebble Accretion at 250--750 AU in a Gravitationally Unstable Ring

We investigate the formation of icy super-Earth mass planets within a gravitationally unstable ring of solids orbiting at 250-750 AU around a 1 solar mass star. Coagulation calculations demonstrate that a system of a few large oligarchs and a swarm of pebbles generates a super-Earth within 100-200 Myr at 250 AU and within 1-2 Gyr at 750 AU. Systems with more than ten oligarchs fail to yield super-Earths over the age of the solar system. As these systems evolve, destructive collisions produce detectable debris disks with luminosities of $10^{-5}$ to $10^{-3}$ relative to the central star.

### The theory of secondary resonances in the spin-orbit problem

We study the resonant dynamics in a simple one degree of freedom, time dependent Hamiltonian model describing spin-orbit interactions. The equations of motion admit periodic solutions associated with resonant motions, the most important being the synchronous one in which most evolved satellites of the Solar system, including the Moon, are observed. Such primary resonances can be surrounded by a chain of smaller islands which one refers to as secondary resonances. Here, we propose a novel canonical normalization procedure allowing to obtain a higher order normal form, by which we obtain analytical results on the stability of the primary resonances as well as on the bifurcation thresholds of the secondary resonances. The procedure makes use of the expansion in a parameter, called the detuning, measuring the shift from the exact secondary resonance. Also, we implement the so-called `book-keeping' method, i.e., the introduction of a suitable separation of the terms in orders of smallness in the normal form construction, which deals simultaneously with all the small parameters of the problem. Our analytical computation of the bifurcation curves is in excellent agreement with the results obtained by a numerical integration of the equations of motion, thus providing relevant information on the parameter regions where satellites can be found in a stable configuration.

### Is there an exoplanet in the Solar System?

We investigate the prospects for the capture of the proposed Planet 9 from other stars in the Sun's birth cluster. Any capture scenario must satisfy three conditions: the encounter must be more distant than ~150 au to avoid perturbing the Kuiper belt; the other star must have a wide-orbit planet (a>~100au); the planet must be captured onto an appropriate orbit to sculpt the orbital distribution of wide-orbit Solar System bodies. Here we use N-body simulations to show that these criteria may be simultaneously satisfied. In a few percent of slow close encounters in a cluster, bodies are captured onto heliocentric, Planet 9-like orbits. During the ~100 Myr cluster phase, many stars are likely to host planets on highly-eccentric orbits with apastron distances beyond 100 au if Neptune-sized planets are common and susceptible to planet--planet scattering. While the existence of Planet 9 remains unproven, we consider capture from one of the Sun's young brethren a plausible route to explain such an object's orbit. Capture appears to predict a large population of Trans-Neptunian Objects (TNOs) whose orbits are aligned with the captured planet, and we propose that different formation mechanisms will be distinguishable based on their imprint on the distribution of TNOs.

### Is there an exoplanet in the Solar System? [Replacement]

We investigate the prospects for the capture of the proposed Planet 9 from other stars in the Sun's birth cluster. Any capture scenario must satisfy three conditions: the encounter must be more distant than ~150 au to avoid perturbing the Kuiper belt; the other star must have a wide-orbit planet (a>~100au); the planet must be captured onto an appropriate orbit to sculpt the orbital distribution of wide-orbit Solar System bodies. Here we use N-body simulations to show that these criteria may be simultaneously satisfied. In a few percent of slow close encounters in a cluster, bodies are captured onto heliocentric, Planet 9-like orbits. During the ~100 Myr cluster phase, many stars are likely to host planets on highly-eccentric orbits with apastron distances beyond 100 au if Neptune-sized planets are common and susceptible to planet--planet scattering. While the existence of Planet 9 remains unproven, we consider capture from one of the Sun's young brethren a plausible route to explain such an object's orbit. Capture appears to predict a large population of Trans-Neptunian Objects (TNOs) whose orbits are aligned with the captured planet, and we propose that different formation mechanisms will be distinguishable based on their imprint on the distribution of TNOs.

### Insights into planet formation from debris disks: I. The solar system as an archetype for planetesimal evolution

Circumstellar disks have long been regarded as windows into planetary systems. The advent of high sensitivity, high resolution imaging in the submillimetre where both the solid and gas components of disks can be detected opens up new possibilities for understanding the dynamical histories of these systems and therefore, a better ability to place our own solar system, which hosts a highly evolved debris disk, in context. Comparisons of dust masses from protoplanetary and debris disks have revealed a stark downturn in mass in millimetre-sized grains around a stellar age of 10 Myr, ostensibly in the "transition disk" phase, suggesting a period of rapid accretion of such grains onto planetesimals. This rapid formation phase is in keeping with radionucleide studies of Kuiper Belt Objects in the solar system. Importantly, this suggests that any thermal gradients in the gas of disks of this era will be "frozen in" to the planetesimals as they rapidly accrete from the solids and ices in their vicinity. Measurements of radial gradients in thermal tracers such as DHO, DCN and other tracers can therefore provide insight into the nascent solar system's abudances. In studies of dynamical evolution of the solar system, it is tacitly assumed that such abundances can reveal the location of formation for bodies now found in the asteroid belt and Kuiper belt. Similarly, evidence of gas detected from collisional evolution in young debris disks could potentially reveal how rapidly objects have dynamically evolved in those systems, most of which will be significantly younger than the solar system.

### A sound nebula: the origin of the Solar System in the field of a standing sound wave

According to the planetary origin conceptual model proposed in this paper, the protosun centre of the pre-solar nebula exploded, resulting in a shock wave that passed through it and then returned to the centre, generating a new explosion and shock wave. Recurrent explosions in the nebula resulted in a spherical standing sound wave, whose antinodes concentrated dust into rotating rings that transformed into planets. The extremely small angular momentum of the Sun and the tilt of its equatorial plane were caused by the asymmetry of the first, most powerful explosion. Differences between inner and outer planets are explained by the migration of solid matter, while the Oort cloud is explained by the division of the pre-solar nebula into a spherical internal nebula and an expanding spherical shell of gas. The proposed conceptual model can also explain the origin and evolution of exoplanetary systems and may be of use in searching for new planets.

### Constraining the Schwarzschild-de Sitter Solution in Models of Modified Gravity

The Schwarzschild-de Sitter (SdS) solution exists in the large majority of modified gravity theories, as expected, and in particular the effective cosmological constant is determined by the specific parameters of the given theory. We explore the possibility to use future extended radio-tracking data from the currently ongoing New Horizons mission in the outskirts peripheries of the Solar System, at about 40 au, in order to constrain this effective cosmological constant, and thus to impose constrain on each scenario's parameters. We investigate some of the recently most studied modified gravities, namely $f(R)$ and $f(T)$ theories, dRGT massive gravity, and Ho\v{r}ava-Lifshitz gravity, and we show that New Horizons mission may bring an improvement of one-two orders of magnitude with respect to the present bounds from planetary orbital dynamics.

### Constraining the Schwarzschild-de Sitter Solution in Models of Modified Gravity [Cross-Listing]

The Schwarzschild-de Sitter (SdS) solution exists in the large majority of modified gravity theories, as expected, and in particular the effective cosmological constant is determined by the specific parameters of the given theory. We explore the possibility to use future extended radio-tracking data from the currently ongoing New Horizons mission in the outskirts peripheries of the Solar System, at about 40 au, in order to constrain this effective cosmological constant, and thus to impose constrain on each scenario's parameters. We investigate some of the recently most studied modified gravities, namely $f(R)$ and $f(T)$ theories, dRGT massive gravity, and Ho\v{r}ava-Lifshitz gravity, and we show that New Horizons mission may bring an improvement of one-two orders of magnitude with respect to the present bounds from planetary orbital dynamics.

### Constraining the Schwarzschild-de Sitter Solution in Models of Modified Gravity [Replacement]

The Schwarzschild-de Sitter (SdS) solution exists in the large majority of modified gravity theories, as expected, and in particular the effective cosmological constant is determined by the specific parameters of the given theory. We explore the possibility to use future extended radio-tracking data from the currently ongoing New Horizons mission in the outskirts peripheries of the Solar System, at about 40 au, in order to constrain this effective cosmological constant, and thus to impose constrain on each scenario's parameters. We investigate some of the recently most studied modified gravities, namely $f(R)$ and $f(T)$ theories, dRGT massive gravity, and Ho\v{r}ava-Lifshitz gravity, and we show that New Horizons mission may bring an improvement of one-two orders of magnitude with respect to the present bounds from planetary orbital dynamics.

### Constraining the Schwarzschild-de Sitter Solution in Models of Modified Gravity [Replacement]

The Schwarzschild-de Sitter (SdS) solution exists in the large majority of modified gravity theories, as expected, and in particular the effective cosmological constant is determined by the specific parameters of the given theory. We explore the possibility to use future extended radio-tracking data from the currently ongoing New Horizons mission in the outskirts peripheries of the Solar System, at about 40 au, in order to constrain this effective cosmological constant, and thus to impose constrain on each scenario's parameters. We investigate some of the recently most studied modified gravities, namely $f(R)$ and $f(T)$ theories, dRGT massive gravity, and Ho\v{r}ava-Lifshitz gravity, and we show that New Horizons mission may bring an improvement of one-two orders of magnitude with respect to the present bounds from planetary orbital dynamics.

### Constraining the Schwarzschild-de Sitter Solution in Models of Modified Gravity [Replacement]

The Schwarzschild-de Sitter (SdS) solution exists in the large majority of modified gravity theories, as expected, and in particular the effective cosmological constant is determined by the specific parameters of the given theory. We explore the possibility to use future extended radio-tracking data from the currently ongoing New Horizons mission in the outskirts peripheries of the Solar System, at about 40 au, in order to constrain this effective cosmological constant, and thus to impose constrain on each scenario's parameters. We investigate some of the recently most studied modified gravities, namely $f(R)$ and $f(T)$ theories, dRGT massive gravity, and Ho\v{r}ava-Lifshitz gravity, and we show that New Horizons mission may bring an improvement of one-two orders of magnitude with respect to the present bounds from planetary orbital dynamics.

### Constraining the Schwarzschild-de Sitter Solution in Models of Modified Gravity [Cross-Listing]

The Schwarzschild-de Sitter (SdS) solution exists in the large majority of modified gravity theories, as expected, and in particular the effective cosmological constant is determined by the specific parameters of the given theory. We explore the possibility to use future extended radio-tracking data from the currently ongoing New Horizons mission in the outskirts peripheries of the Solar System, at about 40 au, in order to constrain this effective cosmological constant, and thus to impose constrain on each scenario's parameters. We investigate some of the recently most studied modified gravities, namely $f(R)$ and $f(T)$ theories, dRGT massive gravity, and Ho\v{r}ava-Lifshitz gravity, and we show that New Horizons mission may bring an improvement of one-two orders of magnitude with respect to the present bounds from planetary orbital dynamics.

### Origin of uranium isotope variations in early solar nebula condensates

High temperature condensates found in meteorites display uranium isotopic variations (235U/238U) that complicate dating of the formation of the Solar System and whose origin remains mysterious. It is possible that these variations are due to decay of the short-lived radionuclide 247Cm (t1/2=15.6 Myr) into 235U but they could also be due to uranium kinetic isotopic fractionation during condensation. We report uranium isotope measurements of meteoritic refractory inclusions that reveal excesses of 235U reaching ~+6 % relative to average solar system composition, which can only be due to decay of 247Cm. This allows us to constrain the 247Cm/235U ratio at Solar System formation to (1.1 +- 0.3) x 10-4. This value provides new clues on the universality of nucleosynthetic r-process of rapid neutron capture.

### Kinematical properties of coronal mass ejections

Coronal mass ejections (CMEs) are the most dynamic phenomena in our solar system. They abruptly disrupt the continuous outflow of solar wind by expelling huge clouds of magnetized plasma into interplanetary space with velocities enabling to cross the Sun-Earth distance within a few days. Earth-directed CMEs may cause severe geomagnetic storms when their embedded magnetic fields and the shocks ahead compress and reconnect with the Earth's magnetic field. The transit times and impacts in detail depend on the initial CME velocity, size, and mass, as well as on the conditions and coupling processes with the ambient solar wind flow in interplanetary space. The observed CME parameters may be severly affected by projection effects and the constant changing environmental conditions are hard to derive. This makes it difficult to fully understand the physics behind CME evolution, preventing to do a reliable forecast of Earth-directed events. This short review focusing on observational data, shows recent methods which were developed to derive the CME kinematical profile for the entire Sun-Earth distance range as well as studies which were performed to shed light on the physical processes that CMEs encounter when propagating from Sun to Earth.

### On the oldest asteroid families in the main belt

Asteroid families are groups of minor bodies produced by high-velocity collisions. After the initial dispersions of the parent bodies fragments, their orbits evolve because of several gravitational and non-gravitational effects,such as diffusion in mean-motion resonances, Yarkovsky and YORP effects, close encounters of collisions, etc. The subsequent dynamical evolution of asteroid family members may cause some of the original fragments to travel beyond the conventional limits of the asteroid family. Eventually, the whole family will dynamically disperse and no longer be recognizable. A natural question that may arise concerns the timescales for dispersion of large families. In particular, what is the oldest still recognizable family in the main belt? Are there any families that may date from the late stages of the Late Heavy Bombardment and that could provide clues on our understanding of the primitive Solar System? In this work, we investigate the dynamical stability of seven of the allegedly oldest families in the asteroid main belt. Our results show that none of the seven studied families has a nominally mean estimated age older than 2.7 Gyr, assuming standard values for the parameters describing the strength of the Yarkovsky force. Most "paleo-families" that formed between 2.7 and 3.8 Gyr would be characterized by a very shallow size-frequency distribution, and could be recognizable only if located in a dynamically less active region (such as that of the Koronis family). V-type asteroids in the central main belt could be compatible with a formation from a paleo-Eunomia family.

### Forming Chondrites in a Solar Nebula with Magnetically Induced Turbulence [Replacement]

Chondritic meteorites provide valuable opportunities to investigate the origins of the solar system. We explore impact jetting as a mechanism of chondrule formation and subsequent pebble accretion as a mechanism of accreting chondrules onto parent bodies of chondrites, and investigate how these two processes can account for the currently available meteoritic data. We find that when the solar nebula is $\le 5$ times more massive than the minimum-mass solar nebula at $a \simeq 2-3$ AU and parent bodies of chondrites are $\le 10^{24}$ g ($\le$ 500 km in radius) in the solar nebula, impact jetting and subsequent pebble accretion can reproduce a number of properties of the meteoritic data. The properties include the present asteroid belt mass, the formation timescale of chondrules, and the magnetic field strength of the nebula derived from chondrules in Semarkona. Since this scenario requires a first generation of planetesimals that trigger impact jetting and serve as parent bodies to accrete chondrules, the upper limit of parent bodies' masses leads to the following implications: primordial asteroids that were originally $\ge 10^{24}$ g in mass were unlikely to contain chondrules, while less massive primordial asteroids likely had a chondrule-rich surface layer. The scenario developed from impact jetting and pebble accretion can therefore provide new insights into the origins of the solar system.

### Accretion of Chondrules formed by Impact Jetting in Magnetically Induced Turbulent Solar Nebula

Chondritic meteorites provide valuable opportunities to investigate origins of the solar system. We explore impact jetting as a mechanism to form chondrules and subsequent pebble accretion as a mechanism to accrete them onto parent bodies of chondrites, and investigate how these two processes can account for the currently available meteoritic data. We find that when the solar nebula is $\le 5$ times more massive than the minimum-mass solar nebula at $a \simeq 2-3$ AU and parent bodies of chondrites are $\le 10^{24}$ g ($\le$ 500 km in radius) there, impact jetting and subsequent pebble accretion can reproduce a number of properties of the meteoritic data. The properties include the present asteroid belt mass, formation timescale of chondrules, and the magnetic field strength of the nebula derived from chondrules in Semarkona. Since this scenario requires a first generation of planetesimals that trigger impact jetting and serve as parent bodies to accrete chondrules, the upper limit of parent bodies' mass leads to the following implications: primordial asteroids that were originally $\ge 10^{24}$ g in mass were unlikely to contain chondrules, while less massive primordial asteroids likely had a chondrule-rich surface layer. The scenario developed from impact jetting and pebble accretion can therefore provide new insights into origins of the solar system.

### Interaction Cross Sections and Survival Rates for Proposed Solar System Member Planet Nine

Motivated by the report of a possible new planetary member of the Solar System, this work calculates cross sections for interactions between passing stars and this proposed Planet Nine. Evidence for the new planet is provided by the orbital alignment of Kuiper Belt objects, and other Solar System properties, which suggest a Neptune-mass object on an eccentric orbit with semimajor axis a_9~400-1500 AU. With such a wide orbit, Planet Nine has a large interaction cross section, and is susceptible to disruption by passing stars. Using a large ensemble of numerical simulations (several million), and Monte Carlo sampling, we calculate the cross sections for different classes of orbit-altering events: [A] scattering the planet into its proposed orbit from a smaller orbit, [B] ejecting it from the Solar System from its current orbit, [C] capturing the planet from another system, and [D] capturing a free-floating planet. Results are presented for a range of orbital elements with planetary mass m_9=10M_\earth. Removing Planet Nine from the Solar System is the most likely outcome. Specifically, we obtain ejection cross sections 4.2\times10^6 AU^2 (4.3\times10^4 AU^2) for environments corresponding to the birth cluster (field). With these cross sections, Planet Nine is likely to be ejected if the Sun resides within its birth cluster longer than t>~100 Myr. The probability of ejecting Planet Nine due to passing field stars is ~10-50% over the age of the Sun. Probabilities for producing the inferred Planet Nine orbit are significantly lower (<~5%).

### Interaction Cross Sections and Survival Rates for Proposed Solar System Member Planet Nine [Replacement]

Motivated by the report of a possible new planetary member of the Solar System, this work calculates cross sections for interactions between passing stars and this proposed Planet Nine. Evidence for the new planet is provided by the orbital alignment of Kuiper Belt objects, and other Solar System properties, which suggest a Neptune-mass object on an eccentric orbit with semimajor axis $a_9\approx400-1500$ AU. With such a wide orbit, Planet Nine has a large interaction cross section, and is susceptible to disruption by passing stars. Using a large ensemble of numerical simulations (several million), and Monte Carlo sampling, we calculate the cross sections for different classes of orbit-altering events: [A] scattering the planet into its proposed orbit from a smaller orbit, [B] ejecting it from the Solar System from its current orbit, [C] capturing the planet from another system, and [D] capturing a free-floating planet. Results are presented for a range of orbital elements with planetary mass $m_9=10M_{earth}$. Removing Planet Nine from the Solar System is the most likely outcome. Specifically, we obtain ejection cross sections $\sigma_{int}\sim5\times10^6$ AU$^2$ ($5\times10^4$ AU$^2$) for environments corresponding to the birth cluster (field). With these cross sections, Planet Nine is likely to be ejected if the Sun resides within its birth cluster longer than $\Delta{t} \gtrsim 100$ Myr. The probability of ejecting Planet Nine due to passing field stars is $\lesssim 3\%$ over the age of the Sun. Probabilities for producing the inferred Planet Nine orbit are low $(\lesssim 5\%)$.

### Evolution and Magnitudes of Candidate Planet Nine

Context. Given the recently renewed interest in a possible additional major body in the outer Solar System, the thermodynamic evolution of such an object was studied, assuming that it is a smaller version of Uranus and Neptune. Aims. We have modeled the temporal evolution of the radius, temperature, intrinsic luminosity, and the black body spectrum of distant ice giants. The aim is to provide also estimates of the magnitudes in different bands to assess the object's detectability. Methods. Simulations of the cooling and contraction were conducted for ice giants with masses of 5, 10, 20, and 50 Mearth containing 10, 14, 21, and 37 % H/He in mass that are located at 280, 700, and 1120 AU from the Sun. The core composition was varied from purely rocky to purely icy as well as 50% rock and 50% ice. The atmospheric opacity was set to 1, 50, and 100 times solar metallicity. Results. We find for the nominal 10 Mearth planet at 700 AU at the current age of the Solar System an effective temperature of 47 K, much more than the equilibrium temperature of about 10 K, a radius of 3.7 Rearth, and an intrinsic luminosity of 0.006 Ljupiter. It has estimated apparent magnitudes of Johnson V, R, I, L, N, Q of 21.7, 21.2, 20.8, 20.1, 19.7, and 11.4, and WISE W1-W4 magnitudes of 20.1, 20.0, 19.5, and 10.4. The Q and W4 band and other observation longward of ~13 microns pick up the intrinsic flux. Conclusions. If candidate Planet 9 has a significant H/He layer and an efficient energy transport in the interior, then its luminosity is dominated by the intrinsic contribution, making it a self-luminous planet. At a likely position on its orbit near the aphelion, we estimate for a mass of 5, 10, 20, and 50 Mearth a V magnitude from the reflected light of 24.2, 23.7, 23.2, and 22.5 and a Q magnitude from the intrinsic radiation of 15.6, 12.4, 9.8, 6.2. The latter would probably have been detected by past surveys.

### Evolution and Magnitudes of Candidate Planet Nine [Replacement]

The recently renewed interest in a possible additional major body in the outer solar system prompted us to study the thermodynamic evolution of such an object. We assumed that it is a smaller version of Uranus and Neptune. We modeled the temporal evolution of the radius, temperature, intrinsic luminosity, and the blackbody spectrum of distant ice giant planets. The aim is also to provide estimates of the magnitudes in different bands to assess whether the object might be detectable. Simulations of the cooling and contraction were conducted for ice giants with masses of 5, 10, 20, and 50 Mearth that are located at 280, 700, and 1120 AU from the Sun. The core composition, the fraction of H/He, the efficiency of energy transport, and the initial luminosity were varied. The atmospheric opacity was set to 1, 50, and 100 times solar metallicity. We find for a nominal 10 Mearth planet at 700 AU at the current age of the solar system an effective temperature of 47 K, much higher than the equilibrium temperature of about 10 K, a radius of 3.7 Rearth, and an intrinsic luminosity of 0.006 Ljupiter. It has estimated apparent magnitudes of Johnson V, R, I, L, N, Q of 21.7, 21.4, 21.0, 20.1, 19.9, and 10.7, and WISE W1-W4 magnitudes of 20.1, 20.1, 18.6, and 10.2. The Q and W4 band and other observations longward of about 13 microns pick up the intrinsic flux. If candidate Planet 9 has a significant H/He layer and an efficient energy transport in the interior, then its luminosity is dominated by the intrinsic contribution, making it a self-luminous planet. At a likely position on its orbit near aphelion, we estimate for a mass of 5, 10, 20, and 50 Mearth a V magnitude from the reflected light of 24.3, 23.7, 23.3, and 22.6 and a Q magnitude from the intrinsic radiation of 14.6, 11.7, 9.2, and 5.8. The latter would probably have been detected by past surveys.

### Constraints on the location of a possible 9th planet derived from the Cassini data

To explain the unusual distribution of Kuiper Belt objects, several authors have advocated the existence of a super-Earth planet in the outer solar system. It has recently been proposed that a 10 M$_{\oplus}$ object with an orbit of 700 AU semi major axis and 0.6 eccentricity can explain the observed distribution of Kuiper Belt objects around Sedna. Here we use the INPOP planetary ephemerides model as a sensor for testing for an additional body in the solar system. We test the possibility of adding the proposed planet without increasing the residuals of the planetary ephemerides, fitted over the whole INPOP planetary data sample. We demonstrate that the presence of such an object is not compatible with the most sensitive data set, the Cassini radio ranging data, if its true anomaly is in the intervals $[-130^\circ:-100^\circ]$ or $[-65^\circ : 85^\circ]$. Moreover, we find that the addition of this object can reduce the Cassini residuals, with a most probable position given by a true anomaly $v = {117.8^\circ}^{ + 11^\circ}_{ - 10^\circ}$.

### Constraints on the location of a possible 9th planet derived from the Cassini data [Replacement]

To explain the unusual distribution of Kuiper Belt objects, several authors have advocated the existence of a super-Earth planet in the outer solar system. It has recently been proposed that a 10 M$_{\oplus}$ object with an orbit of 700 AU semi major axis and 0.6 eccentricity can explain the observed distribution of Kuiper Belt objects around Sedna. Here we use the INPOP planetary ephemerides model as a sensor for testing for an additional body in the solar system. We test the possibility of adding the proposed planet without increasing the residuals of the planetary ephemerides, fitted over the whole INPOP planetary data sample. We demonstrate that the presence of such an object is not compatible with the most sensitive data set, the Cassini radio ranging data, if its true anomaly is in the intervals $[-130^\circ:-100^\circ]$ or $[-65^\circ : 85^\circ]$. Moreover, we find that the addition of this object can reduce the Cassini residuals, with a most probable position given by a true anomaly $v = {117.8^\circ}^{ + 11^\circ}_{ - 10^\circ}$.

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