# Posts Tagged solar system

## Recent Postings from solar system

### The Spherically Symmetric Vacuum in Covariant $F(T) = T + \frac{\alpha}{2}T^{2} + \mathcal{O}(T^{\gamma})$ Gravity Theory [Cross-Listing]

Recently, a fully covariant version of the theory of $F(T)$ torsion gravity has been introduced (arXiv:1510.08432v2 [gr-qc]). In covariant $F(T)$ gravity the Schwarzschild solution is not a vacuum solution for $F(T)\neq T$ and therefore determining the spherically symmetric vacuum is an important open problem. Within the covariant framework we perturbatively solve the spherically symmetric vacuum gravitational equations around the Schwarzschild solution for the scenario with $F(T)=T + (\alpha/2)\, T^{2}$, representing the dominant terms in theories governed by Lagrangians analytic in the torsion scalar. From this we compute the perihelion shift correction to solar system planetary orbits as well as perturbative gravitational effects near neutron stars. This allows us to set an upper bound on the magnitude of the coupling constant, $\alpha$, which governs deviations from General Relativity. We find the bound on this nonlinear torsion coupling constant by specifically considering the uncertainty in the perihelion shift of Mercury. We also analyze a bound from a similar comparison with the periastron orbit of the binary pulsar PSR J0045-7319 as an independent check for consistency. Setting bounds on the dominant nonlinear coupling is important in determining if other effects in the solar system or greater universe could be attributable to nonlinear torsion.

### The Spherically Symmetric Vacuum in Covariant $F(T) = T + \frac{\alpha}{2}T^{2} + \mathcal{O}(T^{\gamma})$ Gravity Theory

Recently, a fully covariant version of the theory of $F(T)$ torsion gravity has been introduced (arXiv:1510.08432v2 [gr-qc]). In covariant $F(T)$ gravity the Schwarzschild solution is not a vacuum solution for $F(T)\neq T$ and therefore determining the spherically symmetric vacuum is an important open problem. Within the covariant framework we perturbatively solve the spherically symmetric vacuum gravitational equations around the Schwarzschild solution for the scenario with $F(T)=T + (\alpha/2)\, T^{2}$, representing the dominant terms in theories governed by Lagrangians analytic in the torsion scalar. From this we compute the perihelion shift correction to solar system planetary orbits as well as perturbative gravitational effects near neutron stars. This allows us to set an upper bound on the magnitude of the coupling constant, $\alpha$, which governs deviations from General Relativity. We find the bound on this nonlinear torsion coupling constant by specifically considering the uncertainty in the perihelion shift of Mercury. We also analyze a bound from a similar comparison with the periastron orbit of the binary pulsar PSR J0045-7319 as an independent check for consistency. Setting bounds on the dominant nonlinear coupling is important in determining if other effects in the solar system or greater universe could be attributable to nonlinear torsion.

### SIOUX project: a simultaneous multiband camera for exoplanet atmospheres studies

The exoplanet revolution is well underway. The last decade has seen order-of-magnitude increases in the number of known planets beyond the Solar system. Detailed characterization of exoplanetary atmospheres provide the best means for distinguishing the makeup of their outer layers, and the only hope for understanding the interplay between initial composition chemistry, temperature-pressure atmospheric profiles, dynamics and circulation. While pioneering work on the observational side has produced the first important detections of atmospheric molecules for the class of transiting exoplanets, important limitations are still present due to the lack of sys- tematic, repeated measurements with optimized instrumentation at both visible (VIS) and near-infrared (NIR) wavelengths. It is thus of fundamental importance to explore quantitatively possible avenues for improvements. In this paper we report initial results of a feasibility study for the prototype of a versatile multi-band imaging system for very high-precision differential photometry that exploits the choice of specifically selected narrow-band filters and novel ideas for the execution of simultaneous VIS and NIR measurements. Starting from the fundamental system requirements driven by the science case at hand, we describe a set of three opto-mechanical solutions for the instrument prototype: 1) a radial distribution of the optical flux using dichroic filters for the wavelength separation and narrow-band filters or liquid crystal filters for the observations; 2) a tree distribution of the optical flux (implying 2 separate foci), with the same technique used for the beam separation and filtering; 3) an exotic solution consisting of the study of a complete optical system (i.e. a brand new telescope) that exploits the chromatic errors of a reflecting surface for directing the different wavelengths at different foci.

### The Asteroid Belt as a Relic From a Chaotic Early Solar System

The orbital structure of the asteroid belt holds a record of the Solar System's dynamical history. The current belt only contains ${\rm \sim 10^{-3}}$ Earth masses yet the asteroids' orbits are dynamically excited, with a large spread in eccentricity and inclination. In the context of models of terrestrial planet formation, the belt may have been excited by Jupiter's orbital migration. The terrestrial planets can also be reproduced without invoking a migrating Jupiter; however, as it requires a severe mass deficit beyond Earth's orbit, this model systematically under-excites the asteroid belt. Here we show that the orbits of the asteroids may have been excited to their current state if Jupiter and Saturn's early orbits were chaotic. Stochastic variations in the gas giants' orbits cause resonances to continually jump across the main belt and excite the asteroids' orbits on a timescale of tens of millions of years. While hydrodynamical simulations show that the gas giants were likely in mean motion resonance at the end of the gaseous disk phase, small perturbations could have driven them into a chaotic but stable state. The gas giants' current orbits were achieved later, during an instability in the outer Solar System. Although it is well known that the present-day Solar System exhibits chaotic behavior, our results suggest that the early Solar System may also have been chaotic.

### ET Probes: Looking Here as Well as There [Cross-Listing]

Almost all SETI searches to date have explicitly targeted stars in the hope of detecting artificial radio or optical transmissions. It is argued that extra-terrestrials (ET) might regard sending physical probes to our own Solar System as a more efficient means for sending large amounts of information to Earth. Probes are more efficient in terms of energy and time expenditures; may solve for the vexing problem of Drake's L factor term, namely, that the civilization wishing to send information may not coexist temporally with the intended recipient; and they alleviate ET's reasonable fear that the intended recipient might prove hostile. It is argued that probes may be numerous and easier to find than interstellar beacons.

### Solar System constraints on Renormalization Group extended General Relativity: The PPN and Laplace-Runge-Lenz analyses with the external potential effect

General Relativity extensions based on Renormalization Group effects are motivated by a known physical principle and constitute a class of extended gravity theories that have some unexplored unique aspects. In this work we develop in detail the Newtonian and post Newtonian limits of a realisation called Renormalization Group extended General Relativity (RGGR). Special attention is taken to the external potential effect, which constitutes a type of screening mechanism typical of RGGR. In the Solar System, RGGR depends on a single dimensionless parameter $\bar \nu_\odot$, and this parameter is such that for $\bar \nu_\odot = 0$ one fully recovers GR in the Solar System. Previously this parameter was constrained to be $|\bar \nu_\odot| \lesssim 10^{-21}$, without considering the external potential effect. Here we show that under a certain approximation RGGR can be cast in a form compatible with the Parametrised Post-Newtonian (PPN) formalism, and we use both the PPN formalism and the Laplace-Runge-Lenz technique to put new bounds on $\bar \nu_\odot$, either considering or not the external potential effect. With the external potential effect the new bound reads $|\bar \nu_\odot| \lesssim 10^{-16}$. We discuss the possible consequences of this bound to the dark matter abundance in galaxies.

### Atmospheric characterization of Proxima b by coupling the SPHERE high-contrast imager to the ESPRESSO spectrograph

Context. The temperate Earth-mass planet Proxima b is the closest exoplanet to Earth and represents what may be our best ever opportunity to search for life outside the Solar System. Aims. We aim at directly detecting Proxima b and characterizing its atmosphere by spatially resolving the planet and obtaining high-resolution reflected-light spectra. Methods. We propose to develop a coupling interface between the SPHERE high-contrast imager and the new ESPRESSO spectrograph, both installed at ESO VLT. The angular separation of 37 mas between Proxima b and its host star requires the use of visible wavelengths to spatially resolve the planet on a 8.2-m telescope. At an estimated planet-to-star contrast of ~10^-7 in reflected light, Proxima b is extremely challenging to detect with SPHERE alone. The use of the high-contrast/high-resolution technique can overcome present limitations by combining a ~10^3-10^4 contrast enhancement from SPHERE to a ~10^4 gain from ESPRESSO. Results. We find that significant but realistic upgrades to SPHERE and ESPRESSO would enable a 5-sigma detection of the planet and yield a measurement of its true mass and albedo in 20-40 nights of telescope time, assuming an Earth-like atmospheric composition. Moreover, it will be possible to probe the O2 bands at 627, 686 and 760 nm, the water vapour band at 717 nm, and the methane band at 715 nm. In particular, a 3.6-sigma detection of O2 could be made in about 60 nights of telescope time. Those would need to be spread over 3 years considering optimal observability conditions for the planet. Conclusions. The very existence of Proxima b and the SPHERE-ESPRESSO synergy represent a unique opportunity to detect biosignatures on an exoplanet in the near future. It is also a crucial pathfinder experiment for the development of Extremely Large Telescopes and their instruments (abridged).

### The imprint of exoplanet formation history on observable present-day spectra of hot Jupiters

The composition of a planet's atmosphere is determined by its formation, evolution, and present-day insolation. A planet's spectrum therefore may hold clues on its origins. We present a "chain" of models, linking the formation of a planet to its observable present-day spectrum. The chain links include (1) the planet's formation and migration, (2) its long-term thermodynamic evolution, (3) a variety of disk chemistry models, (4) a non-gray atmospheric model, and (5) a radiometric model to obtain simulated spectroscopic observations with JWST and ARIEL. In our standard chemistry model the inner disk is depleted in refractory carbon as in the Solar System and in white dwarfs polluted by extrasolar planetesimals. Our main findings are: (1) Envelope enrichment by planetesimal impacts during formation dominates the final planetary atmospheric composition of hot Jupiters. We investigate two, under this finding, prototypical formation pathways: a formation inside or outside the water iceline, called "dry" and "wet" planets, respectively. (2) Both the "dry" and "wet" planets are oxygen-rich (C/O<1) due to the oxygen-rich nature of the solid building blocks. The "dry" planet's C/O ratio is <0.2 for standard carbon depletion, while the "wet" planet has typical C/O values between 0.1 and 0.5 depending mainly on the clathrate formation efficiency. Only non-standard disk chemistries without carbon depletion lead to carbon-rich C/O ratios >1 for the "dry" planet. (3) While we consistently find C/O ratios <1, they still vary significantly. To link a formation history to a specific C/O, a better understanding of the disk chemistry is thus needed.

### Late veneer and late accretion to the terrestrial planets

It is generally accepted that silicate-metal (rocky') planet formation relies on coagulation from a mixture of sub-Mars sized planetary embryos and (smaller) planetesimals that dynamically emerge from the evolving circum-solar disc in the first few million years of our Solar System. Once the planets have, for the most part, assembled after a giant impact phase, they continue to be bombarded by a multitude of planetesimals left over from accretion. Here we place limits on the mass and evolution of these planetesimals based on constraints from the highly siderophile element (HSE) budget of the Moon. Outcomes from a combination of N-body and Monte Carlo simulations of planet formation lead us to four key conclusions about the nature of this early epoch. First, matching the terrestrial to lunar HSE ratio requires either that the late veneer on Earth consisted of a single lunar-size impactor striking the Earth before 4.45 Ga, or that it originated from the impact that created the Moon. An added complication is that analysis of lunar samples indicates the Moon does not preserve convincing evidence for a late veneer like Earth. Second, the expected chondritic veneer component on Mars is 0.06 weight percent. Third, the flux of terrestrial impactors must have been low ( <=10^(-6) M_earth/Myr) to avoid wholesale melting of Earth's crust after 4.4~Ga, and to simultaneously match the number of observed lunar basins. This conclusion leads to an Hadean eon which is more clement than assumed previously. Last, after the terrestrial planets had fully formed, the mass in remnant planetesimals was ~10^(-3) M_earth, lower by at least an order of magnitude than most previous models suggest. Our dynamically and geochemically self-consistent scenario requires that future N-body simulations of rocky planet formation either directly incorporate collisional grinding or rely on pebble accretion.

### Prometheus Induced Vorticity In Saturns F Ring

Saturns rings are known to show remarkable real time variability in their structure. Many of which can be associated to interactions with nearby moons and moonlets. Possibly the most interesting and dynamic place in the rings, probably in the whole Solar System, is the F ring. A highly disrupted ring with large asymmetries both radially and azimuthally. Numerically non zero components to the curl of the velocity vector field (vorticity) in the perturbed area of the F ring post encounter are witnessed, significantly above the background vorticity. Within the perturbed area rich distributions of local rotations is seen located in and around the channel edges. The gravitational scattering of ring particles during the encounter causes a significant elevated curl of the vector field above the background F ring vorticity for the first 1-3 orbital periods post encounter. After 3 orbital periods vorticity reverts quite quickly to near background levels. This new found dynamical vortex life of the ring will be of great interest to planet and planetesimals in proto-planetary disks where vortices and turbulence are suspected of having a significant role in their formation and migrations. Additionally, it is found that the immediate channel edges created by the close passage of Prometheus actually show high radial dispersions in the order ~20-50 cm/s, up to a maximum of 1 m/s. This is much greater than the value required by Toomre for a disk to be unstable to the growth of axisymmetric oscillations. However, an area a few hundred km away from the edge shows a more promising location for the growth of coherent objects.

### Numerical integration of dynamical systems with Lie series: Relativistic acceleration and non-gravitational forces

The integration of the equations of motion in gravitational dynamical systems -- either in our Solar System or for extra-solar planetary system -- being non integrable in the global case, is usually performed by means of numerical integration. Among the different numerical techniques available for solving ordinary differential equations, the numerical integration using Lie series has shown some advantages. In its original form (Hanslmeier 1984), it was limited to the N-body problem where only gravitational interactions are taken into account. We present in this paper a generalisation of the method by deriving an expression of the Lie-terms when other major forces are considered. As a matter of fact, previous studies had been made but only for objects moving under gravitational attraction. If other perturbations are added, the Lie integrator has to be re-built. In the present work we consider two cases involving position and position-velocity dependent perturbations: relativistic acceleration in the framework of General Relativity and a simplified force for the Yarkovsky effect. A general iteration procedure is applied to derive the Lie series to any order and precision. We then give an application to the integration of the equation of motions for typical Near-Earth objects and planet Mercury.

### Dynamics of asteroids and near-Earth objects from Gaia Astrometry

Gaia is an astrometric mission that will be launched in spring 2013. There are many scientific outcomes from this mission and as far as our Solar System is concerned, the satellite will be able to map thousands of main belt asteroids (MBAs) and near-Earth objects (NEOs) down to magnitude < 20. The high precision astrometry (0.3-5 mas of accuracy) will allow orbital improvement, mass determination, and a better accuracy in the prediction and ephemerides of potentially hazardous asteroids (PHAs). We give in this paper some simulation tests to analyse the impact of Gaia data on known asteroids' orbit, and their value for the analysis of NEOs through the example of asteroid (99942) Apophis. We then present the need for a follow-up network for newly discovered asteroids by Gaia, insisting on the synergy of ground and space data for the orbital improvement.

### The fates of Solar system analogues with one additional distant planet

The potential existence of a distant planet ("Planet Nine") in the Solar system has prompted a re-think about the evolution of planetary systems. As the Sun transitions from a main sequence star into a white dwarf, Jupiter, Saturn, Uranus and Neptune are currently assumed to survive in expanded but otherwise unchanged orbits. However, a sufficiently-distant and sufficiently-massive extra planet would alter this quiescent end scenario through the combined effects of Solar giant branch mass loss and Galactic tides. Here, I estimate bounds for the mass and orbit of a distant extra planet that would incite future instability in systems with a Sun-like star and giant planets with masses and orbits equivalent to those of Jupiter, Saturn, Uranus and Neptune. I find that this boundary is diffuse and strongly dependent on each of the distant planet's orbital parameters. Nevertheless, I claim that instability occurs more often than not when the planet is as massive as Jupiter and harbours a semimajor axis exceeding about 300 au, or has a mass of a super-Earth and a semimajor axis exceeding about 3000 au. These results hold for orbital pericentres ranging from 100 to at least 400 au. This instability scenario might represent a common occurrence, as potentially evidenced by the ubiquity of metal pollution in white dwarf atmospheres throughout the Galaxy.

### Prospects for Characterizing the Atmosphere of Proxima Centauri b

The newly detected Earth-mass planet in the habitable zone of Proxima Centauri could potentially host life - if it has an atmosphere that supports surface liquid water. We show that thermal phase curve observations with the James Webb Space Telescope (JWST) from 5-12 microns can be used to test the existence of such an atmosphere. We predict the thermal variation for a bare rock versus a planet with 35% heat redistribution to the nightside and show that a JWST phase curve measurement can distinguish between these cases at $5\sigma$ confidence. We also consider the case of an Earth-like atmosphere, and find that the ozone 9.8 micron band could be detected with longer integration times (a few months). We conclude that JWST observations have the potential to put the first constraints on the possibility of life around the nearest star to the Solar System.

### Prospects for Characterizing the Atmosphere of Proxima Centauri b [Replacement]

The newly detected Earth-mass planet in the habitable zone of Proxima Centauri could potentially host life - if it has an atmosphere that supports surface liquid water. We show that thermal phase curve observations with the James Webb Space Telescope (JWST) from 5-12 microns can be used to test the existence of such an atmosphere. We predict the thermal variation for a bare rock versus a planet with 35% heat redistribution to the nightside and show that a JWST phase curve measurement can distinguish between these cases at $5\sigma$ confidence, assuming photon-limited precision. We also consider the case of an Earth-like atmosphere, and find that the ozone 9.8 micron band could be detected with longer integration times (a few months). We conclude that JWST observations have the potential to put the first constraints on the possibility of life around the nearest star to the Solar System.

### A 1.9 Earth radius rocky planet and the discovery of a non-transiting planet in the Kepler-20 system

Kepler-20 is a solar-type star (V = 12.5) hosting a compact system of five transiting planets, all packed within the orbital distance of Mercury in our own Solar System. A transition from rocky to gaseous planets with a planetary transition radius of ~1.6 REarth has recently been proposed by several publications in the literature (Rogers 2015;Weiss & Marcy 2014). Kepler-20b (Rp ~ 1.9 REarth) has a size beyond this transition radius, however previous mass measurements were not sufficiently precise to allow definite conclusions to be drawn regarding its composition. We present new mass measurements of three of the planets in the Kepler-20 system facilitated by 104 radial velocity measurements from the HARPS-N spectrograph and 30 archival Keck/HIRES observations, as well as an updated photometric analysis of the Kepler data and an asteroseismic analysis of the host star (MStar = 0.948+-0.051 Msun and Rstar = 0.964+-0.018 Rsun). Kepler-20b is a 1.868+0.066-0.034 REarth planet in a 3.7 day period with a mass of 9.70+1.41-1.44 MEarth resulting in a mean density of 8.2+1.5-1.3 g/cc indicating a rocky composition with an iron to silicate ratio consistent with that of the Earth. This makes Kepler-20b the most massive planet with a rocky composition found to date. Furthermore, we report the discovery of an additional non-transiting planet with a minimum mass of 19.96+3.08-3.61 MEarth and an orbital period of ~34 days in the gap between Kepler-20f (P ~ 11 days) and Kepler-20d (P ~ 78 days).

### The Moon as a Recorder of Nearby Supernovae

The lunar geological record is expected to contain a rich record of the galactic environment of the Solar System, including records of nearby (i.e. less than a few tens of parsecs) supernova explosions. This record will be composed of two principal components: (i) cosmogenic nuclei produced within, as well as radiation damage to, surface materials caused by increases in the galactic cosmic ray flux resulting from nearby supernovae; and (ii) the direct collection of supernova ejecta, likely enriched in a range of unusual and diagnostic isotopes, on the lunar surface. Both aspects of this potentially very valuable astrophysical archive will be best preserved in currently buried, but nevertheless near-surface, layers that were directly exposed to the space environment at known times in the past and for known durations. Suitable geological formations certainly exist on the Moon, but accessing them will require a greatly expanded programme of lunar exploration.

### Effective perihelion advance and potentials in a conformastatic background with magnetic field

An Exact solution of the Einstein-Maxwell field equations for a conformastatic metric with magnetized sources is study. In this context, effective potential are studied in order to understand the dynamics of the magnetic field in galaxies. We derive the equations of motion for neutral and charged particles in a spacetime background characterized by this class of solutions. In this particular case, we investigate the main physical properties of equatorial circular orbits and related effective potentials. In addition, we obtain an effective analytic expression for the perihelion advance of test particles. Our theoretical predictions are compared with the observational data calibrated with the ephemerides of the planets of the Solar system and the Moon (EPM2011). We show that, in general, the magnetic punctual mass predicts values that are in better agreement with observations than the values predicted in Einstein gravity alone.

### Isotopic enrichment of forming planetary systems from supernova pollution

Heating by short-lived radioisotopes (SLRs) such as aluminum-26 and iron-60 fundamentally shaped the thermal history and interior structure of Solar System planetesimals during the early stages of planetary formation. The subsequent thermo-mechanical evolution, such as internal differentiation or rapid volatile degassing, yields important implications for the final structure, composition and evolution of terrestrial planets. SLR-driven heating in the Solar System is sensitive to the absolute abundance and homogeneity of SLRs within the protoplanetary disk present during the condensation of the first solids. In order to explain the diverse compositions found for extrasolar planets, it is important to understand the distribution of SLRs in active planet formation regions (star clusters) during their first few Myr of evolution. By constraining the range of possible effects, we show how the imprint of SLRs can be extrapolated to exoplanetary systems and derive statistical predictions for the distribution of aluminum-26 and iron-60 based on N-body simulations of typical to large clusters (1000-10000 stars) with a range of initial conditions. We quantify the pollution of protoplanetary disks by supernova ejecta and show that the likelihood of enrichment levels similar to or higher than the Solar System can vary considerably, depending on the cluster morphology. Furthermore, many enriched systems show an excess in radiogenic heating compared to Solar System levels, which implies that the formation and evolution of planetesimals could vary significantly depending on the birth environment of their host stars.

### A parametrisation of modified gravity on nonlinear cosmological scales

Viable modifications of gravity on cosmological scales predominantly rely on screening mechanisms to recover Einstein's Theory of General Relativity in the Solar System, where it has been well tested. A parametrisation of the effects of such modifications in the spherical collapse model is presented here for the use of modelling the modified nonlinear cosmological structure. The formalism allows an embedding of the different screening mechanisms operating in scalar-tensor theories through large values of the gravitational potential or its first or second derivatives as well as of linear suppression effects or more general transitions between modified and Einstein gravity limits. Each screening or suppression mechanism is parametrised by a time, mass, and environment dependent screening scale, an effective modified gravitational coupling in the fully unscreened limit that can be matched to linear theory, the exponent of a power-law radial profile of the screened coupling, determined by derivatives, symmetries, and potentials in the scalar field equation, and an interpolation rate between the screened and unscreened limits. Along with generalised perturbative methods, the parametrisation may be used to formulate a nonlinear extension to the linear parametrised post-Friedmannian framework to enable generalised tests of gravity with the wealth of observations from the nonlinear cosmological regime.

### A parametrisation of modified gravity on nonlinear cosmological scales [Cross-Listing]

Viable modifications of gravity on cosmological scales predominantly rely on screening mechanisms to recover Einstein's Theory of General Relativity in the Solar System, where it has been well tested. A parametrisation of the effects of such modifications in the spherical collapse model is presented here for the use of modelling the modified nonlinear cosmological structure. The formalism allows an embedding of the different screening mechanisms operating in scalar-tensor theories through large values of the gravitational potential or its first or second derivatives as well as of linear suppression effects or more general transitions between modified and Einstein gravity limits. Each screening or suppression mechanism is parametrised by a time, mass, and environment dependent screening scale, an effective modified gravitational coupling in the fully unscreened limit that can be matched to linear theory, the exponent of a power-law radial profile of the screened coupling, determined by derivatives, symmetries, and potentials in the scalar field equation, and an interpolation rate between the screened and unscreened limits. Along with generalised perturbative methods, the parametrisation may be used to formulate a nonlinear extension to the linear parametrised post-Friedmannian framework to enable generalised tests of gravity with the wealth of observations from the nonlinear cosmological regime.

### The population of long-period transiting exoplanets

The Kepler Mission has discovered thousands of exoplanets and revolutionized our understanding of their population. This large, homogeneous catalog of discoveries has enabled rigorous studies of the occurrence rate of exoplanets and planetary systems as a function of their physical properties. However, transit surveys like Kepler are most sensitive to planets with orbital periods much shorter than the orbital periods of Jupiter and Saturn, the most massive planets in our Solar System. To address this deficiency, we perform a fully automated search for long-period exoplanets with only one or two transits in the archival Kepler light curves. When applied to the $\sim 40,000$ brightest Sun-like target stars, this search produces 16 long-period exoplanet candidates. Of these candidates, 6 are novel discoveries and 5 are in systems with inner short-period transiting planets. Since our method involves no human intervention, we empirically characterize the detection efficiency of our search. Based on these results, we measure the average occurrence rate of exoplanets smaller than Jupiter with orbital periods in the range 2-25 years to be $2.0\pm0.7$ planets per Sun-like star.

### Cometary ices in forming protoplanetary disc midplanes

Low-mass protostars are the extrasolar analogues of the natal Solar System. Sophisticated physicochemical models are used to simulate the formation of two protoplanetary discs from the initial prestellar phase, one dominated by viscous spreading and the other by pure infall. The results show that the volatile prestellar fingerprint is modified by the chemistry en route into the disc. This holds relatively independent of initial abundances and chemical parameters: physical conditions are more important. The amount of CO2 increases via the grain-surface reaction of OH with CO, which is enhanced by photodissociation of H2O ice. Complex organic molecules are produced during transport through the envelope at the expense of CH3OH ice. Their abundances can be comparable to that of methanol ice (few % of water ice) at large disc radii (R > 30 AU). Current Class II disc models may be underestimating the complex organic content. Planet population synthesis models may underestimate the amount of CO2 and overestimate CH3OH ices in planetesimals by disregarding chemical processing between the cloud and disc phases. The overall C/O and C/N ratios differ between the gas and solid phases. The two ice ratios show little variation beyond the inner 10 AU and both are nearly solar in the case of pure infall, but both are sub-solar when viscous spreading dominates. Chemistry in the protostellar envelope en route to the protoplanetary disc sets the initial volatile and prebiotically-significant content of icy planetesimals and cometary bodies. Comets are thus potentially reflecting the provenances of the midplane ices in the Solar Nebula.

### Olivine on Vesta as exogenous contaminants brought by impacts: Constraints from modeling Vesta's collisional history and from impact simulations

The survival of asteroid Vesta during the violent early history of the Solar System is a pivotal constraint on theories of planetary formation. Particularly important from this perspective is the amount of olivine excavated from the vestan mantle by impacts, as this constrains both the interior structure of Vesta and the number of major impacts the asteroid suffered during its life. The NASA Dawn mission revealed that olivine is present on Vesta's surface in limited quantities, concentrated in small patches at a handful of sites and interpreted as the result of the excavation of endogenous olivine. Later works raised the possibility that the olivine had an exogenous origin, based on the geologic and spectral features of the deposits. In this work we quantitatively explore the proposed scenario of a exogenous origin for the detected olivine to investigate whether its presence on Vesta can be explained as a natural outcome of the collisional history of the asteroid. We took advantage of the impact contamination model previously developed to study the origin and amount of dark and hydrated materials observed by Dawn on Vesta, which we updated by performing dedicated hydrocode impact simulations. We show that the exogenous delivery of olivine by impacts can offer a viable explanation for the currently identified olivine-rich sites without violating the constraint posed by the lack of global olivine signatures on Vesta. Our results indicate that no mantle excavation is in principle required to explain the observations of the Dawn mission and support the idea that the vestan crust could be thicker than indicated by simple geochemical models based on the Howardite-Eucrite-Diogenite family of meteorites.

### Olivine on Vesta as exogenous contaminants brought by impacts: Constraints from modeling Vesta's collisional history and from impact simulations [Replacement]

The survival of asteroid Vesta during the violent early history of the Solar System is a pivotal constraint on theories of planetary formation. Particularly important from this perspective is the amount of olivine excavated from the vestan mantle by impacts, as this constrains both the interior structure of Vesta and the number of major impacts the asteroid suffered during its life. The NASA Dawn mission revealed that olivine is present on Vesta's surface in limited quantities, concentrated in small patches at a handful of sites and interpreted as the result of the excavation of endogenous olivine. Later works raised the possibility that the olivine had an exogenous origin, based on the geologic and spectral features of the deposits. In this work we quantitatively explore the proposed scenario of a exogenous origin for the detected olivine to investigate whether its presence on Vesta can be explained as a natural outcome of the collisional history of the asteroid. We took advantage of the impact contamination model previously developed to study the origin and amount of dark and hydrated materials observed by Dawn on Vesta, which we updated by performing dedicated hydrocode impact simulations. We show that the exogenous delivery of olivine by impacts can offer a viable explanation for the currently identified olivine-rich sites without violating the constraint posed by the lack of global olivine signatures on Vesta. Our results indicate that no mantle excavation is in principle required to explain the observations of the Dawn mission and support the idea that the vestan crust could be thicker than indicated by simple geochemical models based on the Howardite-Eucrite-Diogenite family of meteorites.

### Dynamics of Saturn's great storm of 2010-2011 from Cassini ISS and RPWS

Saturn's quasi-periodic planet-encircling storms are the largest convecting outbursts in the Solar System. The last eruption was in 1990. A new eruption started in December 2010 and presented the first-ever opportunity to observe such episodic storms from a spacecraft in orbit around Saturn. Here, we analyze images acquired with the Cassini Imaging Science Subsystem (ISS), which captured the storm's birth, evolution and demise. In studying the end of the convective activity, we also analyze the Saturn Electrostatic Discharge (SED) signals detected by the Radio and Plasma Wave Science (RPWS) instrument. [...]

### The Earth-Moon system as a typical binary in the Solar System

Solid embryos of the Earth and the Moon, as well as trans-Neptunian binaries, could form as a result of contraction of the rarefied condensation which was parental for a binary. The angular momentum of the condensation needed for formation of a satellite system could be mainly acquired at the collision of two rarefied condensations at which the parental condensation formed. The minimum value of the mass of the parental condensation for the Earth-Moon system could be about 0.02 of the Earth mass. Besides the main collision, which was followed by formation of the condensation that was a parent for the embryos of the Earth and the Moon, there could be another main collision of the parental condensation with another condensation. The second main collision (or a series of similar collisions) could change the tilt of the Earth. Depending on eccentricities of the planetesimals that collided with the embryos, the Moon could acquire 0.04-0.3 of its mass at the stage of accumulation of solid bodies while the mass of the growing Earth increased by a factor of ten.

### The analemma criterion: accidental quasi-satellites are indeed true quasi-satellites [Replacement]

In the Solar system, a quasi-satellite is an object that follows a heliocentric path with an orbital period that matches almost exactly with that of a host body (planetary or not). The trajectory is of such nature that, without being gravitationally attached, the value of the angular separation between host and quasi-satellite as seen from the Sun remains confined within relatively narrow limits for time-spans that exceed the length of the host's sidereal orbital period. Here, we show that under these conditions, a quasi-satellite traces an analemma in the sky as observed from the host in a manner similar to that found for geosynchronous orbits. The analemmatic curve (figure-eight-, teardrop-, ellipse-shaped) results from the interplay between the tilt of the rotational axis of the host and the properties of the orbit of the quasi-satellite. The analemma criterion can be applied to identify true quasi-satellite dynamical behaviour using observational or synthetic astrometry and it is tested for several well-documented quasi-satellites. For the particular case of 15810 (1994 JR1), a putative accidental quasi-satellite of dwarf planet Pluto, we show explicitly that this object describes a complex analemmatic curve for several Plutonian sidereal periods, confirming its transient quasi-satellite status.

### The analemma criterion: accidental quasi-satellites are indeed true quasi-satellites

In the Solar system, a quasi-satellite is an object that follows a heliocentric path with an orbital period that matches almost exactly that of a host body (planetary or not). The trajectory is of such nature that, without being gravitationally attached, the value of the angular separation between host and quasi-satellite as seen from the Sun remains confined within relatively narrow limits for time spans that exceed the length of the host's sidereal orbital period. Here, we show that under these conditions, a quasi-satellite traces an analemma in the sky as observed from the host in a manner similar to that found for geosynchronous orbits. The analemmatic curve (figure-eight-, teardrop-, ellipse-shaped) results from the interplay between the tilt of the rotational axis of the host and the properties of the orbit of the quasi-satellite. The analemma criterion can be applied to identify true quasi-satellite dynamical behaviour using observational or synthetic astrometry and it is tested for several well documented quasi-satellites. For the particular case of 15810 (1994 JR1), a putative accidental quasi-satellite of dwarf planet Pluto, we show explicitly that this object describes a complex analemmatic curve for several Plutonian sidereal periods, confirming its transient quasi-satellite status.

### Surveying the Inner Solar System with an Infrared Space Telescope

We present an analysis of surveying the inner Solar System for objects that may pose some threat to the Earth. Most of the analysis is based on understanding the capability provided by Sentinel, a concept for an infrared space-based telescope placed in a heliocentric orbit near the distance of Venus. From this analysis, we show 1) the size range being targeted can affect the survey design, 2) the orbit distribution of the target sample can affect the survey design, 3) minimum observational arc length during the survey is an important metric of survey performance, and 4) surveys must consider objects as small as D=15-30 m to meet the goal of identifying objects that have the potential to cause damage on Earth in the next 100 years. Sentinel will be able to find 50% of all impactors larger than 40 meters in a 6.5 year survey. The Sentinel mission concept is shown to be as effective as any survey in finding objects bigger than D=140 m but is more effective when applied to finding smaller objects on Earth-impacting orbits. Sentinel is also more effective at finding objects of interest for human exploration that benefit from lower propulsion requirements. To explore the interaction between space and ground search programs, we also study a case where Sentinel is combined with the Large Synoptic Survey Telescope and show the benefit of placing a space-based observatory in an orbit that reduces the overlap in search regions with a ground-based telescope. In this case, Sentinel+LSST can find more than 70% of the impactors larger than 40 meters assuming a 6.5 year lifetime for Sentinel and 10 years for LSST.

### The inclination of the planetary system relative to the solar equator may be explained by the presence of Planet 9

We evaluate the effects of a distant planet, commonly known as planet 9, on the dynamics of the giant planets of the Solar System. We find that, given the large distance of planet 9, the dynamics of the inner giant planets can be decomposed into a classic Lagrange-Laplace dynamics relative to their own invariant plane (the plane orthogonal to their total angular momentum vector) and a slow precession of said plane relative to the total angular momentum vector of the Solar System, including planet 9. Under some specific configurations for planet 9, this precession can explain the current tilt of approximately 6 degrees between the invariant plane of the giant planets and the solar equator. An analytical model is developed to map the evolution of the inclination of the inner giant planets' invariant plane as a function of the planet 9's mass, inclination, eccentricity and semimajor axis, and some numerical simulations of the equations of motion of the giant planets and planet 9 are performed to validate our analytical approach. The longitude of the ascending node of planet 9 is found to be linked to the longitude of the ascending node of the giant planets' invariant plane, which also constrain the longitude of the node of planet 9 on the ecliptic. Some of the planet 9 configurations that allow explaining the current solar tilt are compatible with those proposed to explain the orbital confinement of the most distant Kuiper belt objects. Thus, this work on the one hand gives an elegant explanation for the current tilt between the invariant plane of the inner giant planets and the solar equator and, on the other hand, adds new constraints to the orbital elements of planet 9.

### The long-term scientific benefits of a space economy

Utilisation of the material and energy resources of the Solar System will be essential for the development of a sustainable space economy and associated infrastructure. Science will be a major beneficiary of a space economy, even if its major elements (e.g. space tourism, resource extraction activities on the Moon or asteroids, and large-scale in-space construction capabilities) are not developed with science primarily in mind. Examples of scientific activities that would be facilitated by the development of space infrastructure include the construction of large space telescopes, ambitious space missions (including human missions) to the outer Solar System, and the establishment of scientific research stations on the Moon and Mars (and perhaps elsewhere). In the more distant future, an important scientific application of a well-developed space infrastructure may be the construction of interstellar space probes for the exploration of planets around nearby stars.

### New orbits of irregular satellites designed for the predictions of stellar occultations up to 2020, based on thousands of new observations

Gomes-J\'unior et al. (2015) published 3613 positions for the 8 largest irregular satellites of Jupiter and 1787 positions for the largest irregular satellite of Saturn, Phoebe. These observations were made between 1995 and 2014 and have an estimated error of about 60 to 80 mas. Based on this set of positions, we derived new orbits for the eight largest irregular satellites of Jupiter: Himalia, Elara, Pasiphae, Carme, Lysithea, Sinope, Ananke and Leda. For Phoebe we updated the ephemeris from Desmars et al. (2013) using 75% more positions than the previous one. Due to their orbital characteristics, it is common belief that the irregular satellites were captured by the giant planets in the early Solar System, but there is no consensus for a single model explaining where they were formed. Size, shape, albedo and composition would help to trace back their true origin, but these physical parameters are yet poorly known for irregular satellites. The observation of stellar occultations would allow for the determination of such parameters. Indeed Jupiter will cross the galactic plane in 2019-2020 and Saturn in 2018, improving a lot the chances of observing such events in the near future. Using the derived ephemerides and the UCAC4 catalogue we managed to identify 5442 candidate stellar occultations between January 2016 and December 2020 for the 9 satellites studied here. We discussed how the successful observation of a stellar occultation by these objects is possible and present some potential occultations.

### Lightning climatology of exoplanets and brown dwarfs guided by Solar System data

Clouds form on extrasolar planets and brown dwarfs where lightning could occur. Lightning is a tracer of atmospheric convection, cloud formation and ionization processes as known from the Solar System, and may be significant for the formation of prebiotic molecules. We study lightning climatology for the different atmospheric environments of Earth, Venus, Jupiter and Saturn. We present lightning distribution maps for Earth, Jupiter and Saturn, and flash densities for these planets and Venus, based on optical and/or radio measurements from the WWLLN and STARNET radio networks, the LIS/OTD satellite instruments, the Galileo, Cassini, New Horizons and Venus Express spacecraft. We also present flash densities calculated for several phases of two volcano eruptions, Eyjafjallaj\"okull's (2010) and Mt Redoubt's (2009). We estimate lightning rates for sample, transiting and directly imaged extrasolar planets and brown dwarfs. Based on the large variety of exoplanets, six categories are suggested for which we use the lightning occurrence information from the Solar System. We examine lightning energy distributions for Earth, Jupiter and Saturn. We discuss how strong stellar activity may support lightning activity. We provide a lower limit of the total number of flashes that might occur on transiting planets during their full transit as input for future studies. We find that volcanically very active planets might show the largest lightning flash densities. When applying flash densities of the large Saturnian storm from 2010/11, we find that the exoplanet HD 189733b would produce high lightning occurrence even during its short transit.

### Lightning climatology of exoplanets and brown dwarfs guided by Solar System data [Replacement]

Clouds form on extrasolar planets and brown dwarfs where lightning could occur. Lightning is a tracer of atmospheric convection, cloud formation and ionization processes as known from the Solar System, and may be significant for the formation of prebiotic molecules. We study lightning climatology for the different atmospheric environments of Earth, Venus, Jupiter and Saturn. We present lightning distribution maps for Earth, Jupiter and Saturn, and flash densities for these planets and Venus, based on optical and/or radio measurements from the WWLLN and STARNET radio networks, the LIS/OTD satellite instruments, the Galileo, Cassini, New Horizons and Venus Express spacecraft. We also present flash densities calculated for several phases of two volcano eruptions, Eyjafjallaj\"okull's (2010) and Mt Redoubt's (2009). We estimate lightning rates for sample, transiting and directly imaged extrasolar planets and brown dwarfs. Based on the large variety of exoplanets, six categories are suggested for which we use the lightning occurrence information from the Solar System. We examine lightning energy distributions for Earth, Jupiter and Saturn. We discuss how strong stellar activity may support lightning activity. We provide a lower limit of the total number of flashes that might occur on transiting planets during their full transit as input for future studies. We find that volcanically very active planets might show the largest lightning flash densities. When applying flash densities of the large Saturnian storm from 2010/11, we find that the exoplanet HD 189733b would produce high lightning occurrence even during its short transit.

### Lightning climatology of exoplanets and brown dwarfs guided by Solar System data [Replacement]

Clouds form on extrasolar planets and brown dwarfs where lightning could occur. Lightning is a tracer of atmospheric convection, cloud formation and ionization processes as known from the Solar System, and may be significant for the formation of prebiotic molecules. We study lightning climatology for the different atmospheric environments of Earth, Venus, Jupiter and Saturn. We present lightning distribution maps for Earth, Jupiter and Saturn, and flash densities for these planets and Venus, based on optical and/or radio measurements from the WWLLN and STARNET radio networks, the LIS/OTD satellite instruments, the Galileo, Cassini, New Horizons and Venus Express spacecraft. We also present flash densities calculated for several phases of two volcano eruptions, Eyjafjallaj\"okull's (2010) and Mt Redoubt's (2009). We estimate lightning rates for sample, transiting and directly imaged extrasolar planets and brown dwarfs. Based on the large variety of exoplanets, six categories are suggested for which we use the lightning occurrence information from the Solar System. We examine lightning energy distributions for Earth, Jupiter and Saturn. We discuss how strong stellar activity may support lightning activity. We provide a lower limit of the total number of flashes that might occur on transiting planets during their full transit as input for future studies. We find that volcanically very active planets might show the largest lightning flash densities. When applying flash densities of the large Saturnian storm from 2010/11, we find that the exoplanet HD 189733b would produce high lightning occurrence even during its short transit.

### Cosmic ray interactions in the solar system: The Gerasimova-Zatsepin effect [Replacement]

The Gerasimova-Zatsepin effect of collisions of ultra-high-energy cosmic ray nuclei with photons emitted by the sun may cause two simultaneous air showers on Earth. This effect is simulated using the full energy spectrum of solar photons, ray tracing through the interplanetary magnetic field and upper limit values for the iron and oxygen cosmic ray fluxes. Only the most abundant interactions in which a single proton is emitted from the nucleus are considered. For the first time the distributions of distances between the individual showers at Earth as a function of the distance of the primary cosmic ray to the Sun are shown. These distributions are used to estimate the capabilities of current detector arrays to measure the Gerasimova-Zatsepin effect and to show that a dedicated array is capable of measuring this effect.

### Cosmic ray interactions in the solar system: The Gerasimova-Zatsepin effect [Replacement]

The Gerasimova-Zatsepin effect of collisions of ultra-high-energy cosmic ray nuclei with photons emitted by the sun may cause two simultaneous air showers on Earth. This effect is simulated using the full energy spectrum of solar photons, ray tracing through the interplanetary magnetic field and upper limit values for the iron and oxygen cosmic ray fluxes. Only the most abundant interactions in which a single proton is emitted from the nucleus are considered. For the first time the distributions of distances between the individual showers at Earth as a function of the distance of the primary cosmic ray to the Sun are shown. These distributions are used to estimate the capabilities of current detector arrays to measure the Gerasimova-Zatsepin effect and to show that a dedicated array is capable of measuring this effect.

### A Unified Framework for Producing CAI Melting, Wark-Lovering Rims and Bowl-Shaped CAIs

Calcium Aluminium Inclusions (CAIs) formed in the Solar System, some 4,567 million years ago. CAIs are almost always surrounded by Wark-Lovering Rims (WLRs), which are a sequence of thin, mono/bi-mineralic layers of refractory minerals, with a total thickness in the range of 1 to 100 microns. Recently, some CAIs have been found that have tektite-like bowl-shapes. To form such shapes, the CAI must have travelled through a rarefied gas at hypersonic speeds. We show how CAIs may have been ejected from the inner solar accretion disc via the centrifugal interaction between the solar magnetosphere and the inner disc rim. They subsequently punched through the hot, inner disc rim wall at hypersonic speeds. This re-entry heating partially or completely evaporated the CAIs. Such evaporation could have significantly increased the metal abundances of the inner disc rim. High speed movement through the inner disc produced WLRs. To match the observed thickness of WLRs required metal abundances at the inner disc wall that are of order ten times that of standard solar abundances. The CAIs cooled as they moved away from the protosun, the deduced CAI cooling rates are consistent with the CAI cooling rates obtained from experiment and observation. The speeds and gas densities required to form bowl-shaped CAIs are also consistent with the expected speeds and gas densities for larger, ~ 1 cm, CAIs punching through an inner accretion disc wall.

### The Origin of Chaos in the Orbit of Comet 1P/Halley

According to Munoz-Gutierrez et al. (2015) the orbit of comet 1P/Halley is chaotic with a surprisingly small Lyapunov time scale of order its orbital period. In this work we analyse the origin of chaos in Halley's orbit and the growth of perturbations, in order to get a better understanding of this unusually short time scale. We perform N-body simulations to model Halley's orbit in the Solar System and measure the separation between neighbouring trajectories. To be able to interpret the numerical results, we use a semi-analytical map to demonstrate different growth modes, i.e. linear, oscillatory or exponential, and transitions between these modes. We find the Lyapunov time scale of Halley's orbit to be of order 300 years, which is significantly longer than previous estimates in the literature. This discrepancy could be due to the different methods used to measure the Lyapunov time scale. A surprising result is that next to Jupiter, also encounters with Venus contribute to the exponential growth in the next 3000 years. Finally, we note an interesting application of the sub-linear, oscillatory growth mode to an ensemble of bodies moving through the Solar System. Whereas in the absence of encounters with a third body the ensemble spreads out linearly in time, the accumulation of weak encounters can increase the lifetime of such systems due to the oscillatory behaviour.

Comets are considered as the most primitive objects in the Solar System. Their composition provides information on the composition of the primitive solar nebula, 4.6 Gyr ago. The radio domain is a privileged tool to study the composition of cometary ices. Observations of the OH radical at 18 cm wavelength allow us to measure the water production rate. A wealth of molecules (and some of their isotopologues) coming from the sublimation of ices in the nucleus have been identified by observations in the millimetre and submillimetre domains. We present an historical review on radio observations of comets, focusing on the results from our group, and including recent observations with the Nan\c{c}ay radio telescope, the IRAM antennas, the Odin satellite, the Herschel space observatory, ALMA, and the MIRO instrument aboard the Rosetta space probe.

### New Hamiltonian expansions adapted to the Trojan problem

A number of studies, referring to the observed Trojan asteroids of various planets in our Solar System, or to hypothetical Trojan bodies in extrasolar planetary systems, have emphasized the importance of so-called secondary resonances in the problem of the long term stability of Trojan motions. Such resonances describe commensurabilities between the fast, synodic, and secular frequency of the Trojan body, and, possibly, additional slow frequencies produced by more than one perturbing bodies. The presence of secondary resonances sculpts the dynamical structure of the phase space. Hence, identifying their location is a relevant task for theoretical studies. In the present paper we combine the methods introduced in two recent papers (Paez & Efthymiopoulos, 2015, Paez & Locatelli, 2015) in order to analytically predict the location of secondary resonances in the Trojan problem (SEE FILE FOR COMPLETE ABSTRACT)

### Kepler-108: A Mutually Inclined Giant Planet System

The vast majority of well studied giant-planet systems, including the Solar System, are nearly coplanar which implies dissipation within a primordial gas disk. however, intrinsic instability may lead to planet-planet scattering, which often produces non-coplanar, eccentric orbits. Planet scattering theories have been developed to explain observed high eccentricity systems and also hot Jupiters; thus far their predictions for mutual inclination (I) have barely been tested. Here we characterize a highly mutually-inclined (I ~ 15-60 degrees), moderately eccentric (e >~ 0.1) giant planet system: Kepler-108. This system consists of two approximately Saturn-mass planets with periods of ~49 and ~190 days around a star with a wide (~300AU) binary companion in an orbital configuration inconsistent with a purely disk migration origin.

### Magnitude and timing of the giant planet instability: A reassessment from the perspective of the asteroid belt

It is generally accepted today that our solar system has undergone a phase during which the orbits of the giant planets became very unstable. In recent years, many studies have identified traces of this event and have provided reasonable justification for this occurrence. The magnitude (in terms of orbital variation) and the timing of the instability though (early or late with respect to the dispersal of the gas disk) still remains an open debate. The terrestrial planets seem to set a strict constraint: either the giant planet instability happened early, while the terrestrial planets were still forming, or the orbits of Jupiter and Saturn had to separate from each other impulsively, with a large enough jump' in semimajor axis (Brasser et al. 2009; Kaib and Chambers 2016) for the terrestrial planets to remain stable. Because a large orbital jump is a low probability event, the early instability hypothesis seems to be favored. However, the asteroid belt would also evolve in a different way, assuming different instability amplitudes. These two constraints need to match each other in order to favor one scenario over the other. Considering an initially dynamically cold disk of asteroids, Morbidelli et al. (2010) concluded that a comparably large jump is needed to reconstruct the current asteroid belt. Here we confirm the same conclusion, but considering an asteroid population already strongly excited in eccentricity, such as that produced in the Grand Tack scenario (Walsh et al. 2011). Because the asteroids existed since the time of removal of the gas disk, unlike the terrestrial planets, this constraint on the width of the giant planet jump is valid regardless of whether the instability happened early or late. Hence, at this stage, assuming an early instability does not appear to provide any advantage in terms of the probabilistic reconstruction of the solar system structure.

### Variational Principle for Planetary Interiors

In the past few years, the number of confirmed planets has grown above 2000. It is clear that they represent a diversity of structures not seen in our own solar system. In addition to very detailed interior modeling, it is valuable to have a simple analytical framework for describing planetary structures. Variational principle is a fundamental principle in physics, entailing that a physical system follows the trajectory which minimizes its action. It is alternative to the differential equation formulation of a physical system. Applying this principle to planetary interior can beautifully summarize the set of differential equations into one, which provides us some insight into the problem. From it, a universal mass-radius relation, an estimate of error propagation from equation of state to mass-radius relation, and a form of virial theorem applicable to planetary interiors are derived.

### The Paleoclimatic evidence for Strongly Interacting Dark Matter Present in the Galactic Disk

Using a recent geochemical reconstruction of the Phanerozoic climate which exhibits a 32 Ma oscillation with a phase and the secondary modulation expected from the vertical the motion of the solar system perpendicular to the galactic plane (shaviv et al. 2014), we show that a kinematically cold strongly interacting disk dark matter (dDM) component is necessarily present in the disk. It has a local density $\rho_\mathrm{dDM} = 0.11 \pm 0.03$ M$_{\odot}/$pc$^3$. It is also consistent with the observed constraints on the total gravitating mass and the baryonic components, and it is the natural value borne from the Toomre stability criterion. It also has surface density $\Sigma_\mathrm{dDM} = 15 \pm 5$ M$_{\odot}/$pc$^2$ and a vertical velocity dispersion of $\sigma_{W} = 8.0 \pm 4.5$ km/s. A dense ("dinosaur killing") thin disk is ruled out. The "normal" halo dark matter (hDM) component should then have a local density $\rho_\mathrm{hDM} \lesssim 0.01$ M$_{\odot}/$pc$^3$. If the dDM component follows the baryons, its average density parameter is $\Omega_\mathrm{dDM} = 1.5 \pm 0.5\%$ and it comprises about 1/8 to 1/4 of Milky Way (MW) mass within the solar circle.

### The Paleoclimatic evidence for Strongly Interacting Dark Matter Present in the Galactic Disk [Cross-Listing]

Using a recent geochemical reconstruction of the Phanerozoic climate which exhibits a 32 Ma oscillation with a phase and the secondary modulation expected from the vertical the motion of the solar system perpendicular to the galactic plane (shaviv et al. 2014), we show that a kinematically cold strongly interacting disk dark matter (dDM) component is necessarily present in the disk. It has a local density $\rho_\mathrm{dDM} = 0.11 \pm 0.03$ M$_{\odot}/$pc$^3$. It is also consistent with the observed constraints on the total gravitating mass and the baryonic components, and it is the natural value borne from the Toomre stability criterion. It also has surface density $\Sigma_\mathrm{dDM} = 15 \pm 5$ M$_{\odot}/$pc$^2$ and a vertical velocity dispersion of $\sigma_{W} = 8.0 \pm 4.5$ km/s. A dense ("dinosaur killing") thin disk is ruled out. The "normal" halo dark matter (hDM) component should then have a local density $\rho_\mathrm{hDM} \lesssim 0.01$ M$_{\odot}/$pc$^3$. If the dDM component follows the baryons, its average density parameter is $\Omega_\mathrm{dDM} = 1.5 \pm 0.5\%$ and it comprises about 1/8 to 1/4 of Milky Way (MW) mass within the solar circle.

### Near Periodic solution of the Elliptic RTBP for the Jupiter Sun system [Cross-Listing]

Let us consider the elliptic restricted three body problem (Elliptic RTBP) for the Jupiter Sun system with eccentricity $e=0.048$ and $\mu=0.000953339$. Let us denote by $T$ the period of their orbits. In this paper we provide initial conditions for the position and velocity for a spacecraft such that after one period $T$ the spacecraft comes back to the same place, with the same velocity, within an error of 4 meters for the position and 0.2 meters per second for the velocity. Taking this solution as periodic, we present numerical evidence showing that this solution is stable. In order to compare this periodic solution with the motion of celestial bodies in our solar system, we end this paper by providing an ephemeris of the spacecraft motion from February 17, 2017 to December 28, 2028.

### Light propagation in the gravitational field of N arbitrarily moving bodies in the 1.5PN approximation for high-precision astrometry [Replacement]

High-precision astrometry on sub-micro-arcsecond level in angular resolution requires accurate determination of the trajectory of a light-signal from the celestial light source through the gravitational field of the Solar system toward the observer. In this investigation the light trajectory in the gravitational field of N moving bodies is determined in the 1.5 post-Newtonian approximation. In the approach presented two specific issues of particular importance are accounted for: (1) According to the recommendations of International Astronomical Union, the metric of the Solar system is expressed in terms of intrinsic mass-multipoles and intrinsic spin-multipoles of the massive bodies, allowing for arbitrary shape, inner structure and rotational motion of the massive bodies of the Solar system. (2) The Solar system bodies move along arbitrary worldlines which can later be specified by Solar system ephemeris. The presented analytical solution for light trajectory is a primary requirement for extremely high-precision astrometry on sub-micro-arcsecond level of accuracy and associated massive computations in astrometric data reduction. An estimation of the numerical magnitude for time delay and light deflection of the leading multipoles is given.

### Light propagation in the gravitational field of N arbitrarily moving bodies in the 1.5PN approximation for high-precision astrometry

High-precision astrometry on sub-micro-arcsecond level in angular resolution requires accurate determination of the trajectory of a light-signal from the celestial light source through the gravitational field of the Solar system toward the observer. In this investigation the light trajectory in the gravitational field of N moving bodies is determined in the 1.5 post-Newtonian approximation. In the approach presented two specific issues of particular importance are accounted for: (1) According to the recommendations of International Astronomical Union, the metric of the Solar system is expressed in terms of intrinsic mass-multipoles and intrinsic spin-multipoles of the massive bodies, allowing for arbitrary shape, inner structure and rotational motion of the massive bodies of the Solar system. (2) The Solar system bodies move along arbitrary worldlines which can later be specified by Solar system ephemeris. The presented analytical solution for light trajectory is a primary requirement for extremely high-precision astrometry on sub-micro-arcsecond level of accuracy and associated massive computations in astrometric data reduction. An estimation of the numerical magnitude for time delay and light deflection of the leading multipoles is given.