Programme

In this review, I will describe the technique of planetary transits to discover and study exoplanetary systems. I will provide a general summary of the various observables accessible from transit observations, develop how these have been instrumental in our current understanding of exoplanets as a population, and how they have revealed astonishing detail for several individual objects. I will highlight the most relevant successes, but also the challenges we are still working to overcome at this point.

I will review the radial-velocity method, from rough principles to current results, that highlight the continuing relevance of radial velocity measurements to exoplanetary sciences. In addition, I will show instances where radial-velocities offer information about the orbital dynamics of planetary systems.

The architecture of planetary systems is evolving significantly with time, with several mechanisms acting on different timescales: migration within the native disk, expected to occur on few Myrs before disk dissipation; planet-planet dynamical instabilities; gravitational interactions with passing bodies (more frequent for stars born in clusters) and bound companions on wide orbits (through, e.g., the Kozai mechanisms), and circularization of the orbit by tides from the host stars, which could be active on much longer timescales. Understanding the original configurations of the systems and the timescales on which these various mechanisms work is easier when observing planetary systems at young ages, with planets closer to their formation time and possibly also to their birthsites. We will present the emerging results from the study young planetary systems in the framework of the GAPS program ongoing with HARPS-N at TNG and other instruments. We will focus our attention on young multi-planet systems discovered with transits or radial velocity technique and to systems with transiting planets for which additional diagnostics to constrain the system architecture are available (e.g. spin-orbit angle from Rossiter effect). In the study of such young systems, intrinsic stellar variability typically represents the dominant noise source. We will describe the tools for handling magnetic activity simultaneously to radial velocity orbit and/or transit fit which were developed and routinely used in the context of the project.

I present a new very powerful, free, and fast GUI exoplanet toolbox called "Exo-Striker". The tool analyzes exoplanet orbitals, performs N-body simulations, and models the RV stellar reflex motion caused by dynamically interacting planets in multi-planetary systems. It offers a broad range of tools for detailed analysis of transit and Doppler data, including power spectrum analysis for Doppler and transit data; Keplerian and dynamical modeling of multi-planet systems; MCMC and nested sampling; Gaussian Processes modeling; and a long-term stability check of multi-planet systems. The Exo-Striker can also perform Mean Motion Resonance (MMR) analysis, create fast fully interactive plots, and export ready-to-use LaTeX tables with best-fit parameters, errors, and statistics. The Exo-Striker also offers instant online access to the "RVBank" database with over 212 000 RVs and activity indices of about HARPS 3000 stars, and over 64 000 RVs and activity indices of about HIRES 1700 stats. It combines Fortran efficiency and Python flexibility and is cross-platform compatible (MAC OS, Linux, Windows).

All of the fundamental properties of exoplanetary systems known to date (e.g., masses, radii, periods, eccentricities) rely on analyses that are largely inhomogeneous and difficult to update as new data arrives. This complicates their interpretation at several levels, from population studies to up-to-date ephemerides (critical for, e.g., observation scheduling aimed at atmospheric characterization). In this talk, I will present our current efforts on building the foundation for an online cloud-computing service, whose objective is to automatize this process, effectively creating an up-to-date online census of exoplanetary systems that researchers will be able to either use to retrieve up-to-date exoplanetary properties, or use for their own analyses without the need to rely on local (and costly to maintain) high-performance servers.

The orbits and dynamics of exoplanet systems can unveil their tales of formation, migration, interactions with their host star, and even their atmospheric properties. Nowadays, TESS delivers an unprecedented wealth of new data on this matter, but how can we handle all of it? Here, I will present how we can untangle exoplanets' orbits and dynamics using allesfitter, an open-source python software for flexible and robust inference of stars and exoplanets from photometric and radial velocity data. Allesfitter offers a rich selection of orbital and transit/eclipse models, accommodating multiple exoplanets, multi-star systems, transit-timing variations, phase curves. It can also help mitigate "unwanted signals", such as stellar variability, starspots, and stellar flares (or help study them). I will highlight some of allesfitter's science output on examples of exoplanet TTVs (e.g., TOI-216 and TOI-270) and orbital phase curves (e.g., WASP-18 and WASP-121). With TESS' extended mission, a wealth of new data soon face us, allowing TTV and phase curve studies of dozens of such systems over many years.

Ultra-short period planets provide a look at the inner edge of the allowed parameter space for planetary orbits. One particularly intriguing geometry of system containing ultra-short period planets is high multiplicity systems where the ultra-short period planet and the outer planets exist in two different dynamical states. This has manifested in the observational data as a small number of stars hosting systems of tightly packed coplanar inner planets as well as an ultra-short period planet, where the orbit of the latter is misaligned relative to the mutual plane of the former. We describe two different mechanisms that can produce an ultra-short period planet that is misaligned with the rest of its compact planetary system: natural decoupling between the inner and outer system via the stellar quadrupole moment, and decoupling forced by an external companion with fine-tuned orbital parameters. These two processes operate at different timescales and can thus occur simultaneously or independently within a single system. We use the Kepler and TESS systems as examples to illustrate the dynamics of these two processes. We will also discuss the possibility of placing constraints on when ultra-short period planets in multi-planet systems arrive at their final orbital locations using the results of this work.

I will review the theory and analysis of planetary transit times for deriving orbital architecture and mass constraints on exoplanets. I will start with the information content of a transit, and how the times of transit are measured. I will then discuss the dynamical theory of transit timing variations (TTVs), giving an overview of the transit-timing signal near resonance, and its degeneracies. Photodynamics provide an improved way to model transits which show timing and duration variations. Finally, I will summarize some prior successes of transit-timing variations (TTVs), some ongoing problems to be solved.

In this talk, I will review some fundamental notions of celestial mechanics. I will discuss examples showing how the dynamical study of extrasolar systems detected by transits and radial velocities can give clues for their formation, stability, and habitability. I will show how dynamics could also provide additional constraints to the observational data.

In this talk I will review the efforts to understand the formation and evolution of co-orbital planet pairs and the challenges made in the last years to detect this exotic configurations in extrasolar systems. The particular dynamics and formation scenarios convert these this co-orbital pairs into true Rosetta stones of the planet formation and evolution processes. But detecting them and distinguishing their signals from other (more common) scenarios represents a difficult task that involves the combination of different techniques. I will review the efforts of the TROY project (www.troy-project.com) in this regard and present the results obtained so far in this exciting field.

We study the spin evolution of close-in planets in compact multi-planetary systems. The rotation period of these planets is often assumed to be synchronous with the orbital period due to tidal dissipation. Here we show that planet-planet perturbations can drive the spin of these planets into non-synchronous or even chaotic states. These asynchronous configurations are possible even for nearly circular orbits and will impact the habitability of these planets. We also present a very simple method to probe the spin dynamics from the orbital perturbations.

Observations of Tabby’s star have revealed irregular aperiodic transits and secular dimming. They also show that the transits are caused by material that is between 0.05 to 0.6 au from the star when it crosses our line of sight. This has been hypothesised to be caused by a passage of exocomets resulting from the breakup of a large planetesimal that then shears out over an elliptical orbit. Most planetesimals in evolved systems are found in belts at roughly 1 to 100 au, so in this scenario any parent body must have evolved to a highly eccentric orbit before breaking apart. One potential dynamical interaction that could cause this is the eccentric Kozai mechanism (EKM) which arises when two bodies orbiting the same host star have a significant mutual inclination. This can cause orbits to reach very high eccentricities depending on the initial conditions. This talk will first explore the parameter space of the EKM, characterising the regions where high eccentricities are reached. This analysis is then specifically applied to planetesimals around Tabby’s star, which is observed to have a distant M dwarf companion that could act as an inclined perturber. The feasibility of this scenario is assessed, and the likely location of any initial parent belt is also found.

I will give an overview of the N-body code REBOUND and the various symplectic, non-symplectic, and hybrid integrators it includes: WHFast, IAS15, Mercurius, JANUS. I will present several examples of how REBOUND can be used to constrain the current dynamical state as well as the past and future evolution of observed exoplanetary systems. I will highlight the importance of fully reproducible N-body simulations and present some best practices on sharing initial conditions and posterior distributions involving N-body simulations. This will be an interactive presentation where the audience can follow along in a Jupyter Notebook.

We implement a new Bayesian neural network that can accurately predict the instability timescale in compact multiplanet systems. Unlike previous ML algorithms, this model produces accurate error bars on its predictions, and predicts the time of instability rather than classifying stable-or-unstable. On resonant systems, it beats analytical estimates by over 300%, other ML algorithms by over 35%, and is up to five orders of magnitude faster than a numerical integrator. It approaches a limit set by chaos. Despite being trained on 3-planet cases, we show generalization to 5-planet data. While current ML techniques rely on hand-chosen metrics, this algorithm uses raw orbital elements and learns its own instability metrics from time series data. We will also comment on ongoing interpretation work on this trained model; and about what the learned features rely on.

A number of giant-planet pairs with period ratios <~2 discovered by the radial velocity (RV) method may reside in mean motion resonances. Convergent orbital migration and resonant capture at the time of formation would naturally explain the present-day resonant orbital configurations of these systems. Planets that experience smooth migration and eccentricity-damping forces due to a protoplanetary disk should not only be captured into mean motion resonances but also end up in specific dynamical configurations within the resonance, sometimes referred to as apsidal corotation resonances (ACRs). I will describe a method to fit RV data in order to test whether planet pairs reside in these special configurations. The results of these fits can be used to draw conclusions about the migration histories of resonant planets.

Gabriel de Oliveira Gomes - Tidally-induced TTVs for close-in super-Earths

Tyler A. Gordon - Multi-wavelength Gaussian Process Noise Models for Transiting Exoplanets - Withdrawn

Antoine Thuillier - Facing how exoplanets evolve

Computing the orbital properties of directly imaged planets presents unique challenges compared to planets detected via other methods. With orbital periods decades to centuries long, we can only hope to map a small fraction of the planets' orbits in a reasonable amount of time. Given the limited orbital phase coverage, obtaining precise positional measurements for directly imaged planets is critical for inferring any orbital information. I will review the current methods for achieving high precision astrometric measurements in high contrast observations. I will then discuss methods for deriving orbital parameters and lessons learned from working with highly undersampled orbits.

Exoplanet host stars exhibit positional changes caused by the orbiting companion that can in principle be detected with the help of astrometric measurements in an absolute reference frame. This orbital motion is superimposed to parallax and proper motion but usually is much smaller in amplitude. We will describe the basic principles of the astrometry technique for exoplanet characterisation, discuss the typical amplitudes of exoplanet host stars in the context of available instrumentation, and highlight results of relevance for dynamical studies. We will show how the Gaia mission is about to add astrometry to the mainstream of exoplanet characterisation techniques and conclude with an outlook to future developments in this field.

Dynamical studies can be performed once planetary systems are detected. I will make a quick review on the techniques that allow detection of multiplanets. When a planetary system is detected, dynamical studies can be essentially divided in two groups : 1) those directly trying to explain observed dynamical effects, and 2) those where dynamics can be used to explain the history and state of the system. I'll review the kind of system (with example) that fall into these categories which shall be helpful in planning for theoretical study programs that are meaningful to current observational capabilities.

The census of stellar and substellar companions of nearby stars is largely incomplete, in particular toward the low-mass brown dwarf and long-period exoplanets. It is, however, fundamentally important in the understanding of the stellar and planetary formation and evolution mechanisms. Orbiting secondary bodies influence the proper motion of their parent star through their gravitational reflex motion. Using the Hipparcos and Gaia DR2 catalogs, we determined the long-term proper motion of the stars common to these two catalogs. We then searched for a proper motion anomaly (PMa) between the long-term proper motion vector and the GDR2 (or Hipparcos) measurements, indicative of the presence of a perturbing secondary object. The PMa allows us to detect orbiting companions down to planetary masses, or set stringent limits on their presence. The detection of tangential velocity anomalies at a median accuracy of sigma(Delta v_tan)=1.0 m/s per parsec of distance is already possible with the GDR2.

The present-day orbital architecture of planetary systems encode information about their formation history and dynamical evolution. Outer gas giants with large eccentricities and/or mutual inclinations can be responsible for limiting the masses and orbits on which inner super-earth forms, can excite their eccentricities and mutual inclinations, and can drive tidal migration leading to the orbital configuration we observe today. Measuring the inclinations of multi-planet systems has only been done for a handful of systems to-date, and only a small subset of these have a measured and significant mutual inclination. Combining Gaia astrometry with radial velocities will allow us to make these measurements for a larger number of systems. We have demonstrated this combination in our recent analysis of the pi Mensae system. This system hosts a super-earth discovered with TESS on a 6.3 day orbit, and a wide-orbit super-jupiter on a 5.7 year, moderately eccentric (e~0.6) orbit. Using absolute astrometry of the host star from Hipparcos and Gaia, we directly measured the inclination of the outer planet and a significant mutual inclination between the two orbital planes of approximately 40 degrees. The current system configuration is consistent with the scenario where the inner planet formed at a wider separation and underwent high eccentricity tidal migration caused by the Kozai-Lidov cycles induced by the outer eccentric companion.

Upsilon Andromedae hosts a multi-planet system that includes one potential direct imaging target for the Nancy Grace Roman Space Telescope Coronagraph Instrument (CGI). We have used the published orbit of Ups And d to inform a radiative transfer model of its atmosphere, and then predicted the most favorable range of dates for future CGI observations. Ups And d is a rare example of a reflected-light direct imaging target with a complete set of orbital elements. This orbit estimate, originally published in 2010, was established through a combined fit to radial velocities and HST Fine Guidance Sensor reflex-motion astrometry. Similar Gaia detections of the orbits of known RV planets could greatly enhance both the planning accuracy, and the scientific return, of reflected-light exoplanet observations with CGI. To further illustrate the kinds of observations that might be attained in the event that CGI graduates from a successful technology demonstration into a later phase of scientific operations, we present the results of the recently completed Exoplanet Imaging Data Challenge. In this exercise, participants analyzed simulated Roman CGI imaging data and radial velocities to estimate the orbits, masses, and geometric albedos of three fictitious exoplanets, in the presence of speckle noise, exozodiacal light, and background confusion.

The eccentricity of a planet's orbit and the inclination of its orbital plane carry important information about its formation and history. However, exoplanets detected via direct-imaging are often only observed over a very small fraction of their period, making it challenging to perform reliable physical inferences given wide, unconstrained posteriors. The aim of this project is to investigate biases (deviation of the median and mode of the posterior from the true values of orbital parameters, and the width of their credible intervals) in the estimation of orbital parameters of directly-imaged exoplanets, particularly their eccentricities, and to define general guidelines to perform better estimations. For this, we constructed various orbits and generated mock data for each spanning around 0.5 % of the orbital period. We used the Orbits For The Impatient (OFTI) algorithm to get orbit posteriors, and compared those to the true values of the orbital parameters. We found that the inclination of the orbital plane is the parameter that most affects our estimations of eccentricity, with orbits that appear near edge-on producing eccentricity distributions skewed away from the true values, and often bi-modal. We also a degeneracy between eccentricity and inclination that makes it difficult to distinguish posteriors of face-on, eccentric orbits and edge-on, circular orbits. For the exoplanet-imaging community, we propose practical recommendations, guidelines and warnings relevant to orbit-fitting.

I present EnckeHH, an integrator for studying the gravitational dynamics of N-body systems with a dominant mass, such as the Solar System. It achieves Brouwer's Law, and is suitable for testing fundamental physics in the Solar System, or for testing models of the Solar System with various forces. In comparisons with previous versions of the Rebound integrators WHCKL and IAS15, we have achieved a significant improvement in accuracy over long time scales. Rebound has since been updated, but we have not carried out comparisons with the newest version.

Gregory Brandt - Precise Dynamical masses for the beta pictoris system

Yiting Li - Orbit fitting of exoplanets with RV and absolute astrometry

HD 113337 and HD 38529 host pairs of giant planets, a debris disc, and wide M-type stellar companions. We measure the disc orientation with resolved images from Herschel and constrain the 3-D orbits of the outer planets with radial velocity and stellar absolute astrometry from Hipparcos and Gaia DR2. Resolved disc modelling leaves degeneracy in the disc orientation, so we derive four separate planet-disc mutual inclination (Δ𝐼) solutions. The most aligned solutions give Δ𝐼 = 17-32 deg for HD 113337 and Δ𝐼 = 21-45 deg for HD 38529 (both 1𝜎). In both systems, there is a small probability (< 0.3 per cent) that the planet and disc are nearly aligned (Δ𝐼 < 3 deg). We find that the debris discs in both systems could be warped via joint influences of the outer planet and stellar companion, potentially explaining the observed misalignments. However, this explanation requires HD 113337 to be old (0.8-1.7 Gyr), whereas if young (14-21 Myr), the observed misalignment in HD 113337 could be inherited from the protoplanetary disc phase. For both systems, the inclination of the stellar spin axis is consistent with the disc and outer planet inclinations, which instead supports system-wide alignment or near alignment. High-resolution observations of the discs and improved constraints on the planetary orbits from e.g. Gaia epoch astrometry would provide firmer conclusions about the (mis)alignment status.

orbitize! is a set of open-source software tools designed to meet the evolving orbit-fitting needs of the direct imaging community. It is designed to be flexible, robust, and inherently pedagogical, with extensive tutorials navigable by orbit-fitting pro and novice alike. In this presentation, I’ll showcase the package’s current capabilities, highlighting recent additions such as the abilities to jointly fit multiple data types and account for non-Keplerian effects like planet-planet interactions. I’ll also discuss recent scientific results obtained with orbitize!, including the detection of differences in the eccentricity distributions of directly-imaged giant planets and brown dwarfs (Bowler et al 2020), the first measurement of the complete 3D angular momentum architecture of a planetary system (Bryan et al 2020), and the identification of systematic bias in posteriors derived from short orbital arcs (Ferrer Chávez et al, in prep). I will also discuss ongoing improvements and science projects, and call for community involvement in defining our collaboration’s priorities.

I will present an overview of two pillars to fitting exoplanet orbits: a calibrated measure of astrometric acceleration, and software to perform a full orbital fit. The Hipparcos-Gaia Catalog of Accelerations (HGCA) cross-calibrates data from Hipparcos and Gaia to enable their use in orbit fitting: it provides three proper motions in an inertial reference frame for 116,000 stars. I will give a very brief overview of the HGCA: its necessity, its use, and caveats to keep in mind. I will then present new open-source MCMC orbit fitting software that enables fits to Hipparcos and Gaia epoch astrometry, radial velocity, and relative astrometry. This software runs many times faster than existing packages thanks to 1) a much faster eccentric anomaly solver; 2) low-level memory management; and 3) analytic marginalization of the radial velocity zero point(s), barycenter proper motion, and parallax. I will briefly mention caveats, including on the use of Hipparcos intermediate astrometric data. I will then highlight a few results using the HGCA together with this new orbit fitting code to fit orbits to a range of planets and brown dwarfs and measure their masses.

Most exoplanets are detected on close-in orbits and are therefore submitted to tides. In particular, tides drive orbital migration, eccentricity damping, rotation and obliquity evolution. In most studies, simple tidal models are used to either calculate evolution timescales or simulate the full tidal evolution of the star-planet system. These simple tidal models are equilibrium tide models. The equilibrium tide is the deformation of the extended body resulting from the hydrostatic adjustment to the tidal perturbation. By definition, these models therefore do not account for the dynamical tide, which is a wave-like solution to the tidal perturbation. Furthermore, these simple models (like the constant time lag and the constant phase lag, very often used) rely on the hypothesis that the body considered is made of weakly viscous fluid. Of course, rocky planets are not made out weakly viscous fluid, so more realistic models should be used.

I will illustrate the need we have to go beyond these simple models to account for more realistic physics. I will discuss (1) the importance of the dynamical tide in the convective region of a Sun-like star on the early evolution of a hot jupiter and (2) the importance of considering more realistic planetary interiors on the rotation evolution of rocky planets.

Measuring the orbital parameters of directly-imaged companions faces degeneracies and/or biases because a small fraction of the orbit is typically sampled (<20%) due to their long orbital periods (>~20 yr). Precise and robust measurements of the position of the companions over time are critical. Precise measurements allow for improved orbital constraints on shorter monitoring timescales. The dedicated exoplanet imager VLT/SPHERE has allowed for precise position measurements down to ~1–3 mas, whereas the precision reached in pre-SPHERE studies was ~10 mas. This has been made possible thanks to the very high contrasts that it delivers and its good astrometric stability since it has been made available to the community. Dedicated procedures were developed to monitor the location of the star behind the coronagraph and the scale, orientation, and distortion of the images. I will present an initiative to use the SPHERE astrometric experience to improve the observing procedures and calibration strategy of the next exoplanet imaging instruments on the ELT, MICADO, HARMONI, and METIS.

Mass is one of the most important parameters for determining the true nature of an astronomical object. Yet, many published exoplanets in on-line database, such as exoplanet.eu or the NASA exoplanet archive, still lacks a measurement of their true mass, in particular those detected thanks to radial velocity (RV) variations of their host star. For those, only the minimum mass, or m sin(i), is known, owing to the insensitivity of RVs to the inclination of the detected orbit compared to the plane-of-the-sky. The mass that is given in database is generally that of an assumed edge-on system (90 degrees), but many other inclinations are likely, even extreme values closer to 0 degree (face-on configuration). In such case, the mass of the published object could be strongly underestimated, even by 1 or 2 orders of magnitude. We used a recently developed tool, called GASTON (Kiefer et al. 2019 & Kiefer 2019), to take advantage of the voluminous Gaia astrometric database, in order to constrain the inclination and true mass of several hundreds of published exoplanet candidates (Kiefer et al. 2020). In this presentation, I will present the method and report on several exoplanet candidates reclassified in the stellar domain, among which unknown brown/M-dwarf. We also confirm the planetary nature of a few tens of candidates.

We present COPAINS (Code for Orbital Parametrisation of Astrometrically Inferred New Systems), an innovative tool developed to identify new directly-imaged companions based on changes in stellar proper motions. Our procedure allows for the computation of masses and separations of hidden companions compatible with observed astrometric trends, providing a good indication of the region of the parameter space where invisible secondaries may be located. This in turn enables us to robustly select the most promising targets for direct imaging campaigns. Such an informed selection method promises to reduce the null detection rates from current programs. For systems identified via this method, a second functionality of the COPAINS tool then allows us to strongly characterise the orbit of newly-discovered companions using very limited orbital coverage from imaging observations. The calculation of dynamical masses for astrometric companions with minimal observational data offers a powerful way to circumvent the large uncertainties introduced by theoretical models in the substellar regime. Obtaining larger samples of model-independent masses for such benchmark objects will be crucial to calibrate and refine evolutionary, atmospheric and formation models for brown dwarfs and giant exoplanets.

Debris disk constitute the most observable parts of young planetary systems. They often present structures (gaps, asymmetries) that can be related to the perturbing action of inbedded planets. Resonant phenomena with planets are among the strongest phenomena that affect disks mophology and evolution. This concerns Kozai-Lidov, secular and mean-motion resonances, the latter one being the most commonly invoked. I briefly summarize the theory underlying these dynamical phenomena, and show that they can trigger the formation of eccentric rings and gaps. This concerns mean-motion as well as secular resonances. Mean-motion resonances also enhance radial planetesimal transport within the disk, such as the generation of star-grazing comets. This is a common property with Kozai-Lidov resonance, but with different statistical behaviour. This can be used to distinguish both phenomena. Planetary migration acts as a additional process that enhances the efficiency of resonant trapping. I decribe then a few specific examples of systems, including Beta Pictoris, Fomalhaut, HD106906 and HD107146 where resonant processes were invoked to explain various observational facts.

Planets are the likely responsible for gaps inside disks. However, up to date, a very small number of them have been detected, even with very performing instrument such as SPHERE. For this reason we developed analytical tools to determine which planetary architectures can explain the presence of gaps. At the same time, we cross-checked the results (masses, semi-major axis, inclinations, etc.) with detection limits obtained with SPHERE. We thus obtained the most likely configurations that, at the same time, can match the width of the gap of a particular system and the (non) detectability of the planets.

HD 100453 B is a young stellar companion on a ~ 1000 yr orbit around the primary star and its protoplanetary disk. With astrometric data covering only 1-2% of its orbit, orbital fitting algorithms are unable to derive precise constraints on the orbital elements. I will present a recent study, Gonzalez et al. 2020, where we took advantage of the disk features to complement the orbital fitting approach. We found that the most likely orbit from both the MCMC and OFTI fitting algorithms is not consistent with the observed spirals, and suggest that the orbit is eccentric.

Recently, VLTI/GRAVITY demonstrated the first detection of an exoplanet using long-baseline optical interferometry. With baselines up to 130 m, GRAVITY observations of beta Pic b and HR 8799 e have reported uncertainties down to 50 μas, and a goal of the GRAVITY instrument is to reach down to 10 μas precision. Using this 20-100x improvement over previous imaging astrometry, I will discuss the new scientific opportunities this opens us with orbit fitting analysis. Despite only seeing a small orbital arc, GRAVITY can constrain orbital elements like eccentricity within 5% of their true values with just a few measurements. Furthermore, GRAVITY will be sensitive to non-Keplerian motion due to planet-planet interactions. In known multi-planet systems, non-Keplerian motion will allow us to measure the dynamical masses of planets with relative astrometry alone, giving us another way to obtain model-independent masses. In single planet systems, GRAVITY will be able to search for unseen planets in the system due to the astrometric acceleration it imparts on the known planet. In the best case, it has the potential to be sensitive to an unseen Jupiter mass planet at 3 au. I will discuss the science potential for these cases, and the open-source tools we have developed to make these analyses possible.

A key component of characterizing multi-planet exosystems is testing the orbital stability based on the observed properties. Orbital dynamics is also a critically important component of testing habitability scenarios for terrestrial planets within the system, and can play a major role in driving the evolution of terrestrial planet climates. In this talk I will describe recent work regarding the effects of orbital dynamics on planetary habitability, including the effect of giant planets on terrestrial planet orbital stability, the maximum number of terrestrial planets dynamically allowed in the Habitable Zone, and global circulation models that demonstrate the climate impacts and water loss rates for eccentric orbits. I will discuss examples of orbital dynaimcal effects on habitability, including the HR 5183, Beta CVn, and Kepler-1649 systems. This work emphasizes the need for refining Keplerian orbits as a crucial input for climate studies and the potential impact of eccentricity on terrestrial planet surface conditions.