Crater counting on the Moon and other bodies is crucial to constrain the dynamical history of the Solar System. This has traditionally been done by visual inspection of images, thus limiting the scope, efficiency, and/or accuracy of retrieval. In this paper we demonstrate the viability of using convolutional neural networks (CNNs) to determine the positions and sizes of craters from Lunar digital elevation maps (DEMs). We recover 92% of craters from the human-generated test set and almost double the total number of crater detections. Of these new craters, 15% are smaller in diameter than the minimum crater size in the ground-truth dataset. Our median fractional longitude, latitude and radius errors are 11% or less, representing good agreement with the human-generated datasets. From a manual inspection of 361 new craters we estimate the false positive rate of new craters to be 11%. Moreover, our Moon-trained CNN performs well when tested on DEM images of Mercury, detecting a large fraction of craters in each map. Our results suggest that deep learning will be a useful tool for rapidly and automatically extracting craters on various Solar System bodies. We make our code and data publicly available at https://github.com/ silburt/DeepMoon.git and https://doi.org/10.5281/zenodo.1133969.

Using the cumulative catalog of planets detected by the NASA Kepler mission, we reconstruct the intrinsic occurrence of Earth-to Neptune-size (1 -4R ⊕ ) planets and their distributions with radius and orbital period. We analyze 76,711 solar-type (0.8 < R * /R ⊙ < 1.2) stars with 430 planets on 20-200 d orbits, excluding close-in planets that may have been affected by the proximity to the host star. Our analysis considers errors in planet radii and includes an "iterative simulation" technique that does not bin the data. We find a radius distribution that peaks at 2-2.8 Earth radii, with lower numbers of smaller and larger planets. These planets are uniformly distributed with logarithmic period, and the mean number of such planets per star is 0.46±0.03. The occurrence is ∼ 0.66 if planets interior to 20 d are included. We estimate the occurrence of Earth-size planets in the "habitable zone" (defined as 1-2R ⊕ , 0.99-1.7 AU for solar-like stars) as 6.4 +3.4 −1.1 %. Our results largely agree with those of Petigura et al. (2013), although we find a higher occurrence of 2.8-4 Earth-radii planets. The reasons for this excess are the inclusion of errors in planet radius, updated Huber et al. (2014) stellar parameters, and also the exclusion of planets which may have been affected by proximity to the host star.

We combine analytical understanding of resonant dynamics in two-planet systems with machine-learning techniques to train a model capable of robustly classifying stability in compact multiplanet systems over long timescales of 109 orbits. Our Stability of Planetary Orbital Configurations Klassifier (SPOCK) predicts stability using physically motivated summary statistics measured in integrations of the first 104 orbits, thus achieving speed-ups of up to 105 over full simulations. This computationally opens up the stability-constrained characterization of multiplanet systems. Our model, trained on ∼100,000 three-planet systems sampled at discrete resonances, generalizes both to a sample spanning a continuous period-ratio range, as well as to a large five-planet sample with qualitatively different configurations to our training dataset. Our approach significantly outperforms previous methods based on systems’ angular momentum deficit, chaos indicators, and parametrized fits to numerical integrations. We use SPOCK to constrain the free eccentricities between the inner and outer pairs of planets in the Kepler-431 system of three approximately Earth-sized planets to both be below 0.05. Our stability analysis provides significantly stronger eccentricity constraints than currently achievable through either radial velocity or transit-duration measurements for small planets and within a factor of a few of systems that exhibit transit-timing variations (TTVs). Given that current exoplanet-detection strategies now rarely allow for strong TTV constraints [S. Hadden, T. Barclay, M. J. Payne, M. J. Holman, Astrophys. J. 158, 146 (2019)], SPOCK enables a powerful complementary method for precisely characterizing compact multiplanet systems. We publicly release SPOCK for community use.

Hybrid symplectic integrators such as MERCURY are widely used to simulate complex dynamical phenomena in planetary dynamics that could otherwise not be investigated. A hybrid integrator achieves high accuracy during close encounters by using a high order integration scheme for the duration of the encounter while otherwise using a standard 2nd order Wisdom-Holman scheme, thereby optimizing both speed and accuracy. In this paper we reassess the criteria for choosing the switching function that determines which parts of the Hamiltonian are integrated with the high order integrator. We show that the original motivation for choosing a polynomial switching function in MERCURY is not correct. We explain the nevertheless excellent performance of the MERCURY integrator and then explore a wide range of different switching functions including an infinitely differentiable function and a Heaviside function. We find that using a Heaviside function leads to a significantly simpler scheme compared to MERCURY, while maintaining the same accuracy in short term simulations.

The requirement that planetary systems be dynamically stable is often used to vet new discoveries or set limits on unconstrained masses or orbital elements. This is typically carried out via computationally expensive N-body simulations. We show that characterizing the complicated and multidimensional stability boundary of tightly packed systems is amenable to machine learning methods. We find that training an XGBoost machine learning algorithm on physically motivated features yields an accurate classifier of stability in packed systems. On the stability timescale investigated (10 7 orbits), it is 3 orders of magnitude faster than direct N-body simulations. Optimized machine learning classifiers for dynamical stability may thus prove useful across the discipline, e.g., to characterize the exoplanet sample discovered by the upcoming Transiting Exoplanet Survey Satellite (TESS). This proof of concept motivates investing computational resources to train algorithms capable of predicting stability over longer timescales and over broader regions of phase space.

A number of Kepler planet pairs lie just wide of first-order mean motion resonances (MMRs). Tides have been frequently proposed to explain these pileups, but it is still an ongoing discussion. We contribute to this discussion by calculating an optimistic theoretical estimate on the minimum initial eccentricity required by Kepler planets to explain the current observed spacing, and compliment these calculations with Nbody simulations. In particular, we investigate 27 Kepler systems having planets within 6% of the 2:1 MMR, and find that the initial eccentricities required to explain the observed spacings are unreasonable from simple dynamical arguments. Furthermore, our numerical simulations reveal resonant tugging, an effect which conspires against the migration of resonant planets away from the 2:1 MMR, requiring even higher initial eccentricities in order to explain the current Kepler distribution. Overall, we find that tides alone cannot explain planets close to 2:1 MMR, and additional mechanisms are required to explain these systems.

Two Jovian-sized planets are orbiting the star HD155358 near exact mean motion resonance (MMR) commensurability. In this work we re-analyze the radial velocity (RV) data previously collected by Robertson et al. (2012). Using a Bayesian framework we construct two models -one that includes and one that excludes gravitational planetplanet interactions (PPI). We find that the orbital parameters from our PPI and noPPI models differ by up to 2σ, with our noPPI model being statistically consistent with previous results. In addition, our new PPI model strongly favours the planets being in MMR while our noPPI model strongly disfavours MMR. We conduct a stability analysis by drawing samples from our PPI model's posterior distribution and simulating them for 10 9 years, finding that our best-fit values land firmly in a stable region of parameter space.We explore a series of formation models that migrate the planets into their observed MMR. We then use these models to directly fit to the observed RV data, where each model is uniquely parameterized by only three constants describing its migration history. Using a Bayesian framework we find that a number of migration models fit the RV data surprisingly well, with some migration parameters being ruled out.Our analysis shows that planet-planet interactions are important to take into account when modelling observations of multi-planetary systems. The additional information that one can gain from interacting models can help constrain planet migration parameters.

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