Planetary Orbits Research Articles

SPOCK 2.0: Updates to the FeatureClassifier in the Stability of Planetary Orbital Configurations Klassifier

Abstract The Stability of Planetary Orbital Configurations Klassifier (SPOCK) package collects machine learning models for predicting the stability and collisional evolution of compact planetary systems. In this paper we explore improvements to SPOCK’s binary stability classifier (FeatureClassifier), which predicts orbital stability by collecting data over a short N-body integration of a system. We find that by using a system-specific timescale (rather than a fixed 104 orbits) for the integration, and by using this timescale as an additional feature, we modestly improve the model’s AUC metric from 0.943 to 0.950 (AUC = 1 for a perfect model). We additionally discovered that ≈10% of N-body integrations in SPOCK’s original training data set were duplicated by accident, and that <1% were misclassified as stable when they in fact led to ejections. We provide a cleaned data set of 100,000+ unique integrations, release a newly trained stability classification model, and make minor updates to the API.

Anisotropic tidal dissipation in misaligned planetary systems

Context. Tides are the main driving force behind the long-term evolution of planetary systems. The associated energy dissipation and momentum exchanges are commonly described by Love numbers, which relate the exciting potential to the tidally perturbed potential. These transfer functions are generally assumed to depend solely on tidal frequency and body rheology, following the isotropic assumption, which presumes invariance of properties by rotation about the centre of mass. Aims. We examine the limitations of the isotropic assumption for fluid bodies, in which Coriolis acceleration breaks spherical symmetry, resulting in rotational scattering and complex tidal responses. Methods. Using angular momentum theory, we derived a new formalism to calculate the tidal rates of energy and momentum transfers in non-isotropic cases. We applied this formalism to the Earth-Moon system to assess the effects of anisotropy in planet-satellite systems with misaligned spin and orbital angular momenta. Results. Our findings indicate that the isotropic assumption can introduce significant errors in planetary evolution models, particularly in the dynamical tide regime. These errors stem from forced wave resonances, with inaccuracies in energy dissipation scaling in proportion to resonance amplification factors.

Spectroscopically Resolved Partial Phase Curve of the Rapid Heating and Cooling of the Highly Eccentric Hot Jupiter HAT-P-2b with WFC3

Abstract The extreme environments of transiting close-in exoplanets in highly eccentric orbits are ideal for testing exoclimate physics. Spectroscopically resolved phase curves not only allow for the characterization of their thermal response to irradiation changes but also unveil phase-dependent atmospheric chemistry and dynamics. We observed a partial phase curve of the highly eccentric close-in giant planet HAT-P-2b (e = 0.51, M = 9M Jup) with the Wide Field Camera 3 aboard the Hubble Space Telescope. Using these data, we updated the planet's orbital parameters and radius and retrieved high-frequency pulsations consistent with the planet-induced pulsations reported in Spitzer data. We found that the peak in planetary flux occurred at 6.7 ± 0.6 hr after periastron, with heating and cooling timescales of 9 . 0 − 2.1 + 3.5 hr and 3 . 6 − 0.6 + 0.7 hr, respectively. We compare the light curve to various 1D and 3D forward models, varying the planet's chemical composition. The strong contrast in flux increase and decrease timescales before and after periapse indicates an opacity term that emerges during the planet's heating phase, potentially due to more H− than expected from chemical equilibrium models. The phase-resolved spectra are largely featureless, which we interpret as indicative of an inhomogeneous dayside. However, we identified an anomalously high flux in the spectroscopic bin coinciding with the hydrogen Paβ line, and that is likely connected to the planet's orbit. We interpret this as due to shock heating of the upper atmosphere given the short timescale involved, or evidence for other star−planet interactions.

Characterising WASP-43b's interior structure: Unveiling tidal decay and apsidal motion

Recent developments in exoplanetary research highlight the importance of Love numbers in understanding the internal dynamics, formation, migration history, and potential habitability of exoplanets. Love numbers represent crucial parameters that gauge how exoplanets respond to external forces such as tidal interactions and rotational effects. By measuring these responses, insights into the internal structure, composition, and density distribution of exoplanets can be gained. The rate of apsidal precession of a planetary orbit is directly linked to the second-order fluid Love numbers. Thus, Love numbers can also offer valuable insights into the mass distribution of a planet. In this context, we aim to re-determine the orbital parameters of WASP-43b - in particular, the orbital period, eccentricity, and argument of the periastron - and its orbital evolution. We study the outcomes of the tidal interaction with the host star in order to identify whether tidal decay and periastron precession occur in the system. We observed WASP-43b with HARPS, whose data we present for the first time, and we also analysed the newly acquired JWST full-phase light curve. We jointly fit new and archival radial velocity and transit and occultation mid-times, including tidal decay, periastron precession, and long-term acceleration in the system. We detected a tidal decay rate of dot P _a= (-1.99±0.50) ms yr^-1 and a periastron precession rate of )^∘ d^-1 = (621.72 ^ This is the first time that both periastron precession and tidal decay are simultaneously detected in an exoplanetary system. The observed tidal interactions can neither be explained by the tidal contribution to apsidal motion of a non-aligned stellar or planetary rotation axis nor by assuming a non-synchronous rotation for the planet, and a value for the planetary Love number cannot be derived. Moreover, we excluded the presence of a second body (e.g. a distant companion star or a yet undiscovered planet) down to a planetary mass of ≳0.3 M_J and up to an orbital period of lesssim 3,700 days. We leave the question of the cause of the observed apsidal motion open.

Assessment of Mangrove Cover Change Based on Combining Remote Sensing Technique and Hydrodynamic Model Simulation

Mangrove ecosystems along Vietnam's coastline face significant degradation due to human activities, despite their crucial role in coastal protection against natural hazards. This study aims to assess the spatial and temporal changes in mangrove coverage along Vietnam's southern coast by integrating remote sensing techniques with hydrodynamic model simulations. The research methodology combines the Collect Earth tool analysis of Spot-4 and Planet satellite imagery (2000-2020) with Mike 21-HD two-dimensional (2D) hydrodynamic modeling to evaluate mangrove coverage changes by simulating shoreline erosion. Results analysis reveals that a significant increase of 109.83 ha in mangrove area within Vinh Chau Town of Soc Trang Province during the period 2010-2020, predominantly in the eastern region. Hydrodynamic simulations demonstrate that the coastal zone is primarily influenced by the interaction of nearshore currents, East Sea tides, and seasonal monsoon wave patterns. The model results effectively capture the complex interactions between these hydrodynamic factors and mangrove distribution. These findings not only validate the effectiveness of combining remote sensing and hydrodynamic modeling for mangrove assessment but also provide crucial insights for sustainable coastal ecosystem management. The study's integrated approach offers a robust framework for monitoring mangrove dynamics and developing evidence-based conservation strategies, highlighting the importance of maintaining these vital ecosystems for coastal protection.

Extreme exomoons in WASP-49 Ab: Dynamics and detectability

WASP-49Ab, a low-density Saturn-like planet in a tight orbit around a Sun-like star within a wide binary system, is a compelling candidate for hosting a volcanic moon, as suggested by the detection of Doppler-shifted sodium. This study evaluates the stability of potential satellites around WASP-49Ab under the influence of planetary oblateness, relativistic effects, and perturbations from a close companion star, focusing on their impact on light curve parameters such as transit duration and impact parameter variations, driven by the evolution of the planet's orbit in this extreme environment. Using N-body simulations and semi-analytical methods, we analysed moon's dynamics across varied initial conditions and gravitational frameworks including the potential of an oblate planet and the effects of the general relativity. We find that `selenity', a moon survival indicator, is high in close orbits with low eccentricity and near the Roche limit, especially for masses higher than Io's. Stability decreases as eccentricity or distance from the planet increases. Additionally, we observe a strong destabilising resonance near $1.4 when planetary eccentricities are considered to be ≳ 0. This study confirms the potential for stable exomoons around WASP-49Ab despite its hostile environment, emphasising the importance of incorporating diverse physical effects in stability analyses, aiding future detection efforts.

Basins of Convergence in a Multi-Perturbed CR3BP

The circular restricted three-body problem (CR3BP) is analyzed to introduce additional factors into the dynamic model, such as radiation forces, flattening of the primary bodies, relativity effects, and the presence of natural satellites. The introduction of these factors increases the accuracy when obtaining the position of the Lagrange points and the basins of convergence of the system. The Newton–Raphson methodis used to implement a searching algorithm. Finally, an application to the Sun–Mars system including the presence of Phobos and Deimos is developed.

Interpretation of the transit light curve in the presence of one principal minimum taking into account the eccentricity of the transit (planet) orbit

Using a high-precision algorithm for interpreting transit light curves in a model of a classical eclipsing binary star-exoplanet system, we investigated the possibility of determining the system parameters in the absence of a priori knowledge of the orbital eccentricity. It was shown that it is impossible to determine the exact value of the eccentricity and periastron longitude based on the main minimum of the transit light curve alone. Also, with an observational accuracy of about 1% of the eclipse depth, the uncertainty in the eccentricity and periastron longitude together causes a significant uncertainty in the values of the component radii (an error of 2–3 times relative to the true values) and the orbital inclination angle. However, the ratios of the system component radii and the limb darkening coefficients are determined with good accuracy. With an increase in the observational accuracy to 0.1% of the eclipse depth, it becomes possible to determine the component radii and the orbital inclination angle when interpreting the light curve taking into account the eccentricity.

Orbital Eccentricity Study of Planets: A Comparative Analysis of Manual Simulation and Digital Visualization

Understanding planetary orbits is a fundamental concept in astronomy. Many secondary school students encounter difficulties comprehending the shape and characteristics of orbits, which are not perfect circles but ellipses with varying degrees of eccentricity. These challenges are particularly evident when students are tasked with sketching or calculating the eccentricity of a planet's orbit, a measure of how elongated the orbit is. This study aims to explore and compare the efficacy of two pedagogical approaches manual simulation and digital simulation—in enhancing students' understanding of planetary orbit shapes and the concept of eccentricity. A descriptive-comparative research design is employed to depict and contrast the effectiveness of these two teaching methods. The experiment, crafted based on expert design, involves four qualified astronomy educators to apply both approaches. The manual simulation requires students to draw orbits and compute eccentricity manually, whereas the digital simulation leverages software to visualize the motion of planetary orbits. Evaluation is conducted through Focus Group Discussions (FGD) with four subject matter experts to provide feedback on the effectiveness of the two methods, the challenges faced by students, and the level of comprehension achieved. The results from the manual experiment indicate that the orbital eccentricity ranges between 0.2 and 0.4, suggesting that the planets' orbits are elliptical. These findings align with Kepler’s laws, which state that planetary orbits are elliptical, with the Sun at one of the foci. Results from the NASA Eyes application further corroborate this, showing that the orbits of planets in the solar system are indeed elliptical, both at perihelion (the point closest to the Sun) and aphelion (the end farthest from the Sun). In conclusion, this research substantiates that the orbits of planets in the solar system are elliptical, consistent with Kepler's laws.

Machine-learning approach for mapping stable orbits around planets

Numerical N-body simulations are typically employed to map stability regions around exoplanets. This provides insights into the potential presence of satellites and ring systems. We used machine-learning (ML) techniques to generate predictive maps of stable regions surrounding a hypothetical planet. This approach can also be applied to planet-satellite systems, planetary ring systems, and other similar systems. From a set of $10^5$ numerical simulations, each incorporating nine orbital features for the planet and test particle, we created a comprehensive dataset of three-body problem outcomes (star-planet-test particle). Simulations were classified as stable or unstable based on the stability criterion that a particle must remain stable over a time span of 104 orbital periods of the planet. Various ML algorithms were compared and fine-tuned through hyperparameter optimization to identify the most effective predictive model. All tree-based algorithms demonstrated a comparable accuracy performance. The optimal model employs the extreme gradient boosting algorithm and achieved an accuracy of 98.48<!PCT!> , with 94<!PCT!> recall and precision for stable particles and 99<!PCT!> for unstable particles. ML algorithms significantly reduce the computational time in three-body simulations. They are approximately $10^ $ times faster than traditional numerical simulations. Based on the saved training models, predictions of entire stability maps are made in less than a second, while an equivalent numerical simulation can take up to a few days. Our ML model results will be accessible through a forthcoming public web interface, which will facilitate a broader scientific application.

The Impact of Observing Cadence and Undetected Companions on the Accuracy of Planet Mass Measurements from Radial Velocity Monitoring

We conduct experiments on both real and synthetic radial velocity (RV) data to quantify the impact that observing cadence, the number of RV observations, and undetected companions all have on the accuracy of small planet mass measurements. We run resampling experiments on four systems with small transiting planets and substantial public data from the High Resolution Echelle Spectrometer in order to explore how degrading observing cadence and the number of RVs affects the planets’ mass measurement relative to a baseline value. From these experiments, we recommend that observers obtain 2–3 RVs per orbit of the innermost planet and acquire at minimum 40 RVs. Following these guidelines, we then conduct simulations using synthetic RVs to explore the impact of undetected companions and untreated red noise on the masses of planets with known orbits. While undetected companions generally do not bias the masses of known planets, in some cases, when coupled with an inadequate observing baseline, they can cause the mass of an inner transiting planet to be systematically overestimated on average.

Significant Mutual Inclinations Between the Stellar Spin and the Orbits of Both Planets in the HAT-P-11 System

Planet–star obliquity and planet–planet mutual inclination encode a planetary system’s dynamical history, but both of their values are hard to measure for misaligned systems with close-in companions. HAT-P-11 is a K4 star with two known planets: a close-in, misaligned super-Neptune with a ≈5 day orbit, and an outer super-Jupiter with a ≈10 yr orbit. In this work we present a joint orbit fit of the HAT-P-11 system with astrometry and S-index corrected radial velocity data. By combining our results with previous constraints on the orientation of the star and the inner planet, we find that all three angular momenta—those of the star, planet b, and planet c—are significantly misaligned. We confirm the status of planet c as a super-Jupiter, with 2.68 ± 0.41 M Jup at a semimajor axis of 4.10 ± 0.06 au, and planet b’s mass of M b sini b = 0.074 ± 0.004 M Jup. We present the posterior probability distribution of obliquity between star A and planet c, and mutual inclination between planet b and planet c.

Orbital Migration Through Atmospheric Mass Loss

Abstract Atmospheric mass loss is thought to have strongly shaped the sample of close-in exoplanets. These atmospheres should be lost isotropically, leading to no net migration on the planetary orbit. However, strong stellar winds can funnel the escaping atmosphere into a tail trailing the planet. We derive a simple kinematic model of the gravitational interaction between the planet and this anisotropic wind, and derive expressions for the expected migration of the planet. Over the expected range of parameters, we find typical migrations of a few tenths to a few percent inward. We argue that this modest migration may be observable for planet pairs near mean motion resonances, which would provide an independent observational constraint on atmospheric mass loss models.

CHEOPS observations confirm nodal precession in the WASP-33 system

We aim to observe the transits and occultations of which orbits a rapidly rotating delta Scuti pulsator, with the goal of measuring the orbital obliquity via the gravity-darkening effect, and constraining the geometric albedo via the occultation depth. We observed four transits and four occultations with CHEOPS, and employ a variety of techniques to remove the effects of the stellar pulsations from the light curves, as well as the usual CHEOPS systematic effects. We also performed a comprehensive analysis of low-resolution spectral and Gaia data to re-determine the stellar properties of system. We measure an orbital obliquity degrees, which is consistent with previous measurements made via Doppler tomography. We also measure the planetary impact parameter, and confirm that this parameter is undergoing rapid secular evolution as a result of nodal precession of the planetary orbit. This precession allows us to determine the second-order fluid Love number of the star, which we find agrees well with the predictions of theoretical stellar models. We are unable to robustly measure a unique value of the occultation depth, and emphasise the need for long-baseline observations to better measure the pulsation periods.

Dual-frequency electromagnetic sounding of a Triton ocean from a single flyby.

Triton, the largest satellite of Neptune, is in a retrograde orbit and is likely a captured Kuiper Belt Object (KBO). Triton has a mean density of only 2.061 gm/cm3 and is therefore believed to have a 250-400 km thick hydrosphere. Triton is also one of the few planetary satellites to possess a thick ionosphere whose height-integrated Pedersen conductivity exceeds 104 S, complicating the sounding of Triton's subsurface using electromagnetic induction. Triton experiences a time-varying magnetic field dominated by two periods, one at 14.4 h, at the synodic rotation period of Neptune (from Neptune's tilted field) and one at 141 h, at the orbital period of Triton (from large inclination of Triton's orbit). We show that for most models of ionospheric conductivity, the 14.4 h wave creates a large response from the ionosphere itself and is unable to sound the putative ocean below. However, the 141 h wave penetrates the ionosphere easily and provides information on Triton's ocean. We introduce a technique that allows us to determine the complex magnetic moments generated at the two key periods from the magnetic data from a single flyby, allowing us to infer the presence of a subsurface ocean.This article is part of the theme issue 'Magnetometric remote sensing of Earth and planetary oceans'.

Mapping Seagrass Distribution and Abundance: Comparing Areal Cover and Biomass Estimates Between Space-Based and Airborne Imagery

This study evaluated the effectiveness of Planet satellite imagery in mapping seagrass coverage in Santa Rosa Sound, Florida. We compared very-high-resolution aerial imagery (0.3 m) collected in September 2022 with high-resolution Planet imagery (~3 m) captured during the same period. Using supervised classification techniques, we accurately identified expansive, continuous seagrass meadows in the satellite images, successfully classifying 95.5% of the 11.18 km2 of seagrass area delineated manually from the aerial imagery. Our analysis utilized an occurrence frequency (OF) product, which was generated by processing ten clear-sky images collected between 8 and 25 September 2022 to determine the frequency with which each pixel was classified as seagrass. Seagrass patches encompassing at least nine pixels (~200 m2) were almost always detected by our classification algorithm. Using an OF threshold equal to or greater than >60% provided a high level of confidence in seagrass presence while effectively reducing the impact of small misclassifications, often of individual pixels, that appeared sporadically in individual images. The image-to-image uncertainty in seagrass retrieval from the satellite images was 0.1 km2 or 2.3%, reflecting the robustness of our classification method and allowing confidence in the accuracy of the seagrass area estimate. The satellite-retrieved leaf area index (LAI) was consistent with previous in situ measurements, leading to the estimate that 2700 tons of carbon per year are produced by the Santa Rosa Sound seagrass ecosystem, equivalent to a drawdown of approximately 10,070 tons of CO2. This satellite-based approach offers a cost-effective, semi-automated, and scalable method of assessing the distribution and abundance of submerged aquatic vegetation that provides numerous ecosystem services.

The inflated, eccentric warm Jupiter TOI-4914 b orbiting a metal-poor star, and the hot Jupiters TOI-2714 b and TOI-2981 b

Recent observations of giant planets have revealed unexpected bulk densities. Hot Jupiters, in particular, appear larger than expected for their masses compared to planetary evolution models, while warm Jupiters seem denser than expected. These differences are often attributed to the influence of the stellar incident flux, but it has been unclear if they also result from different planet formation processes, and if there is a trend linking the planetary density to the chemical composition of the host star. In this work, we present the confirmation of three giant planets in orbit around solar analogue stars. TOI-2714 b (P ≃ 2.5 d, Rp ≃ 1.22 RJ, Mp = 0.72 MJ) and TOI-2981 b (P ≃ 3.6 d, RP ≃ 1.2 RJ, MP = 2 MJ) are hot Jupiters on nearly circular orbits, while TOI-4914 b (P ≃ 10.6 d, RP ≃ 1.15 RJ, Mp = 0.72 MJ) is a warm Jupiter with a significant eccentricity (e = 0.41 ± 0.02) that orbits a star more metal-poor ([Fe/H] = −0.13) than most of the stars known to host giant planets. Similarly, TOI-2981 b orbits a metal-poor star ([Fe/H] = −0.11), while TOI-2714 b orbits a metal-rich star ([Fe/H] = 0.30). Our radial velocity follow-up with the HARPS spectrograph allows us to detect their Keplerian signals at high significance (7, 30, and 23σ, respectively) and to place a strong constraint on the eccentricity of TOI-4914 b (18σ). TOI-4914 b, with its large radius (Rp ≃ 1.15 RJ) and low insolation flux (F⋆ < 2 × 108 erg s−1 cm−2), appears to be more inflated than what is supported by current theoretical models for giant planets. Moreover, it does not conform to the previously noted trend that warm giant planets orbiting metal-poor stars have low eccentricities. This study thus provides insights into the diverse orbital characteristics and formation processes of giant exoplanets, in particular the role of stellar metallicity in the evolution of planetary systems.

Orbits of particles with magnetic dipole moment around magnetized Schwarzschild black holes: Applications to the S2 star orbit

This study provides a comprehensive analytical investigation of the bound and unbound motion of magnetized particles orbiting a Schwarzschild black hole immersed in an external asymptotically uniform magnetic field, which includes all conceivable types of bounded and unbounded orbits. In particular, for planetary orbits, we perform a comparative analysis of our findings with the observed position of the S2 star carrying magnetic dipole moment around Sagittarius A*. We found maximum and minimum values for the parameter of magnetic interaction between the magnetic dipole of the star and the external magnetic field, as well as the energy and angular momentum of the S2 star. As a result, we obtain estimations of the magnetic dipole of the star in the order of 106 G·cm3. Additionally, we explore deflecting trajectories akin to gravitational Rutherford scattering. In obtaining the solutions for the orbital equations, we articulate the elliptic integrals and Jacobi elliptic functions, and illustrative figures and simulations augment our study. Published by the American Physical Society 2024

Natural satellites database (NSDB) revisited

Any study of the dynamics of the natural planetary satellites requires as many astrometric observations as possible. This type of work is partially made by each astronomer starting this type of study but it has never been done for all the natural planetary systems. The goal of our work is to build a database of all available astrometric observations along with all the information needed for an efficient use of these data so that the astronomers interested in the dynamics of planetary satellites do not have to repeat the search for these data. To do this, we sought and carefully read all the publications containing observational data, so that we are able to include the astrometric positions of satellites, the reference frame used by the observer, the corrections and reductions made, and timescale. Direct contact with observers was sometimes necessary to obtain raw unpublished data. A new database containing about 90 <!PCT!> of all the observations that are useful for studying the dynamics of the planetary satellites is now available for the interested community of astronomers.

Empirical Stability Criteria for 3D Hierarchical Triple Systems. I. Circumbinary Planets

In this work we revisit the problem of the dynamical stability of hierarchical triple systems with applications to circumbinary planetary orbits. We derive critical semimajor axes based on simulating and analyzing the dynamical behavior of 3 × 108 binary star–planet configurations. For the first time, three-dimensional and eccentric planetary orbits are considered. We explore systems with a variety of binary and planetary mass ratios, binary and planetary eccentricities from 0 to 0.9, and orbital mutual inclinations ranging from 0° to 180°. Planetary masses range between the size of Mercury and the lower fusion boundary (approximately 13 Jupiter masses). The stability of each system is monitored over 106 planetary orbital periods. We provide empirical expressions in the form of multidimensional, parameterized fits for two borders that separate dynamically stable, unstable, and mixed zones. In addition, we offer a machine learning model trained on our data set as an alternative tool for predicting the stability of circumbinary planets. Both the empirical fits and the machine learning model are tested for their predictive capabilities against randomly generated circumbinary systems with very good results. The empirical formulae are also applied to the Kepler and TESS circumbinary systems, confirming that many planets orbit their host stars close to the stability limit of those systems. Finally, we present a REST application programming interface with a web-based application for convenient access to our simulation data set.