We investigate how the variation of the obliquity (the axial tilt) of a hypothetical exo-Earth is effected by the presence of a satellite, an exo-Moon. Namely, we study analytically and numerically how the range of obliquity of the exo-Earth changes if an exo-Moon is added to a system comprised of exo-Sun, exo-Earth and exo-planets. We say that the impact of the exo-Moon is stabilising if upon the addition of the exo-Moon the range of obliquity decreases, while we call the impact destabilising if the range increases as the exo-Moon is added to the system. The problem is considered in a general setup. The exo-Earth is assumed to be rigid, axially symmetric and almost spherical, the difference between the largest and the smallest principal moments of inertia being a small parameter of the problem. Assuming the orbits of the celestial bodies to be quasiperiodic, we apply time averaging to study rotation of the exo-Earth at times large compared to the respective periods. Non-resonant frequencies are assumed. We identify a class of systems for which we prove analytically that the impact of the exo-Moon is stabilising and a class where it is destabilising. We also investigate numerically how the impact of the exo-Moon in a particular system comprised of a star and two planets varies on modifying the geometry of the orbits of the exo-Moon and the second planet and the initial obliquity.
Accurate estimation of cratering asymmetry on the Moon is crucial for understanding Moon evolution history. Early studies of cratering asymmetry have omitted the contributions of high lunar obliquity and inclination. Here, we include lunar obliquity and inclination as new controlling variables to derive the cratering rate spatial variation as a function of longitude and latitude. With examining the influence of lunar obliquity and inclination on the asteroids population encountered by the Moon, we then have derived general formulas of the cratering rate spatial variation based on the crater sc…
A giant impact origin for the Moon is generally accepted, but many aspects of lunar formation remain poorly understood and debated. Ćuk et al. (2016) proposed that an impact that left the Earth-Moon system with high obliquity and angular momentum could explain the Moon's orbital inclination and isotopic similarity to Earth. In this scenario, instability during the Laplace Plane transition, when the Moon's orbit transitions from the gravitational influence of Earth's figure to that of the Sun, would both lower the system's angular momentum to its present-day value and generate the Moon's orbita…
Matija Cuk et.al (2016) have proposed a new model for the birth and tidal evolution of our natural satellite Moon, born from impact generated terrestrial debris in the equatorial plane of high obliquity, high angular momentum Earth. This paper examines their findings critically in the light of advanced kinematic model (AKM) which includes Earth's obliquity (ϕ), Moon's orbital plane inclination (α) , Moon's obliquity (β) and lunar's orbit eccentricity (e). For the real Earth-Moon (E-M) system, the history of evolution of ϕ, α, β, e and (length of month)/(length of day) or LOM/LOD is traced from…
In the giant impact hypothesis for lunar origin, the Moon accreted from an equatorial circum-terrestrial disk; however the current lunar orbital inclination of 5 degrees requires a subsequent dynamical process that is still debated. In addition, the giant impact theory has been challenged by the Moon's unexpectedly Earth-like isotopic composition. Here, we show that tidal dissipation due to lunar obliquity was an important effect during the Moon's tidal evolution, and the past lunar inclination must have been very large, defying theoretical explanations. We present a new tidal evolution model …
The variation of a planet's obliquity is influenced by the existence of satellites with a high mass ratio. For instance, the Earth's obliquity is stabilized by the Moon, and would undergo chaotic variations in the Moon's absence. In turn, such variations can lead to large-scale changes in the atmospheric circulation, rendering spin-axis dynamics a central issue for understanding climate. The relevant quantity for dynamically-forced climate change is the rate of chaotic diffusion. Accordingly, here we reexamine the spin-axis evolution of a Moonless Earth within the context of a simplified pertu…
The Earth's obliquity is stabilized by the Moon, which facilitates a rapid precession of the Earth's spin-axis, de-tuning the system away from resonance with orbital modulation. It is however, likely that the architecture of the Solar System underwent a dynamical instability-driven transformation, where the primordial configuration was more compact. Hence, the characteristic frequencies associated with orbital perturbations were likely faster in the past, potentially allowing for secular resonant encounters. In this work we examine if at any point in the Earth's evolutionary history, the obliq…
Almost all meteorite impacts occur at oblique incidence angles, but the effect of impact angle on crater size is not well understood, especially for large craters. To improve oblique impact crater scaling, we present a suite of simulations of complex crater formation on Earth and the Moon over a range of impact angles, velocities and impactor sizes. We show that crater diameter is larger than predicted by existing scaling relationships for oblique impacts and for impacts steeper than 45$^{\circ}$ shows little dependence on obliquity. Crater depth, volume and diameter depend on impact angle in …
Changes in planetary obliquity, or axial tilt, influence the climates on Earth-like planets. In the solar system, the Earth's obliquity is stabilized due to interactions with our moon and the resulting {small amplitude variations ($\sim$2.4\degree)} are beneficial for advanced life. Most Sun-like stars have at least one stellar companion and the habitability of circumstellar exoplanets is shaped by their stellar companion. We show that a stellar companion can dramatically change whether {Earth-like obliquity stability is} possible through planetary orbital precession relative to the binary orb…
Obliquity variability could play an important role in the climate and habitability of a planet. Orbital modulations caused by planetary companions and the planet's spin axis precession due to the torque from the host star may lead to resonant interactions and cause large-amplitude obliquity variability. Here we consider the spin axis dynamics of Kepler-62f and Kepler-186f, both of which reside in the habitable zone around their host stars. Using {\emph{N}}-body simulations and secular numerical integrations, we describe their obliquity evolution for particular realizations of the planetary sys…
We performed numerical simulations of the obliquity evolution of Mars during the Noachian era, at which time the giant planets were on drastically different orbits than today. For the preferred primordial configuration of the planets we find that there are two large zones where the Martian obliquity is stable and oscillates with an amplitude lower than 20$^\circ$. These zones occur at obliquities below 30$^\circ$ and above 60$^\circ$; intermediate values show either resonant or chaotic behaviour depending on the primordial orbits of the terrestrial planets.
Various theories have been proposed to explain the Moon's current inclined orbit. We test the viability of these theories by reconstructing the thermal-orbital history of the Moon. We build on past thermal-orbital models and incorporate the evolution of the lunar figure including a fossil figure component. Obliquity tidal heating in the lunar magma ocean would have produced rapid inclination damping, making it difficult for an early inclination to survive to the present-day. An early inclination is preserved only if the solid-body of the early Moon were less dissipative than at present. If ins…
The obliquity of the Earth, which controls our seasons, varies by only ~2.5 degrees over ~40,000 years, and its eccentricity varies by only ~0.05 over 100,000 years. Nonetheless, these small variations influence Earth's ice ages. For exoplanets, however, variations can be significantly larger. Previous studies of the habitability of moonless Earth-like exoplanets have found that high obliquities, high eccentricities, and dynamical variations can extend the outer edge of the habitable zone by preventing runaway glaciation (snowball states). We expand upon these studies by exploring the orbital …
The migration and encounter histories of the giant planets in our Solar System can be constrained by the obliquities of Jupiter and Saturn. We have performed secular simulations with imposed migration and N-body simulations with planetesimals to study the expected obliquity distribution of migrating planets with initial conditions resembling those of the smooth migration model, the resonant Nice model and two models with five giant planets initially in resonance (one compact and one loose configuration). For smooth migration, the secular spin-orbit resonance mechanism can tilt Saturn's spin ax…
Jupiter and Saturn play host to an impressive array of satellites, making it reasonable to suspect that similar systems of moons might exist around giant extrasolar planets. Furthermore, a significant population of such planets is known to reside at distances of several Astronomical Units (AU), leading to speculation that some moons thereof might support liquid water on their surfaces. However, giant planets are thought to undergo inward migration within their natal protoplanetary disks, suggesting that gas giants currently occupying their host star's habitable zone formed further out. Here we…
We present a comprehensive theoretical study on the spin evolution of a planet under the combined effects of tidal dissipation and gravitational perturbation from an external companion. Such a "spin + companion" system (called Colombo's top) appears in many [exo]planetary contexts. The competition between the tidal torque (which drives spin-orbit alignment and synchronization) and the gravitational torque from the companion (which drives orbital precession of the planet) gives rise to two possible spin equilibria ("Tidal Cassini Equilibria", tCE) that are stable and attracting: the "simple" tC…
Scattered lights from terrestrial exoplanets provide valuable information about the planetary surface. Applying the surface reconstruction method proposed by Fujii et al. (2010) to both diurnal and annual variations of the scattered light, we develop a reconstruction method of land distribution with both longitudinal and latitudinal resolutions. We find that one can recover a global map of an idealized Earth-like planet on the following assumptions: 1) cloudless, 2) a face-on circular orbit, 3) known surface types and their reflectance spectra 4) no atmospheric absorption, 5) known rotation ra…
Inspired by the close-proximity pair of planets in the Kepler-36 system, we consider two effects that may have important ramifications for the development of life in similar systems where a pair of planets may reside entirely in the habitable zone of the hosting star. Specifically, we run numerical simulations to determine whether strong, resonant (or non-resonant) planet-planet interactions can cause large variations in planet obliquity---thereby inducing large variations in climate. We also determine whether or not resonant interactions affect the rate of lithopanspermia between the planet p…
We investigate the obliquity and spin period of Earth-Moon like systems after 4.5 Gyr of tidal evolution with various satellite masses and initial planetary obliquity and discuss their relations to the habitability of the planet. We find three possible outcomes: either i) the system is still evolving, ii) the system is double synchronous or iii) the satellite has collided with the planet. The transition between case i) and ii) is abrupt and occurs at slightly larger satellite mass ($m_s \sim 0.02m_p$) than the lunar mass. We suggest that cases ii) and iii) are less habitable than case i). Usin…
Previous studies have shown that planets that rotate retrograde (backwards with respect to their orbital motion) generally experience less severe obliquity variations than those that rotate prograde (the same direction as their orbital motion). Here we examine retrograde-rotating planets on eccentric orbits and find a previously unknown secular spin-orbit resonance that can drive significant obliquity variations. This resonance occurs when the frequency of the planet's rotation axis precession becomes commensurate with an orbital eigenfrequency of the planetary system. The planet's eccentricit…
Context. Saturn has an excess of irregular moons. This is thought to be the result of past collisional events. Debris produced during such episodes in the neighborhood of a host planet can evolve into co-orbitals trapped in quasi-satellite and/or horseshoe resonant states. A recently announced centaur, 2013 VZ70, follows an orbit that could be compatible with those of prograde Saturn's co-orbitals. Aims. We perform an exploration of the short-term dynamical evolution of 2013 VZ70 to confirm or reject a co-orbital relationship with Saturn. A possible connection with Saturn's irregular moon popu…
Recently Kipping (2021) identified the so-called "exomoon corridor", a potentially powerful new tool for identifying possible exomoon hosts, enabled by the observation that fully half of all planets hosting an exomoon will exhibit transit timing variation (TTV) periodicities of 2-4 epochs. One key outstanding problem in the search for exomoons, however, is the question of how well the methods we have developed under the single moon assumption extend to systems with multiple moons. In this work we use $N$-body simulations to examine the exomoon corridor effect in the more general case of $N \ge…
Due to tidal interactions in the Earth-Moon system, the spin of the Earth slows down and the Moon drifts away. This recession of the Moon is now measured with great precision, but it has been realized, more than fifty years ago, that simple tidal models extrapolated back in time lead to an age of the Moon that is by far incompatible with the geochronological and geochemical evidence. In order to evade this problem, more elaborate models have been proposed, taking into account the oceanic tidal dissipation. However, these models did not fit both the estimated lunar age and the present rate of l…
We build a conceptual coupled model of the climate and tidal evolution of the Earth-Moon system to find the influence of the former on the latter. An energy balance model is applied to calculate steady-state temperature field from the mean annual insolation as a function of varying astronomical parameters. A harmonic oscillator model is applied to integrate the lunar orbit and Earth's rotation with the tidal torque dependent on the dominant natural frequency of ocean. An ocean geometry acts as a bridge between temperature and oceanic frequency. On assumptions of a fixed hemispherical continent…
The four major satellites of Jupiter, known as the Galilean moons, and Saturn's most massive satellite, Titan, are believed to have formed in a predominantly gaseous circum-planetary disk, during the last stages of formation of their parent planet. Pebbles from the protoplanetary disk are blocked from flowing into the circumplanetary disk by the positive pressure gradient at the outer edge of the planetary gap, so the gas drag assisted capture of planetesimals should be the main contributor to the delivery of solids onto circum-planetary disks. However, a consistent framework for the subsequen…
Stellar spin-orbit misalignments (obliquities) in hot Jupiter systems have been extensively probed. Such obliquities may reveal clues about hot Jupiter dynamical histories. Common explanations for generating obliquities include high-eccentricity migration and primordial disk misalignment. This paper investigates another mechanism for producing stellar spin-orbit misalignments in systems hosting a close-in planet with an external, modestly inclined companion. Spin-orbit misalignment may be excited due to a secular resonance, occurring when the precession rate of the stellar spin axis (driven by…
The Pluto-Charon (PC) pair is usually thought of as a binary in the dual synchronous state, which is the endpoint of its tidal evolution. The discovery of the small circumbinary moons, Styx, Nix, Kerberos, and Hydra, placed close to the mean motions resonances (MMRs) 3/1, 4/1, 5/1, and 6/1 with Charon, respectively, reveals a complex dynamical architecture of the system. Several formation mechanisms for the PC system have been proposed. Our goal is to analyse the past and current orbital dynamics of the satellite system. We study the past and current dynamics of the PC system through a large s…
Are Thalassa and Despina in Resonance Lock with Neptune's Oscillations?
SETI Institute（SETI研究所）；Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange（蔚蓝海岸大学、蔚蓝海岸天文台、法国国家科学研究中心、拉格朗日实验室）；Centre national d’études spatiales (CNES)（法国国家空间研究中心）；Jet Propulsion Laboratory（喷气推进实验室）；University of Idaho（爱达荷大学）
We examine the effects that planetary encounters have on the moon systems of ejected gas giant planets. We conduct a suite of numerical simulations of planetary systems containing three Jupiter-mass planets (with the innermost planet at 3 AU) up to the point where a planet is ejected from the system. The ejected planet has an initial system of 100 test-particle moons. We determine the survival probability of moons at different distances from their host planet, measure the final distribution of orbital elements, examine the stability of resonant configurations, and characterize the properties o…
In this work we analyze the orbital evolution and the dynamical stability in the vicinity of the small Saturnian moons Aegaeon, Methone, Anthe and Pallene. We numerically resolve the exact equations of motions to investigate the orbital motion of thousands of test particles within and near to the domain of the 7/6, 14/15, 10/11 mean motion resonances of Aegaeon, Methone and Anthe with Mimas, respectively. We show that, for massless small moons, the orbits of particles initially restricted to the resonant domains remain stable for at least $10^4$ yr. We also conduct numerical simulations consid…
Exploration of vertical self-resonant bifurcations from Distant Retrograde Orbits (DROs) in the Earth-Moon Circular Restricted Three-Body Problem (CR3BP)
Context. The 98°-obliquity of Uranus is commonly attributed to giant impacts that occurred at the end of the planetary formation. This picture, however, is not devoid of weaknesses. Aims. On a billion-year timescale, the tidal migration of the satellites of Jupiter and Saturn has been shown to strongly affect their spin-axis dynamics. We aim to revisit the scenario of tilting Uranus in light of this mechanism. Methods. We analyse the precession spectrum of Uranus and identify the candidate secular spin-orbit resonances that could be responsible for the tilting. We determine the properties of t…
The origins of the Galilean satellites - namely Io, Europa, Ganymede, and Callisto - is not fully understood yet. Here we use N-body numerical simulations to study the formation of Galilean satellites in a gaseous circumplanetary disk around Jupiter. Our model includes the effects of pebble accretion, gas-driven migration, and gas tidal damping and drag. Satellitesimals in our simulations first grow via pebble accretion and start to migrate inwards. When they reach the trap at the disk inner edge, scattering events and collisions take place promoting additional growth. Growing satellites event…
The geometric arrangement of planet and moon orbits into a regularly spaced pattern of distances is the result of a self-organizing system. The positive feedback mechanism that operates a self-organizing system is accomplished by harmonic orbit resonances, leading to long-term stable planet and moon orbits in solar or stellar systems. The distance pattern of planets was originally described by the empirical Titius-Bode law, and by a generalized version with a constant geometric progression factor (corresponding to logarithmic spacing). We find that the orbital periods $T_i$ and planet distance…
Minor planet 2002 VE68 was identified as a quasi-satellite of Venus shortly after its discovery. At that time its data-arc span was only 24 days, now it is 2,947 days. Here we revisit the topic of the dynamical status of this remarkable object as well as look into its dynamical past and explore its future orbital evolution which is driven by close encounters with both the Earth-Moon system and Mercury. In our calculations we use a Hermite integration scheme, the most updated ephemerides and include the perturbations by the eight major planets, the Moon and the three largest asteroids. We confi…
Many science missions require an unobstructed view of space and a stable thermal environment but lack the technical or programmatic resources to reach orbits that satisfy these needs. This paper presents a high Earth orbit in 2:1 resonance with the Moon that provides these conditions, reached via lunar gravity assist. Analytical guidance and numerical investigation yielded deep insight into this unconventional orbit's behavior, making it possible to select a robust mission design. Solutions are available for a broad range of missions, from smaller Explorer-class missions such as the Transiting…
This work shows the dynamical instability that can happen to close-in satellites when planet oblateness is not accounted for in non-coplanar multiplanet systems. Simulations include two secularly interacting Jupiter-mass planets mutually inclined by 10 degrees, with the host planet either oblate or spherical. With a spherical host planet, moons within a critical planetocentric distance experience high inclinations and in some cases high eccentricities, while more distant moons orbit stably with low inclinations and eccentricities, as expected. These counter-intuitive dynamical phenomena disapp…
Satellite systems around giant planets are immersed in a region of complex resonant configurations. Understanding the role of satellite resonances contributes to comprehending the dynamical processes in planetary formation and posterior evolution. Our main goal is to analyse the resonant structure of small moons around Uranus and propose different scenarios able to describe the current configuration of these satellites. We focus our study on the external members of the regular satellites interior to Miranda, namely Rosalind, Cupid, Belinda, Perdita, Puck, and Mab, respectively. We use N-body i…
Life in the dark: Potential urability of moons of rogue planets
HUN-REN Konkoly Observatory, Research Centre for Astronomy and Earth Science（匈牙利科学院孔科伊天文台，地球与天文学研究中心）；CSFK, MTA Centre of Excellence（孔科伊天文台，匈牙利科学院卓越中心）；ELTE Eötvös Loránd University, Institute of Physics and Astronomy（布达佩斯罗兰大学物理与天文学研究所）
Aegaeon, Methone, Anthe, and Pallene are four Saturnian small moons, discovered by the Cassini spacecraft. Although their orbital characterization has been carried on by a number of authors, their long-term evolution has not been studied in detail so far. In this work, we numerically explore the long-term evolution, up to $10^5$ yr, of the small moons in a system formed by an oblate Saturn and the five largest moons close to the region: Janus, Epimetheus, Mimas, Enceladus, and Tethys. By using frequency analysis we determined the stability of the small moons and characterize, through diffusion…
Over the course of the last two decades, traditional models of planet formation have been repeatedly challenged by the emerging census of extrasolar planets. Key among them is the orbital architecture problem: while standard models of orbital migration predict resonant orbits for short-period objects, most planets do not appear to lie in orbital resonances. Here we show that the four-planet system Kepler-221, not previously recognized to have active orbital resonances, has a three-body commensurability relation unique within the Kepler sample. Using a suite of numerical experiments as well as …
A high-angular momentum giant impact with the Earth can produce a Moon with a silicate isotopic composition nearly identical to that of Earth's mantle, consistent with observations of terrestrial and lunar rocks. However, such an event requires subsequent angular momentum removal for consistency with the current Earth-Moon system. The early Moon may have been captured into the evection resonance, occurring when the lunar perigee precession period equals one year. It has been proposed that after a high-angular momentum giant impact, evection removed the angular momentum excess from the Earth-Mo…
HARPS-N Reveals a Well-aligned Orbit for the Highly Eccentric Warm Jupiter TOI-4127 b
The University of New Mexico（新墨西哥大学）；Instituto de Astrofísica de Canarias (IAC)（加那利天体物理研究所）；Universidad de La Laguna (ULL)（拉帕鲁纳大学）；Center for Computational Astrophysics, Flatiron Institute（平顿研究所计算天体物理学中心）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；INAF – Osservatorio Astrofisico di Torino（意大利国家天体物理研究所都灵天文台）
Detecting Planetary Oblateness in the Era of JWST: A Case Study of Kepler-167e
Tsinghua University（清华大学）；Nankai University（南开大学）；University of Virginia（弗吉尼亚大学）；Institute for Astronomy, University of Hawaii（夏威夷大学天文研究所）；Osaka University（大阪大学）
As the number of discovered extrasolar planets has been increasing, diversity of planetary systems requires studies of new formation scenarios. It is important to study satellite formation in circumplanetary disks, which is often viewed as analogous to formation of rocky planets in protoplanetary disks. We investigated satellite formation from satellitesimals around giant planets through N-body simulations that include gravitational interactions with a circumplanetary gas disk. Our main aim is to reproduce the observable properties of the Galilean satellites around Jupiter through numerical si…
Near-Earth objects (NEOs) moving in resonant, Earth-like orbits are potentially important. On the positive side, they are the ideal targets for robotic and human low-cost sample return missions and a much cheaper alternative to using the Moon as an astronomical observatory. On the negative side and even if small in size (2-50 m), they have an enhanced probability of colliding with the Earth causing local but still significant property damage and loss of life. Here, we show that the recently discovered asteroid 2013 BS45 is an Earth co-orbital, the sixth horseshoe librator to our planet. In con…
