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We examined the motion of asteroids across the three-body mean motion resonances (MMRs) with Jupiter and Saturn and with the Yarkovsky drift speed in the semimajor axis of the asteroids. The research was conducted using numerical integrations performed using the Orbit9 integrator with 84 000 test asteroids. We calculated time delays, dtr, caused by the seven three-body MMRs on the mobility of test asteroids with 10 positive and 10 negative Yarkovsky drift speeds, which are reliable for Main Belt asteroids. Our final results considered only test asteroids that successfully crossed over the MMRs without close approaches to the planets. We have devised two equations that approximately describe the functional relation between the average time 〈dtr〉 spent in the resonance, the strength of the resonance SR, and the semimajor axis drift speed da/dt (positive and negative) with the orbital eccentricities of asteroids in the range (0, 0.1). Comparing the values of 〈dtr〉 obtained from the numerical integrations and from the derived functional relations, we analysed average values of 〈dtr〉 in all three-body MMRs for every da/dt. The main conclusion is that the analytical and numerical estimates of the average time 〈dtr〉 are in very good agreement, for both positive and negative da/dt. Finally, this study shows that the functional relation we obtain for three-body MMRs is analogous to that previously obtained for two-body MMRs.

The paper presents the results of studying the dynamic structure of near-Earth orbital space in the regions of orbital resonances 1 : 4, 1 : 6, and 1 : 8 with the speed of the Earth’s rotation and studying the orbital evolution of objects moving in these regions. The action zones of five components for each of the listed orbital resonances, apsidal–nodal secular resonances and resonances with the mean motion of the third body (the Moon and the Sun) in the indicated regions of near-Earth orbital space are revealed. Distribution maps of the revealed resonances are presented. The dynamic maps of the studied areas obtained using the MEGNO indicator are presented. Areas of randomness corresponding to the overlap of resonances of different types are revealed.

The paper analyses possible transfers of bodies from the main asteroid belt (MBA) to the Centaur region. The orbits of asteroids in the 2:1 mean motion resonance (MMR) with Jupiter are analysed. We selected the asteroids that are in resonant orbits with e > 0.3 whose absolute magnitudes H do not exceed 16m. The total number of the orbits amounts to 152. Numerical calculations were performed to evaluate the evolution of the orbits over 100,000-year time interval with projects for the future. Six bodies are found to have moved from the 2:1 commensurability zone to the Centaur population. The transfer time of these bodies to the Centaur zone ranges from 4,600 to 70,000 yr. Such transfers occur after orbits leave the resonance and the bodies approach Jupiter. Where after reaching sufficient orbital eccentricities bodies approach a terrestrial planet, their orbits go out of the MMR. Accuracy estimations are carried out to confirm the possible asteroid transfers to the Centaur region., 11 pages, 10 figures, 1 table. Accepted in MNRAS

The noteworthy four-planet HR 8799 system teeters on the brink of gravitational instability and contains an A-type host star which is characteristic of the progenitors of the majority of known white dwarf planetary system hosts. Gozdziewski and Migaszewski (2020) have demonstrated that the system can retain all four planets for at least 1 Gyr along the main sequence if the planets evolve within an externally unperturbed 8:4:2:1 mean motion resonance configuration. Here we propagate forward their most stable fit beyond the main sequence, and incorporate external effects from Galactic tides and stellar flybys. We find that (i) giant branch mass loss always breaks the resonance, and usually triggers the ejection of two of the planets, (ii) stellar flybys and Galactic tides rarely break the resonance during the main-sequence and giant branch phases, but play a crucial role in determining the final planetary configurations around the eventual white dwarf host star, and (iii) the meanderings of the surviving planets vary significantly, occupying regions from under 1 au to thousands of au. The ubiquitous survival of at least one planet and the presence of the debris discs in the system should allow for dynamical pathways for the white dwarf to be metal-polluted., Accepted for publication in MNRAS

The non-resonant Kuiper belt objects (KBOs) between the 3:2 and 2:1 Neptunian mean motion resonances can be largely divided between a cold classical belt (CCB) and a hot classical belt (HCB). A notable difference between these two subpopulations is the prevalence of widely spaced, equal-mass binaries in the CCB and a much smaller but non-zero number in the HCB. The primary reason for this difference in binary rate remains unclear. Here using N-body simulations we examine whether close encounters with the giant planets during an early outer solar system instability may have disrupted primordial Kuiper Belt binaries that existed within the primordial Kuiper belt before they attained HCB orbits. We find that such encounters are very effective at disrupting binaries down to separations of ~1% of their Hill radius (as measured in the modern Kuiper belt), potentially explaining the paucity of widely spaced, equal mass binaries in the modern HCB. Moreover, we find that the widest binaries observed in the modern HCB are quite unlikely to survive planetary encounters, but these same planetary encounters can widen a small subset of tighter binaries to give rise to the small population of very wide binaries seen in today's HCB., Accepted 2021 April 28. Received 2021 April 26; in original form 2021 February 22. 5 pages, 3 figures, 2 tables

Artificial neural networks (ANN) have been successfully used in the last years to identify patterns in astronomical images. The use of ANN in the field of asteroid dynamics has been, however, so far somewhat limited. In this work we used for the first time ANN for the purpose of automatically identifying the behaviour of asteroid orbits affected by the M1:2 mean-motion resonance with Mars. Our model was able to perform well above 85% levels for identifying images of asteroid resonant arguments in term of standard metrics like accuracy, precision and recall, allowing to identify the orbital type of all numbered asteroids in the region. Using supervised machine learning methods, optimized through the use of genetic algorithms, we also predicted the orbital status of all multi-opposition asteroids in the area. We confirm that the M1:2 resonance mainly affects the orbits of the Massalia, Nysa, and Vesta asteroid families., Comment: 11 pages, 10 figures, 1 table. Accepted for publication in MNRAS

In this work, we investigate the near 2:1 mean motion resonance (MMR) capture scenario and tidal evolution for the hot-Neptune system HD 106315 by theoretical analysis and numerical simulations. To make a deeper understanding of migration for this system, we extensively explore the initial semi-major axis (SMA), eccentricity, as well as the attenuation coefficient of the eccentricity of HD 106315c that affect the orbital configuration of the system. The numerical simulations show that when the initial orbital elements of two planets are a b ∼ 0.4 au, a c ∼ 0.8 au, e b and e c lower than 0.03, HD 106315b and HD 106315c can migrate to currently observed location, and form near 2:1 mean motion resonance in about 65000 years. This scenario takes into account the gravitational effect of the central star and the viscosity of disk. In addition, the tidal dissipation that originates from the host star, can influence the MMR configuration for planets. From the point of theoretical analysis, the results show that for the tidal dissipation factor Q = 100 , the ratio of orbital period of two planets will change over the evolution. This may be indicative of the resonant departure for two planets in the system. However, according to numerical simulations, the tidal dissipation factor Q may be larger than 10 3 for the two planets, therefore we may safely conclude that tidal effect cannot play a major role in driving two Neptunian planets of the HD 106315 system move out of 2:1 mean motion resonance within the residual lifetime of the star.

Polar motion (PM) series from various observation methods and sources are analyzed using one and the same simple analysis tool. The maximum time resolution of the Earth Rotation Parameter (ERP) series considered here is one day, which leaves out ERP series with sub-daily time resolution. A longer spacing between subsequent epochs is permissible, a variable spacing between epochs like in the VLBI (Very Long Baseline Interferometry) series as well. The shortest length of the PM time series analyzed, based on GNSS (Global Navigation Satellite Systems), is 26+ years, the longest one, the IERS C01 series, 173+ years. Following the tradition, PM is decomposed into a mean motion, i.e., the motion of the center of the PM curve on the surface of the Earth, a prograde Chandler motion with a nominal period of 432.25 days, and a prograde annual motion with a nominal period of 365.25 days. In our analysis, Secular PM is not assumed as linear, but as piecewise linear and continuous. The defining parameters of the periodic parts of polar motion are not assumed as constant either, but as piecewise linear and continuous functions of time as well. All parameters of the PM model based on one particular ERP series are determined in one and the same linear least squares estimation. Parameters of the same type may be purely deterministic or filtered (smoothed) by constraining the second time differences of the parameters (the second time derivative of the parameter functions) of the same kind. The key results achieved by applying our method to a wide variety of ERP series are visualized and discussed. They include: (a) the description of a sharp bend of mean PM around 1996, (b) strong evidence for a multi-component model for Chandler motion with periods separated by few days, similar to that proposed by Chandler (1901), (c) a reconstruction of mean PM from 1846 to present taking into account the composite nature of the series, and (d) a prediction of Chandler motion for the next decades. A sharp bend of mean PM was found around 1995/96, along the meridian at about 70 ° West to the meridian at about 12–15° West. All PM curves analyzed show a mean motion in this new direction after 1995/95. Smaller excursions w.r.t.d this mean exist, with periods 10 years. A periodic variation with a period of about 180 years was observed in the Chandler signal of PM with an amplitude of more than 200 mas. The variation may be explained approximately by a composite nature of Chandler motion, similar to the model already proposed by Chandler (1901). This simple model was generalized using a Fourier series separated in period by few days. This alternative model of Chandler motion is used to predict the Chandler part of PM, with an amplitude close to zero currently, to reach values of the order of 100 mas around 2028–2030.

Extensive numerical experiments on the long-term dynamics of planetesimals near the orbits of planets around single stars with debris disks have been carried out. The radial sizes of planetesimal clusters and the planetary chaotic zone as a function of mass parameter $$\mu$$ (planet–star mass ratio) have been determined numerically with a high accuracy separately for the outer and inner parts of the chaotic zone. The results obtained have been analyzed and interpreted in light of existing analytical theories (based on the planet–planetesimal mean motion resonance overlap criterion) and in comparison with previous numerical-experiment approaches to the problem. We show and explain how the stepwise dependence of the chaotic zone sizes on $$\mu$$ is determined by the marginal resonances.

International audience; We present the analysis of the multi-planetary system Kepler-117, which is part of our program of observations of Kepler planets. This system is composed of a ~ 30 MEarth planet in a ~ 19 days orbit and a ~ 2 MJ planet orbiting in ~ 51 days. Both the orbits have low eccentricity. The planets are not close to an exact low-order mean motion resonance, but exhibit significant transit timing variations (TTVs) nevertheless. We perform a combined Markov Chain Monte Carlo fit on all the available data: the Kepler photometry, the TTVs, the radial velocities we obtained with SOPHIE/OHP and the stellar parameters. The prime result is that the modelling of the TTVs allows to increase the precision on the system parameters which are not constrained by the radial velocities alone.

Background: The location and stability of the equilibrium points are studied for the Planar Circular Restricted Three-Body Problem where the more massive primary is an oblate spheroid. Methods: The mean motion of the equations of motion is formulated from the secular perturbations as derived by(1) and used in(2–4). The singularities of the equations of motion are found for locating the equilibrium points. Their stability is analysed using the linearized variational equations of motion at the equilibrium points. Findings: As the effect of oblateness in the mean motion expression increases, the location and stability of the equilibrium points are affected by the oblateness of the more massive primary. It is interesting to note that all the three collinear points move towards the more massive primary with oblateness. It is a new result. Among the shifts in the locations of the five equilibrium points, the y–location of the triangular equilibrium points relocate the most. It is very interesting to note that the eccentricities (e) of the orbits around L1 and L3 increase, while it decreases around L2 with the addition of oblateness with the new mean motion. The decrease in e is significant in Saturn-Mimas system from 0.95036 to 0.87558. Similarly, the value of the critical mass ratio mc, which sets the limit for the linear stability of the triangular points, further reduces significantly from 0:285: : :A1 to 0:365: : :A1 with the new mean motion. The mean motion sz in the z-direction increases significantly with the new mean motion from 9A1/4 to 9A1/2. Keywords: Circular Restricted Three-Body Problem (CRTBP); oblateness; mean motion; equilibrium points; critical mass ratio; tadpole orbits

Some systems of close-in "super-Earths" contain five or more planets on non-resonant but compact and nearly coplanar orbits. The Kepler-11 system is an iconic representative of this class of system. It is challenging to explain their origins given that planet-disk interactions are thought to be essential to maintain such a high degree of coplanarity, yet these same interactions invariably cause planets to migrate into chains of mean motion resonances. Here we mine a large dataset of dynamical simulations of super-Earth formation by migration. These simulations match the observed period ratio distribution as long as the vast majority of planet pairs in resonance become dynamically unstable. When instabilities take place resonances are broken during a late phase of giant impacts, and typical surviving systems have planet pairs with significant mutual orbital inclinations. However, a subset of our unstable simulations matches the Kepler-11 system in terms of coplanarity, compactness, planet-multiplicity and non-resonant state. This subset have dynamical instability phases typically much shorter than ordinary systems. Unstable systems may keep a high degree of coplanarity post-instability if planets collide at very low orbital inclinations ($\lesssim1^\circ$) or if collisions promote efficient damping of orbital inclinations. If planetary scattering during the instability takes place at low orbital inclinations ($\text{i}\lesssim1^\circ$), orbital inclinations are barely increased by encounters before planets collide.When planetary scattering pumps orbital inclinations to higher values ($\gtrsim 1^\circ$) planets tend to collide at higher mutual orbital inclinations, but depending on the geometry of collisions mergers' orbital inclinations may be efficiently damped. Each of these formation pathways can produce analogues to the Kepler-11 system., Comment: Accepted by MNRAS, 9 pages, 10 figures, 1 appendix

In this work, we investigate configuration formation of two inner terrestrial planets near mean motion resonance (MMRs) induced by the perturbation of a distant gas-giant for the Kepler-68 system, by conducting thousands of numerical simulations. The results show that the formation of terrestrial planets is relevant to the speed of Type I migration, the mass of planets, and the existence of giant planet. The mass and eccentricity of the giant planet may play a crucial role in shaping the final configuration of the system. The inner planet pair can be trapped in 5:3 or 7:4 MMRs if the giant planet revolves the central star with an eccentric orbit, which is similar to the observed configuration of Kepler-68. Moreover, we find that the eccentricity of the middle planet can be excited to roughly 0.2 if the giant planet is more massive than 5 $M_J$,otherwise the terrestrial planets are inclined to remain near-circular orbits. Our study may provide a likely formation scenario for the planetary systems that harbor several terrestrial planets near MMRs inside and one gas-giant exterior to them., Comment: 13 pages, 8 figures, accepted for publication in MNRAS

Zeipel–Lidov–Kozai cycles is the name given to long-term interrelated changes in the inclinations and eccentricities of the orbits of natural and artificial celestial bodies. They were discovered independently by H. von Zeipel (1910), M. Lidov (1961), and Y. Kozai (1962). Originally, the existence of Zeipel–Lidov–Kozai cycles was established for nonresonant motions of celestial bodies. Approaches to studying such secular effects in the case of resonance of orbital movements appeared much later. It turned out that, at resonance, the Zeipel–Lidov–Kozai cycles may not have the symmetry that these cycles always have in nonresonant situations within the framework of the restricted three-body problem. Moreover, results of numerical studies indicate the presence of asymmetric Zeipel–Lidov–Kozai cycles in the dynamics of a number of Kuiper belt objects moving in resonance with Neptune.

Made available in DSpace on 2020-12-12T02:42:43Z (GMT). No. of bitstreams: 0 Previous issue date: 2020-05-01 Near the turning of this millennium (1996–2004) it was detected that Prometheus and Pandora were not in their angular positions as predicted from their discoveries by the Voyager spacecrafts (1980). This is known as the problem of the lags of Prometheus and Pandora. The explanation for the origin of these lags is the chaotic motion associated with 121:118 mean motion resonance between the satellites. In the present work we revisit this problem and adopting the most extensive set of lags data, given by [R.G. French et al., Icarus 162, 143 (2003)], to show the need of unaccounted effects to produce the measured lags. By the analysis of conservation of angular momentum it can be verified that the mutual interaction between Prometheus and Pandora should be inversely proportional to the ratio of their masses. In this way, only the gravitational interaction between the two satellites does not explain such values. Consequently, the ratio between the lags of Prometheus and Pandora, Q, should be constant, and approximately the value of the inverse ratio between their masses (0.56, from [R.G. French et al., Icarus 162, 143 (2003)]). However, the values of Q from the measured lags are much higher, ranging from 48% up to 68% larger. Beyond that, the values increase over time in a rate given by the equation Q(t = 0.067 + 0.013t). Therefore, this analysis clearly shows the need of other mechanisms beyond the mutual interaction between Prometheus and Pandora in order to produce such values of lags. We estimate that at least one effect that produces an additional variation of mean motion of about 0.45°/year in one of the satellites for about 20 years would be necessary. UNESP – São Paulo State University School of Engineering Guaratinguetá Grupo de Dinâmica Orbital & Planetologia UNESP – São Paulo State University School of Engineering Guaratinguetá Grupo de Dinâmica Orbital & Planetologia

Background/Objectives: This study deals wit h the stationary solutions of the planar circular restricted three-body problem when the more massive primary is a source of radiation and the smaller primary is an oblate spheroid with its equatorial plane coincident with the plane of motion. The objective is to study the location of the Lagrangian points and to find the values of critical mass. Also, to study the periodic orbits around the Lagrangian points. Methods: A new mean motion expression by including the secular perturbation due to oblateness utilized by(1,2) is used in the present studies. The characteristic roots are obtained by linearizing the equation of the motion around the Lagrangian points. Findings: The critical mass parameter µcrit(3,4) , which decreases radiation force, whereas it increases with oblateness when we consider the value of new mean motion. Through special choice of initial conditions, retrograde elliptical periodic orbits exist for the case µ = µcrit, whose eccentricity increases with oblateness and decreases with radiation force for non-zero oblateness, although there is slight variation in L2 location. Keywords: Restricted three body problem; Lagrangian points; Eccentricity; Oblateness; Critical mass; Radiation force; Mean motion.

There is evidence that most chains of mean motion resonances of type $k$:$k-1$ among exoplanets become unstable once the dissipative action from the gas is removed from the system, particularly for large $N$ (the number of planets) and $k$ (indicating how compact the chain is). We present a novel dynamical mechanism that can explain the origin of these instabilities and thus the dearth of resonant systems in the exoplanet sample. It relies on the emergence of secondary resonances between a fraction of the synodic frequency $2 \pi (1/P_1-1/P_2)$ and the libration frequencies in the mean motion resonance. These secondary resonances excite the amplitudes of libration of the mean motion resonances thus leading to an instability. We detail the emergence of these secondary resonances by carrying out an explicit perturbative scheme to second order in the planetary masses and isolating the harmonic terms that are associated with them. Focusing on the case of three planets in the 3:2 -- 3:2 mean motion resonance as an example, a simple but general analytical model of one of these resonances is obtained which describes the initial phase of the activation of one such secondary resonance. The dynamics of the excited system is also briefly described. This scheme shows how one can obtain analytical insight into the emergence of these resonances, and into the dynamics that they trigger. Finally, a generalisation of this dynamical mechanism is obtained for arbitrary $N$ and $k$. This leads to an explanation of previous numerical experiments on the stability of resonant chains, showing why the critical planetary mass allowed for stability decreases with increasing $N$ and $k$., Comment: Submitted to MNRAS

According to statistics of planetary period ratios in multi-planet extrasolar systems, evident excesses appear just over the exact integral ratios 2 : 1 and 3 : 2 , while deficits exist on the near left side. There are various dynamical explanations for the phenomenon. For three observed planets in Kepler-9 system, the period ratio of the planet b and c approximately equals to 2.03, which cause this planet pair as a typical sample close to the 2:1 resonance. For two situations where secular interactions are considered only and resonance perturbations are added in, we applied Hamiltonian functions with second-order eccentricity terms to provide positions of current orbital configurations located in the level curves of energy as well as surfaces of section, then discussed the probable near resonance configurations of the two planets.

In this paper, we investigate the Kozai mechanism inside the inclined mean motion resonance (MMR) through a three-dimensional (3D) phase space. The Hamiltonian approximation for both prograde and retrograde MMRs is established by a semi-analytical method. We pick Jupiter as the disturber and study the Kozai mechanism in the Sun–Jupiter circular restricted three-body problem. Kozai islands of the prograde and retrograde MMRs are found in the 3D phase space. Numerical integration demonstrates that the locus of the orbit on the Kozai island is bounded by the Kozai island in the 3D phase space, so the orbit is locked in the Kozai+MMR state. The study of the Kozai dynamics inside a retrograde 1:1 MMR indicates that Kozai islands in the 3D phase space are just a sufficient condition for the Kozai+MMR mechanism rather than a necessary condition. There is no Kozai island in the 3D space for the retrograde 1:1 MMR, but the resonant coupling of Kozai with the retrograde 1:1 MMR appears in the phase space. Finally, dynamical behaviours of the two test particles located on Kozai islands are demonstrated in the ephemeris model.

The Yarkovsky effect is an important force to consider in order to understand the long-term dynamics of asteroids. This non-gravitational force affects the orbital elements of objects revolving around a source of heat, especially their semi-major axes. Following the recently defined `limiting' value of the Yarkovsky drift speed at 7x10-5 au/Myr in Milic Žitnik (2019) (below this value of speed asteroids typically jump quickly across the mean motion resonances), we decided to investigate the relation between the asteroid family Yarkovsky V-shape and the `limiting' Yarkovsky drift speed of asteroid's semi-major axes. We have used the known scaling formula to calculate the Yarkovsky drift speed (Spoto et al. 2015) in order to determine the inner and outer `limiting' diameters (for the inner and outer V-shape borders) from the `limiting' Yarkovsky drift speed. The method was applied to 11 asteroid families of different taxonomic classes, origin type and age, located throughout the Main Belt. Here, we present the results of our calculation on relationship between asteroid families' V-shapes (crossed by strong and/or weak mean motion resonances) and the `limiting' diameters in the (a, 1=D) plane. Our main conclusion is that the `breakpoints' in changing V-shape of the very old asteroid families, crossed by relatively strong mean motion resonances on both sides very close to the parent body, are exactly the inverse of `limiting' diameters in the a versus 1=D plane. This result uncovers a novel interesting property of asteroid families' Yarkovsky V-shapes.

A hybrid forecasting methodology to predict one-minute averaged solar irradiance one to ten minutes in advance is presented and evaluated. The methodology combines the use of all-sky images and irradiance measurements which are both processed in real time to produce the forecast. Pre-existing image processing techniques are locally adapted to estimate the mean motion of clouds, which is used to predict the future sun disk cover by clouds. Then, the predicted cloud information is converted into a solar irradiance estimate using the proposed model which uses real time measurements to extract its parameters for prediction. The validation of the method is done with a sample of 5238 forecasting time points, spread over a six-month period. The forecast uncertainty is assessed separately for clear, cloudy and partly cloudy days, revealing important characteristics of the model's performance under the different conditions. Under partly cloudy and highly variable conditions, positive forecasting skills with respect to regular persistence are achieved above forecasting horizons of two minutes, with a peak performance of 11.4% for forecasting horizons of six and ten minutes. The proposed model also outperforms a smart persistence model for all time horizons under these sky conditions. The model's ramp detection index (RDI, as defined in Chu et al. (2015)) is also evaluated for high and moderate ramps, achieving RDI indexes between 55 and 62% and between 43 and 49% for high and moderate ramps, respectively. These results show that in challenging highly variable solar irradiance conditions the proposed model is suitable for the very short term solar resource forecasting.

In this paper, we investigate planar near-Earth asteroids (NEAs) in resonance with the Earth. Integrable approximations for both prograde and retrograde two-body mean motion resonances (MMRs) are introduced in the planar circular restricted three-body problem (CRTBP). A preliminary analysis is implemented in the CRTBP to select candidate planar resonant NEAs. Based on limitations on the inclinations and semimajor axes, 510 candidate resonant NEAs are obtained. We propose a parameter to measure the minimum distance of the trajectory from the collision curve in the CRTBP. The obtained candidate resonant NEAs are further investigated in the ephemeris model, where the gravities of the nine planets are considered and the initial states of the nine planets are obtained from the Jet Propulsion Laboratory (JPL) database. Encounter times are defined as the time intervals between two successive encounters and are recorded through numerical integration. Among 510 candidate resonant NEAs, 386 Earth-crossing NEAs with encounter times smaller than 10,000 years are analyzed in detail. NEAs with distances from the nearest neighboring resonance below 0.015 au are defined as compact NEAs, while those with distances above 0.015 au are defined as sparse NEAs. Numerical tests indicate that compact NEAs have a weak correlation between the minimum distance to the collision curve and the encounter time, but sparse NEAs, whether with or without other planets' encounters have a strong linear correlation between the minimum distance to the collision curve and the encounter time in a statistical sense. Depending on the value of the minimum distance to the collision curve, Earth-crossing NEAs are classified into resonant and nonresonant NEAs in the CRTBP. Numerical results show that a resonant NEA in the CRTBP is more likely to have a larger encounter time in the ephemeris model than a nonresonant NEA in the CRTBP, especially for sparse NEAs. Finally, three resonant sparse NEAs and three compact NEAs are demonstrated in detail.

This work examines asteroid’s motion with orbital eccentricity e in the range (0.1, 0.2) across the two-body mean motion resonance (MMR) with Jupiter due to the Yarkovsky effect. We calculated time delays dtr caused by the resonance on the mobility of an asteroid with the Yarkovsky drift speed. Our results considered only asteroids that successfully cross over the resonance without close encounters with planets. We found a functional relation that accurately describes dependence between the average time lead/lag dtr, the strength of the resonance (SR), and the semimajor axis drift speed da/dt with asteroids' orbital eccentricities in the range (0.1, 0.2). We analysed average values of dtr using this functional relation comparing with obtained values of dtr from the numerical integrations, which were performed in an ORBIT9 integrator with a very large number of test asteroids. We checked the validity of our previous functional relation, derived for asteroids’ orbital eccentricities in the range (0, 0.1) (Figure 1), on the present results for eccentricities in the range (0.1, 0.2) (Figure 2). Also, we tried to find a unique functional relation for the whole interested interval of asteroids' orbital eccentricities (0, 0.2) and discussed it.

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 considering Aegaeon, Methone, Anthe and Pallene as massive bodies. The results show that most particles undergo significant perturbations in their orbital motions, ultimately destabilizing in timescales of a few hundreds of years or even less through collisions with the four small moons. In addition, we also simulate the orbital evolution of test particles initially distributed in form of arc around Aegaeon, Methone and Anthe. We show that the initial arcs are dynamically eroded on timescales of hundreds of years, allowing us to constraint the timescales for which gravitational forces operate to remove particles from the observed arcs., Comment: Published in MNRAS

We examine the Poynting-Robertson (PR) effect under the influence of a logarithmic predicted as a correction to the Newtonian gravitational potential in the solar system. Our motivation emanates from the fact that today’s gravitational theories predict various corrections such that exponential, logarithmic to describe and understand the existence of dark matter, postulated to resolve discrepancies in astrophysical observations in today’s accepted theories of gravity. By saying that we simply mean that our main interest is to calculate the times that dust particles take to reach the Earth’s orbit and derive analytical expressions for the time changes of basic orbital elements in the influence of the PR effect. We use dust particle starting at a distance $r = 2.7~\text{AU}$ or approximately in the asteroid belt. In a first order perturbation treatment we obtain time solutions for the orbital elements of semi major axis, eccentricity, and mean motion, as well as expressions for the time taken for these particles to reach Earth’s orbit. We find that for circular orbits in a logarithmic potential the time taken to reach Earth is slightly larger that the elliptical orbits. Newtonian potential circular orbits require more times when compared to the logarithmic ones. Finally elliptical orbits time to reach Earth are of the same order of magnitude with a dependence on the eccentricity, density, and particle diameter.

We explore the orbital dynamics of systems consisting of three planets, each as massive as the Earth, on coplanar, initially circular, orbits about a star of one solar mass. The initial semimajor axes of the planets are equally spaced in terms of their mutual Hill radius, which is equivalent to a geometric progression of orbital periods for small planets of equal mass. Our simulations explore a wide range of spacings of the planets, and were integrated for virtual times of up to 10 billion years or until the orbits of any pair of planets crossed. We find the same general trend of system lifetimes increasing exponentially with separation between orbits seen by previous studies of systems of three or more planets. One focus of this paper is to go beyond the rough trends found by previous numerical studies and quantitatively explore the nature of the scatter in lifetimes and the destabilizing effects of mean motion resonances. In contrast to previous results for five-planet systems, a nontrivial fraction of three-planet systems survive at least several orders of magnitude longer than most other systems with similar initial separation between orbits, with some surviving 1010 years at much smaller orbital separations than any found for five-planet systems. Substantial shifts in the initial planetary longitudes cause a scatter of roughly a factor of two in system lifetime, whereas the shift of one planet's initial position by 100 m along its orbit results in smaller changes in the logarithm of the time to orbit crossing, especially for systems with short lifetimes.

Recent works on three-planet mean motion resonances (MMRs) have highlighted their importance for understanding the details of the dynamics of planet formation and evolution. While the dynamics of two-planet MMRs are well understood and approximately described by a one degree of freedom Hamiltonian, little is known of the exact dynamics of three-bodies resonances besides the cases of zeroth-order MMRs or when one of the body is a test particle. In this work, I propose the first general integrable model for first-order three-planet mean motion resonances. I show that one can generalize the strategy proposed in the two-planet case to obtain a one degree of freedom Hamiltonian. The dynamics of these resonances are governed by the second fundamental model of resonance. The model is valid for any mass ratio between the planets and for every first-order resonance. I show the agreement of the analytical model with numerical simulations. As examples of application I show how this model could improve our understanding of the capture into MMRs as well as their role on the stability of planetary systems., Accepted in Celestial Mechanics and Dynamical Astronomy

Few solar system asteroids and comets are found in high-eccentricity orbits (e > 0.9), but in the primordial planetesimal disks and in exoplanet systems around dying stars such objects are believed to be common. For 2006 HY51, the main belt asteroid with the highest known eccentricity 0.9684, we investigate the probable rotational states today using our computer-efficient chaotic process simulation method. Starting with random initial conditions, we find that this asteroid is inevitably captured into stable spin–orbit resonances typically within tens to a hundred megayears. The resonances are confirmed by direct integration of the equation of motion in the vicinity of endpoints. Most resonances are located at high spin values above 960 times the mean motion (such as 964:1 or 4169:4), corresponding to rotation periods of a few days. We discover three types of resonance in the high-eccentricity regime: (1) regular circulation with weakly librating aphelion velocities and integer-number spin–orbit commensurabilities, (2) switching resonances of higher order with orientation alternating between aligned (0 or π) and sidewise (π/2) angles at aphelia and perihelia, (3) jumping resonances with aphelion spin alternating between two quantum states in the absence of spin–orbit commensurability. The islands of equilibrium are numerous at high spin rates but small in parameter space area, so that it takes millions of orbits of chaotic wandering to accidentally entrap in one of them. We discuss the implications of this discovery for the origins and destiny of high-eccentricity objects and the prospects of extending this analysis to the full 3D treatment.

This work expands on the implementation of three-dimensional (3D) normalized gradient fields to correct for whole-body motion and cardiac creep in [N-13]-ammonia patient studies and evaluates its accuracy using a dynamic phantom simulation model. METHODS A full rigid-body algorithm was developed using 3D normalized gradient fields including a multi-resolution step and sampling off the voxel grid to reduce interpolation artifacts. Optimization was performed using a weighted similarity metric that accounts for opposing gradients between images of blood pool and perfused tissue without the need for segmentation. Forty-three retrospective dynamic [N-13]-ammonia PET/CT rest/adenosine-stress patient studies were motion corrected and the mean motion parameters plotted at each frame time point. Motion correction accuracy was assessed using a comprehensive dynamic XCAT simulation incorporating published physiologic parameters of the heart's trajectory following adenosine infusion as well as corrupted attenuation correction commonly observed in clinical studies. Accuracy of the algorithm was assessed objectively by comparing the errors between isosurfaces and centers of mass of the motion corrected XCAT simulations. RESULTS In the patient studies, the overall mean cranial-to-caudal translation was 7 mm at stress over the duration of the adenosine infusion. Noninvasive clinical measures of relative flow reserve and myocardial flow reserve were highly correlated with their invasive analogues. Motion correction accuracy assessed with the XCAT simulations showed an error of

Head motion continues to be a major problem in fMRI research, particularly in developmental studies where an inverse relationship exists between head motion and age. Despite multifaceted and costly efforts to mitigate motion and motion-related signal artifact, few studies have characterized in-scanner head motion itself.This study leverages a large public dataset (N=1388, age 5-21y, The Healthy Brain Network Biobank) to characterize pediatric head motion in space, frequency, and time. We focus on practical aspects of head motion that could impact future study design, including comparing motion across groups (low, medium, and high movers), across conditions (movie-watching and rest), and between males and females.Analyses showed that in all conditions, high movers exhibited a different pattern of motion than low and medium movers that was dominated by x-rotation, and z- and y-translation. High motion spikes (>0.3mm) from all participants also showed this pitch-z-y pattern. Problematic head motion is thus composed of a single type of biomechanical motion, which we infer to be a nodding movement, providing a focused target for motion reduction strategies. A second type of motion was evident via spectral analysis of raw displacement data. This was observed in low and medium movers and was consistent with respiration rates. We consider this to be a baseline of motion best targeted in data preprocessing. Further, we found that males moved more than, but not differently from, females.Significant cross-condition differences in head motion were found. Movies had lower mean motion, and especially in high movers, movie-watching reduced within-run linear increases in head motion (i.e., temporal drift). Finally, we used intersubject correlations of framewise displacement (FD-ISCs) to assess for stimulus-correlated motion trends. Subject motion was more correlated in movie than rest and stimulus-correlated stillness occurred more often than stimulus-correlated motion. Possible reasons and future implications of these findings are discussed.

We address the attitude dynamics of a triaxial rigid body in a circular orbit. This task is done by means of an intermediary model, which is obtained by splitting the Hamiltonian in the form H = H 0 + H 1 , where H 0 is required to be a non-degenerate integrable Hamiltonian system. A numerical study is presented comparing the dynamics of the new intermediary model with the full system (MacCullagh’s truncation) and showing a competitive performance for the cases Sun-asteroid and Earth-spacecraft. This model defines a Poisson flow endowed with invariants defining a S M 2 × S M 2 reduced space. We analyze the coupling between the orbital mean motion and rotational variables. The key role played by the moments of inertia and the value of the angular momentum is shown in detail. The analysis of the intermediary shows that, under slow rotation regime, the classic dynamics of the free rigid body is no longer maintained: bifurcations with changes of stability are displayed for several critical inclinations of the rotational angular momentum plane and for critical orientations of the body frame. Moreover, the evolution of the angular momentum plane is given by a time dependent harmonic oscillator.

In 2010 the first planet was discovered around star HD 34445. Recently, another five planets were announced orbiting the same star. It is a rather dense multi-planet system with some of its planets having separations of fractions of an au and minimum masses ranging from Neptune to sub-Jupiter ones. Given the number of planets and the various uncertainties in their masses and orbital elements, the HD 34445 planetary system is quite interesting as there is the potential for mean motion and secular resonances that could render the outcome of its dynamical evolution and fate an open question. In this paper we investigate the dynamical stability of the six planet system in order to check the validity of the orbital solution acquired. This is achieved by a series of numerical experiments, where the dynamical evolution of the system is tested on different timescales. We vary the orbital elements and masses of the system within the error ranges provided. We find that for a large area of the parameter space we can produce stable configurations and therefore conclude it is very likely that the HD 34445 planetary system is real. Some discussion about the potential habitability of the system is also done., Comment: Accepted for publication in MNRAS

Newly forming proto-planets are expected to create cavities and substructures in young, gas-rich proto-planetary disks, but they are difficult to detect as they could be confused with disk features affected by advanced image-analysis techniques. Recently, a planet was discovered inside the gap of the transitional disk of the T-Tauri star PDS 70. Here we report on the detection of strong H-alpha emission from two distinct locations in the PDS 70 system, one corresponding to the previously discovered planet PDS 70 b, which confirms the earlier H$\alpha$ detection, and another located close to the outer-edge of the gap, coinciding with a previously identified bright dust spot in the disk and with a small opening in a ring of molecular emission. We identify this second H$\alpha$ peak as a second proto-planet in the PDS 70 system. The H$\alpha$ emission spectra of both proto-planets indicate ongoing accretion onto the proto-planets, which appear to be near a 2:1 mean motion resonance. Our observations show that adaptive-optics-assisted, medium-resolution, integral-field spectroscopy with MUSE targeting accretion signatures will be a powerful way to trace ongoing planet formation in transitional disks at different stages of their evolution. Finding more young planetary systems in mean motion resonance would give credibility to the Grand Tack hypothesis in which Jupiter and Saturn migrated in a resonance orbit during the early formation period of our Solar System., Comment: Nature Astronomy, June 3, 2019; 15 pages, 3 Figs, 1 Table

Applying the technique of dynamical maps we study the orbital stability of test particles in the Solar System in the space (a,e,i) defined by 0.1

The paper is focused on studying the motion of asteroid 3200 Phaethon which approached the Earth in December 2017. We consider the dynamics of asteroid 3200 Phaethon, reveal its encounters with planets, mean motion and secular resonances, and estimate the predictability time and the causes of chaoticity. A peculiar feature in the dynamics of the object is that it passes through the unstable orbital resonance 3/7 with Venus and exhibits a gamut of apsidal-nodal resonances with Mercury, Venus, Earth, Mars, and Jupiter, as well as a large number of close encounters with terrestrial planets. These properties result in a chaotic character of the motion beyond a time interval between the years 1780 and 2350.

Protoplanetary disks are thought to be truncated at orbital periods of around 10 days. Therefore, origin of rocky short period planets with $P < 10$ days is a puzzle. We propose that many of these planets may form through the Type-I migration of planets locked into a chain of mutual mean motion resonances. We ran N-body simulations of planetary embryos embedded in a protoplanetary disk. The embryos experienced gravitational scatterings, collisions, disk torques, and dampening of orbital eccentricity and inclination. We then modelled Kepler observations of these planets using a forward model of both the transit probability and the detection efficiency of the Kepler pipeline. We found that planets become locked into long chains of mean motion resonances that migrate in unison. When the chain reaches the edge of the disk, the inner planets are pushed past the edge due to the disk torques acting on the planets farther out in the chain. Our simulated systems successfully reproduce the observed period distribution of short period Kepler planets between 1 and 2 $R_\oplus$. However, we obtain fewer closely packed short period planets than in the Kepler sample. Our results provide valuable insight into the planet formation process, and suggests that resonance locks, migration, and dynamical instabilities play important roles the the formation and evolution of close-in small exoplanets., 12 pages, 11 figures, submitted to MNRAS

Large asset values of satellites and demand for orbital slots in the Geostationary orbit belt motivates on-orbit servicing and active debris removal strategies. The challenge of on-orbit capture of tumbling serviceable satellites or debris targets is primarily overcome by including a target detumble prior to any mechanical interface. Of the many methods proposed, touchless electrostatic detumbling shows significant advantages in collision avoidance and preservation of the target object. Previous studies demonstrated that the electrostatic interaction is sufficient to touchlessly despin the fixed-axis rotation of a rocket body-sized object within several days. This work focuses on large, generally tumbling axi-symmetric targets in the Geostationary Orbit which form a large component of the GEO debris population. The deep-space controller is augmented for tugging, pushing, and nominal detumbling configurations, providing a complete analysis of the stability and convergence properties. The effectiveness of this detumble control is numerically illustrated by simultaneously detumbling and tugging the target in GEO. The controller reduces the tumbling to the order of the mean motion allowing for mechanical docking methods.

Constellation design theory has been studied extensively. However, analysis of longitude-dependent perturbation effects on inter-satellite distance drift has not received much attention. In addition to oblateness-related perturbations, sectoral and tesseral perturbations are non-negligible for low Earth orbits, due to their effect on inter-satellite distance evolution. This paper introduces the idea of reducing the tesseral/sectoral relative drift by including these perturbations in the short-periodic correction of the mean elements. An analytical expression of the correction is derived based on the Lie transform theory. Different from previous works, the ratio between the Earth rotation rate and the satellite’s mean motion is chosen as the small parameter in the Lie theory formulation. The independent variables of the generating-function-related partial differential equations can be reduced to a single variable when using this small parameter. Numerical simulations validate that the sectoral and tesseral effects on the inter-satellite distance drift in satellite constellations can be mitigated by using the proposed correction of the mean elements.

In this work, retrograde mean motion resonances (MMRs) are investigated by means of analytical and numerical approaches. Initially, we define a new resonant angle to describe the retrograde MMRs and then perform a series of canonical transformations to formulate the resonant model, in which the phase portrait, resonant centre and resonant width can be analytically determined. To validate the analytical developments, the non-perturbative analysis is made by taking advantage of Poincar\'e surfaces of section. Some modifications are introduced in the production of Poincar\'e sections and, in particular, it becomes possible to make direct comparisons between the analytical and numerical results. It is found that there exists an excellent correspondence between the phase portraits and the associated Poincar\'e sections, and the analytical results agree well with the numerical results in terms of the resonant width and the location of resonant centre. Finally, the numerical approach is utilized to determine the resonant widths and resonant centres over the full range of eccentricity. In particular, seven known examples of retrograde asteroids including 2015 BZ509, 2008 SO218, 1999 LE31, 2000 DG8, 2014 AT28, 2016 LS and 2016 JK24 are found inside the libration zones of retrograde MMRs with Jupiter. The results obtained in this work may be helpful for understanding the dynamical evolution for asteroids inside retrograde MMRs., Comment: Accepted for publication in MNRAS

Background: Here we aimed to evaluate the respiratory and cardiac-induced motion of a ICD lead used as surrogate in the heart during stereotactic body radiotherapy (SBRT) of ventricular tachycardia (VT). Data provides insight regarding motion and motion variations during treatment. Materials and methods: We analyzed the log files of surrogate motion during SBRT of ventricular tachycardia performed in 20 patients. Evaluated parameters included the ICD lead motion amplitudes; intrafraction amplitude variability; correlation error between the ICD lead and external markers; and margin expansion in the superior-inferior (SI), latero-lateral (LL), and anterior-posterior (AP) directions to cover 90% or 95% of all amplitudes. Results: In the SI, LL, and AP directions, respectively, the mean motion amplitudes were 5.0 +/- 2.6, 3.4. +/- 1.9, and 3.1 +/- 1.6 mm. The mean intrafraction amplitude variability was 2.6 +/- 0.9, 1.9 +/- 1.3, and 1.6 +/- 0.8 mm in the SI, LL, and AP directions, respectively. The margins required to cover 95% of ICD lead motion amplitudes were 9.5, 6.7, and 5.5 mm in the SI, LL, and AP directions, respectively. The mean correlation error was 2.2 +/- 0.9 mm. Conclusions: Data from online tracking indicated motion irregularities and correlation errors, necessitating an increased CTV-PTV margin of 3 mm. In 35% of cases, the motion variability exceeded 3 mm in one or more directions. We recommend verifying the correlation between CTV and surrogate individually for every patient, especially for targets with posterobasal localization where we observed the highest difference between the lead and CTV motion. Web of Science 26 1 137 128

This study aims at developing a new set of equations of mean motion in the presence of surface waves, which is practically applicable from deep water to the coastal zone, estuaries, and outflow areas. The generalized Lagrangian mean (GLM) method is employed to derive a set of quasi-Eulerian mean three-dimensional equations of motion, where effects of the waves are included through source terms. The obtained equations are expressed to the second-order of wave amplitude. Whereas the classical Eulerian-mean equations of motion are only applicable below the wave trough, the new equations are valid until the mean water surface even in the presence of finite-amplitude surface waves. A two-dimensional numerical model (2DV model) is developed to validate the new set of equations of motion. The 2DV model passes the test of steady monochromatic waves propagating over a slope without dissipation (adiabatic condition). This is a primary test for equations of mean motion with a known analytical solution. In addition to this, experimental data for the interaction between random waves and a mean current in both non-breaking and breaking waves are employed to validate the 2DV model. As shown by this successful implementation and validation, the implementation of these equations in any 3D model code is straightforward and may be expected to provide consistent results from deep water to the surf zone, under both weak and strong ambient currents.

A distant, massive planet in the outer solar system has recently been proposed to explain some observed features of extreme trans-Neptunian objects (TNOs). Here we use N-body simulations of the formation of the Kuiper belt and Oort cloud as well as a survey simulator to compare models of the solar system with and without a 9th planet to one another as well as to observations. The main mechanism for TNOs to be deposited into the distant ($a$ > au), detached ($q$ > au) region of the Kuiper Belt in the 8-planet model is Kozai-Lidov oscillation of objects in mean motion resonances (MMR) with Neptune. This effect does not deposit low-inclination ($i \lesssim$ 20��) objects into this region. However, we find that the 9th planet generates a group of distant, detached TNOs at low inclinations that are not present in the 8-planet model. This disparity between the 8-planet and the 9-planet models could provide a strong constraint on a possible planet 9 with further detections of TNOs in the distant, detached region of the Kuiper Belt., 8 pages, 3 figures, accepted to ApJL

We derive a semi-analytic criterion for the presence of chaos in compact, eccentric multiplanet systems. Beyond a minimum semimajor-axis separation, below which the dynamics are chaotic at all eccentricities, we show that (i) the onset of chaos is determined by the overlap of two-body mean motion resonances (MMRs), like it is in two-planet systems; (ii) secular evolution causes the MMR widths to expand and contract adiabatically, so that the chaotic boundary is established where MMRs overlap at their greatest width. For closely spaced two-planet systems, a near-symmetry strongly suppresses this secular modulation, explaining why the chaotic boundaries for two-planet systems are qualitatively different from cases with more than two planets. We use these results to derive an improved angular-momentum-deficit (AMD) stability criterion, i.e., the critical system AMD below which stability should be guaranteed. This introduces an additional factor to the expression from Laskar and Petit (2017) that is exponential in the interplanetary separations, which corrects the AMD threshold toward lower eccentricities by a factor of several for tightly packed configurations. We make routines for evaluating the chaotic boundary available to the community through the open-source SPOCK package., Comment: Accepted in AJ. Routines for estimating whether compact planetary configurations are chaotic, together with example notebooks are available as part of the SPOCK package: https://github.com/dtamayo/spock

Resonant planetary systems contain at least one planet pair with orbital periods librating at a near-integer ratio (2/1, 3/2, 4/3, etc.) and are a natural outcome of standard planetary formation theories. Systems with multiple adjacent resonant pairs are known as resonant chains and can exhibit three-body resonances -- characterized by a critical three-body angle. Here we study three-body angles as a diagnostic of resonant chains through tidally-damped N-body integrations. For each combination of the 2:1, 3:2, 4:3, and 5:4 mean motion resonances (the most common resonances in the known resonant chains), we characterize the three-body angle equilibria for several mass schemes, migration timescales, and initial separations. We find that under our formulation of the three-body angle, which does not reduce coefficients, 180 deg is the preferred libration center, and libration centers shifted away from 180 deg are associated with non-adjacent resonances. We then relate these angles to observables, by applying our general results to two transiting systems: Kepler-60 and Kepler-223. For these systems, we compare N-body models of the three-body angle to the zeroth order in e approximation accessible via transit phases, used in previous publications. In both cases, we find the three-body angle during the Kepler observing window is not necessarily indicative of the long-term oscillations and stress the role of dynamical models in investigating three-body angles. We anticipate our results will provide a useful diagnostic in the analysis of resonant chains., Comment: Accepted for publication in Astronomical Journal