Dynamical Lifetime Research Articles

Neptune’s resonances in the scattered disk

The Scattered Disk Objects (SDOs) are thought to be a small fraction of the ancient population of leftover planetesimals in the outer solar system that were gravitationally scattered by the giant planets and have managed to survive primarily by capture and sticking in Neptune's exterior mean motion resonances (MMRs). In order to advance understanding of the role of MMRs in the dynamics of the SDOs, we investigate the phase space structure of a large number of Neptune's MMRs in the semi-major axis range 33--140~au by use of Poincar\'e sections of the circular planar restricted three body model for the full range of particle eccentricity pertinent to SDOs. We find that, for eccentricities corresponding to perihelion distances near Neptune's orbit, distant MMRs have stable regions with widths that are surprisingly large and of similar size to those of the closer-in MMRs. We identify a phase-shifted second resonance zone that exists in the phase space at planet-crossing eccentricities but not at lower eccentricities; this second resonance zone plays an important role in the dynamics of SDOs in lengthening their dynamical lifetimes. Our non-perturbative measurements of the sizes of the stable resonance zones confirm previous results and provide an additional explanation for the prominence of the $N$:1 sequence of MMRs over the $N$:2, $N$:3 sequences and other MMRs in the population statistics of SDOs; our results also provide a tool to more easily identify resonant objects.

THE IMPORTANCE OF HISTORICAL MEASURES FOR DYNAMICAL MODELS OF THE EVOLUTION OF TRAPEZIUM-TYPE MULTIPLE SYSTEMS

As an illustration of the value of historical measures we present some examples of the dynamical evolution of multiple systems resembling the Orion Trapezium. We constructed models by combining carefully selected historical measures of the separations among components of young massive stellar systems with modern observations. By computing large numbers of fictitious systems resembling real trapezia we were able to simulate the dynamical evolution of such systems. Our results on the dynamical fate of the Orion Trapezium and of ten additional young clusters resembling the Orion Trapezium show extremely short dynamical lifetimes for these systems.

The Creston, California, meteorite fall and the origin of L chondrites

AbstractIt has been proposed that all L chondrites resulted from an ongoing collisional cascade of fragments that originated from the formation of the ~500 Ma old asteroid family Gefion, located near the 5:2 mean‐motion resonance with Jupiter in the middle Main Belt. If so, L chondrite pre‐atmospheric orbits should be distributed as expected for that source region. Here, we present contradictory results from the orbit and collisional history of the October 24, 2015, L6 ordinary chondrite fall at Creston, CA (here reclassified to L5/6). Creston's short 1.30 ± 0.02 AU semimajor axis orbit would imply a long dynamical evolution if it originated from the middle Main Belt. Indeed, Creston has a high cosmic ray exposure age of 40–50 Ma. However, Creston's small meteoroid size and low 4.23 ± 0.07° inclination indicate a short dynamical lifetime against collisions. This suggests, instead, that Creston originated most likely in the inner asteroid belt and was delivered via the ν6 resonance. The U‐Pb systematics of Creston apatite reveals a Pb‐Pb age of 4,497.1 ± 3.7 Ma, and an upper intercept U‐Pb age of 4,496.7 ± 5.8 Ma (2σ), circa 70 Ma after formation of CAI, as found for other L chondrites. The K‐Ar (age ~4.3 Ga) and U,Th‐He (age ~1 Ga) chronometers were not reset at ~500 Ma, while the lower intercept U‐Pb age is poorly defined as 770 ± 320 Ma. So far, the three known L chondrites that impacted on orbits with semimajor axes a <2.0 AU all have high (>3 Ga) K‐Ar ages. This argues for a source of some of our L chondrites in the inner Main Belt. Not all L chondrites originate in a continuous population of Gefion family debris stretching across the 3:1 mean‐motion resonance.

Steady State Scenario in Asteroids Orbital Simulation with Yarkovsky Effect Inclusion

As one result in our orbital simulation of the 3372 samples of real NEAs (Near-Earth Asteroids) whose orbits were considered to be well-known, as many as 480 asteroids evolved out of the four major classes (Amor, Apollo, Aten and Atira) of NEAsat the end of the first 500,000 yearsperiodinto Mars-Crossers asteroids in majority. To test the steady statehypothesis for NEAs population, these evolved asteroids had been used as a sample for further simulation to obtain the entrance flux from the Intermediate Sources/IS (in this case the Intermediate Mars-Crossers/IMC only) to NEAs region. The entrance flux from IMC → NEAs region is 71 ± 17 objects per million year for H< 18. Asteroids of this amount as a contribution from IMC (along with contributions from other sources in the Main Asteroid Belt) will be delivered to near-Earth space to replenish this region due to the decay of NEAs population into the Sinks (collide with the Sun/planets or being thrown to the outer Solar System).After5 million years of simulation we found there were 1898 asteroids eliminated from further computational process with the majority endedtheir liveas Sun-grazer and ejected from the Solar System.The near-Earth space lost a total of 114 ± 17 objects per million year for H< 18.The median dynamical lifetime obtained directly from our NEAs sample decay is3.7x106 years.

523676 (2013 UL10): the first active red centaur

Aims. We present observations of 523676 (2013 UL10), a centaur orbiting between Jupiter and Uranus that is dynamically similar to the few tens of active centaurs that are currently known. Methods. We analysed visible BVR images of the centaur obtained at the Telescopio Nazionale Galileo (La Palma, Canary Islands, Spain) to investigate the weak comet-like activity and to derive information on the nucleus surface colours and size. Results. Centaur 523676 (2013 UL10) is the only centaur known so far that has both comet-like activity and red surface colours: its nucleus has a colour index [B – R] = 1.88 ± 0.11. The nucleus R magnitude (R = 20.93 ± 0.09) allowed us to derive an upper limit for its nucleus size of D ≤ 10 km. We estimated its dust production rate to be Qd ~ 10 kg s−1 at 6.2 au (just after its perihelion passage), resulting in a timescale for the surface blanketing process τB of approximately tens of years, which is very short with respect to typical dynamical lifetime inside the group. Future monitoring of 523676 (2013 UL10) is needed to further constrain the blanketing model for active centaurs and its timescale.

Dynamical lifetime survey of geostationary transfer orbits

In this paper, we study the long-term dynamical evolution of highly-elliptical orbits (HEOs) in the medium-Earth orbit (MEO) region around the Earth. The real population consists primarily of Geosynchronous Transfer Orbits (GTOs), launched at specific inclinations, Molniya-type satellites and related debris. We performed a suite of long-term numerical integrations (up to 200 years) within a realistic dynamical model, aimed primarily at recording the dynamical lifetime of such orbits (defined as the time needed for atmospheric reentry) and understanding its dependence on initial conditions and other parameters, such as the area-to-mass ratio (A/m). Our results are presented in the form of 2-D lifetime maps, for different values of inclination, A/m, and drag coefficient. We find that the majority of small debris (> 70%, depending on the inclination) can naturally reenter within 25-90 years, but these numbers are significantly less optimistic for large debris (e.g., upper stages), with the notable exception of those launched from high latitude (Baikonur). We estimate the reentry probability and mean dynamical lifetime for different classes of GTOs and we find that both quantities depend primarily and strongly on initial perigee altitude. Atmospheric drag and higher A/m values extend the reentry zones, especially at low inclinations. For high inclinations, this dependence is weakened, as the primary mechanisms leading to reentry are overlapping lunisolar resonances. This study forms part of the EC-funded (H2020) "ReDSHIFT" project.

The dynamical evolution of multiple systems of trapezium type

We have selected archival observational data for several O and B trapezia in the Milky Way. For each of the main components of the trapezia we obtained transverse velocities from the historical separation data. With this information, and with the stellar masses of the main components, we studied the dynamical evolution of ensembles of multiple systems mimicking each one of the trapezia. For this purpose we conducted numerical $N-$body integrations using the best available values for the masses, the observed positions and {\bf transverse} velocities, randomly generated radial velocities, and random line-of-sight ($z$) positions for all components. Random perturbations were assigned to the observed quantities, compatible with the observational errors. A large fraction of the simulated systems ({\bf between 70 and 90 percent}) turned out to be unbound. The properties of the evolving systems are studied at different values of the evolution time. We find that the dynamical lifetimes of both the bound and unbound seems to be quite short, of less than 10~000 yr for the unbound systems, and of 10~000 to 20~000 yr for the bound systems. The end result of the simulations is usually a binary {\bf with semiaxes of a few hundred AU} sometimes a triple of hierarchical on non-hierarchical type. Non-hierarchical triples formed during the integrations (which are dynamically unstable) were found to have much longer lifetimes, of 250~000 to 500~000 yr. The frequency distributions of the major semi-axes and eccentricities of the resulting binaries are discussed and compared with observational properties of binary systems from the literature.

Water inventory from beyond the Jupiter’s orbit to the terrestrial planets and the Moon

AbstractComputer simulations of migration of planetesimals from beyond the Jupiter’s orbit to the terrestrial planets have been made. Based on obtained arrays of orbital elements of planetesimals and planets during the dynamical lifetimes of planetesimals, we calculated the probabilities of collisions of planetesimals with planets, the Moon, and their embryos. The results of calculations showed that for the total mass of planetesimals of about 200 Earth masses, the mass of water delivered to the Earth from beyond the orbit of Jupiter could be about the mass of the terrestrial oceans. For the growth of the mass of the Earth embryo up to a half of the present mass of the Earth, the mass of water delivered to the embryo could be up to 30% of all water delivered to the Earth from the zone of Jupiter and Saturn. The water of the terrestrial oceans and its D/H ratio could be the result of mixing of water from several exogenic and endogenic sources with large and low D/H ratios. The ratio of the mass of water delivered from beyond the orbit of Jupiter to a planet to the mass of the planet for Venus, Mars, and Mercury was not smaller than that for the Earth. The mass of water in planetesimals that collided the Moon and migrated from beyond the Jupiter’s orbit could be not more than 20 times smaller than that for the Earth.

Dynamical evolution and end states of active and inactive Centaurs

We numerically study the dynamical evolution of observed samples of active and inactive Centaurs and clones that reach the Jupiter-Saturn region. Our aim is to compare the evolution between active and inactive Centaurs, their end states and their transfer to Jupiter family comets and Halley-type comets. We find that the median lifetime of inactive Centaurs is about twice longer than that for active Centaurs, suggesting that activity is related to the residence time in the region. This view is strengthened by the observation that high-inclination and retrograde Centaurs (Tisserand parameters with respect to Jupiter TJ<2) which have the longest median dynamical lifetime (=1.37×106 yr) are all inactive. We also find that the perihelion distances of some active, comet-like Centaurs have experienced drastic drops of a few au in the recent past (∼102−103 yr), while such drops are not found among inactive Centaurs. Inactive Centaurs with TJ≲2.5 usually evolve to Halley-type comets, whereas inactive Centaurs with TJ≳2.5 and active Centaurs (that also have TJ≳2.5) evolve almost always to Jupiter family comets and very seldom to Halley type comets. Inactive Centaurs are also more prone to end up as sungrazers, and both inactive and active Centaurs transit through different mean motion resonances (generally with Jupiter) during their evolution.

How long will asteroids on retrograde orbits survive?

Generally, a common scenario for the origin of minor planets with high orbital inclinations does not exist. This applies especially to objects whose orbital inclinations are much greater than 90° (retrograde asteroids).Since the discovery of Dioretsa in 1999, approximately 100 small bodies now are classified as retrograde asteroids. A small number of them were reclassified as comets, due to cometary activity. There are only 25 multi-opposition retrograde asteroids, with a relatively large number of observations and well-determined orbits.We studied the orbital evolution of numbered and multi-opposition retrograde asteroids by numerical integration up to 1 Gy forward and backward in time. Additionally, we analyzed the propagation of orbital elements with the observational errors, determined dynamical lifetimes and studied their chaotic properties.Conclusively, we obtained quantitative parameters describing the long-term stability of orbits relating to the past and the future. In turn, we were able to estimate their lifetimes and how long these objects will survive in the Solar System.

Long-Lived Near-Earth Asteroid 2013 RB6

The search for asteroids that maintain stable motion in the zone between the Earth and Mars has been performed. The near-Earth object 2013 RB6, which has avoided close encounters with the planets for a long period of time, has been found. Integration of the equations of motion of the object shows that its dynamical lifetime in the zone between the Earth and Mars significantly exceeds 100 Myr. 2013 RB6 moves away from orbital resonances with the planets, but is in the secular resonance ν5. Solving the question of its origin requires further observations.

Dynamical lifetimes of asteroids in retrograde orbits

The population of known minor bodies in retrograde orbits ($i > 90 ^{\circ}$) that are classified as asteroids is still growing. The aim of our study was to estimate the dynamical lifetimes of these bodies by use of the latest observational data, including astrometry and physical properties. We selected 25 asteroids with the best determined orbital elements. We studied their dynamical evolution in the past and future for $\pm$ 100 My ($\pm$ 1 Gy for three particular cases). We first used orbit determination and cloning to produce swarms of test particles. These swarms were then input into long-term numerical integrations and orbital elements were averaged. Next, we collected the available thermal properties of our objects and used them in an enhanced dynamical model with Yarkovsky forces. We also used a gravitational model for comparison. Finally, we estimated the median lifetimes of 25 asteroids. We found three objects whose retrograde orbits were stable with a dynamical lifetime $\tau \sim 10 \div 100$ My. A large portion of the objects studied displayed smaller values of $\tau$ ($\tau \sim 1$ My). In addition, we studied the possible influence of the Yarkovsky effect on our results. We found that the Yarkovsky effect can have a significant influence on the lifetimes of asteroids in retrograde orbits. Due to the presence of this effect, it is possible that the median lifetimes of these objects are extended. Additionally, the changes in orbital elements, caused by Yarkovsky forces, appear to depend on the integration direction. To explain this more precisely, the same model based on new physical parameters, determined from future observations, will be required.

On the dynamical evolution of the Orion Trapezium

We discuss recent observational data on the transverse and radial velocities, as well as on the masses of the main components of the Orion Trapezium. Based on the most reliable values of these quantities we study the dynamical evolution of ensembles of multiple systems mimicking the Orion Trapezium. To this end we conduct numerical $N-$body integrations using the observed masses, planar positions and velocities, radial velocities, and random line-of-sight ($z$) positions for all components. We include perturbations in these quantities compatible with the observational errors. We find the dynamical lifetimes of such systems to be quite short, of the order of 10 to 50 thousand years. The end result of the simulations is usually a tight binary, or sometimes a hierarchical triple. The properties of the evolved systems are studied at different values of the crossing times. The frequency distributions of the major semiaxes and eccentricities of the resulting binaries are discussed and compared with observations.

Dynamical modeling and lifetime analysis of geostationary transfer orbits

The dynamics and lifetime reduction of geostationary transfer orbits (GTOs) are of great importance to space debris mitigation. The orbital dynamics, subjected to a complex interplay of multiple perturbations, are complicated and sensitive to the initial conditions and model parameters. In this paper, a simple but effective non-singular orbital dynamics model in terms of Milankovitch elements is derived. The orbital dynamics, which include the Earth oblateness, luni-solar perturbations, and atmospheric drag, are averaged over the orbital motion of the GTO object, or, as needed, also over the orbital motions of the Moon and Sun, to eliminate the short-period terms. After the averaging process, the effect of the atmospheric drag assumes a simple analytical form. The averaged orbital model is verified through a numerical simulation compared with commercial orbit propagators. GTO lifetime reduction by using the luni-solar perturbations is studied. It is shown that the long-period luni-solar perturbation is induced by the precession of the GTO orbital plane and apsidal line, whereas the short-period perturbation is induced by the periodic luni-solar orbital motions. The long- and short-period perturbations are isolated and studied separately, and their global distribution with respect to the orbital geometry is given. The desired initial orbital geometry with a short orbital lifetime is found and verified by a numerical simulation.

Asteroid flux towards circumprimary habitable zones in binary star systems

Secular and mean motion resonances (MMR) are effective perturbations for shaping planetary systems. In binary star systems, they play a key role during the early and late phases of planetary formation, as well as for the dynamical stability of a planetary system. In this study, we aim to correlate the presence of orbital resonances with the rate of icy asteroids crossing the habitable zone (HZ), from a circumprimary disk of planetesimals in various binary star systems. We modelled a belt of small bodies in the inner and outer regions, interior and exterior to the orbit of a gas giant planet, respectively. The planetesimals are equally placed around a primary G-type star and move under the gravitational influence of the two stars and the gas giant. We numerically integrated the system for 50 Myr, considering various parameters for the secondary star. Its stellar type varies from a M- to F-type; its semimajor axis is either 50 au or 100 au, and its eccentricity is either 0.1 or 0.3. For comparison, we also varied the gas giant's orbital and physical parameters. Our simulations highlight that a disk of planetesimals will suffer from perturbations owing to a perturbed gas giant, mean motion, and secular resonances. We show that a secular resonance -- with location and width varying according to the secondary star's characteristics -- can exist in the icy asteroid belt region and overlap with MMRs which have an impact on the dynamical lifetime of the disk. In addition, we point out that in any case, the 2:1 MMR, the 5:3 MMR and the secular resonance are powerful perturbations for the flux of icy asteroids towards the HZ and the transport of water therein.

COMET 322P/SOHO 1: AN ASTEROID WITH THE SMALLEST PERIHELION DISTANCE?*

ABSTRACT We observed comet 322P/SOHO 1 (P/1999 R1) from the ground and with the Spitzer Space Telescope when it was between 2.2 and 1.2 au from the Sun. These are the first observations of any Solar and Heliospheric Observatory (SOHO)-discovered periodic comet by a non-solar observatory and allow us to investigate its behavior under typical cometary circumstances. 322P appeared inactive in all images. Its light curve suggests a rotation period of 2.8 ± 0.3 hr and has an amplitude ≳0.3 mag, implying a density of at least 1000 kg m−3, considerably higher than that of any known comet. It has average colors of g ′ − r ′ = 0.52 ± 0.04 and r ′ − i ′ = 0.03 ± 0.06 . We converted these to Johnson colors and found that the V − R color is consistent with average cometary colors, but R − I is somewhat bluer; these colors are most similar to V- and Q-type asteroids. Modeling of the optical and IR photometry suggests it has a diameter of 150–320 m and a geometric albedo of 0.09–0.42, with diameter and albedo inversely related. Our upper limits to any undetected coma are still consistent with a sublimation lifetime shorter than the typical dynamical lifetimes for Jupiter-family comets. These results suggest that 322P may be of asteroidal origin and only active in the SOHO fields of view via processes different from the volatile-driven activity of traditional comets. If so, it has the smallest perihelion distance of any known asteroid.

ON THE MASS AND ORIGIN OF CHARIKLO’S RINGS

ABSTRACT Observations in 2013 and 2014 of the Centaur 10199 Chariklo and its ring system consistently indicated that the radial width of the inner, more massive ring varies with longitude. That strongly suggests that this ring has a finite eccentricity despite the fast differential precession that Chariklo’s large quadrupole moment should induce. If the inferred apse alignment is maintained by the ring’s self-gravity, as it is for the Uranian rings, we estimate a ring mass of a few times 1016 g and a typical particle size of a few meters. These values imply a collisional spreading time of ∼105 years, which is somewhat shorter than the typical Centaur dynamical lifetime of a few million years and much shorter than the age of the solar system. In light of this time constraint, we evaluate previously suggested ring formation pathways including collisional ejection and satellite disruption. We also investigate in detail a contrasting formation mechanism, the lofting of dust particles off Chariklo’s surface into orbit via outflows of sublimating CO and/or N2 triggered after Chariklo was scattered inward by giant planets. This alternate scenario predicts that rings should be common among 100 km class Centaurs but rare among Kuiper Belt objects and smaller Centaurs. It also predicts that Centaurs should show seasonal variations in cometary activity with activity maxima occurring shortly after equinox.

Stability of a planet in the HD 41004 binary system

AbstractThe Hill stability criterion is applied to analyse the stability of a planet in the binary star system of HD 41004 AB, with the primary and secondary separated by 22 AU, and masses of 0.7 M⊙ and 0.4 M⊙, respectively. The primary hosts one planet in an S‐type orbit, and the secondary hosts a brown dwarf (18.64 MJ) on a relatively close orbit, 0.0177 AU, thereby forming another binary pair within this binary system. This star‐brown dwarf pair (HD 41004 B+Bb) is considered a single body during our numerical calculations, while the dynamics of the planet around the primary, HD 41004 Ab, is studied in different phase‐spaces. HD 41004 Ab is a 2.6 MJ planet orbiting at the distance of 1.7 AU with orbital eccentricity 0.39. For the purpose of this study, the system is reduced to a three‐body problem and is solved numerically as the elliptic restricted three‐body problem (ERTBP). The Hill stability function is used as a chaos indicator to configure and analyse the orbital stability of the planet, HD 41004 Ab. The indicator has been effective in measuring the planet's orbital perturbation due to the secondary star during its periastron passage. The calculated Hill stability time series of the planet for the coplanar case shows the stable and quasi‐periodic orbits for at least ten million years. For the reduced ERTBP the stability of the system is also studied for different values of planet's orbital inclination with the binary plane. Also, by recording the planet's ejection time from the system or collision time with a star during the integration period, stability of the system is analysed in a bigger phase‐space of the planet's orbital inclination, ≤ 90°, and its semimajor axis, 1.65–1.75 AU. Based on our analysis it is found that the system can maintain a stable configuration for the planet's orbital inclination as high as 65° relative to the binary plane. The results from the Hill stability criterion and the planet's dynamical lifetime map are found to be consistent with each other. (© 2016 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

The origin of long-lived asteroids in the 2:1 mean-motion resonance with Jupiter

The 2:1 mean-motion resonance with Jupiter harbours two distinct groups of asteroids. The short-lived population is known to be a transient group sustained in steady state by the Yarkovsky semimajor axis drift. The long-lived asteroids, however, can exhibit dynamical lifetimes comparable to $4\,\mathrm{Gyr}$. They reside near two isolated islands of the phase space denoted $\mathrm{A}$ and $\mathrm{B}$, with an uneven population ratio $\mathrm{B}/\mathrm{A} \simeq 10$. The orbits of $\mathrm{A}$-island asteroids are predominantly highly inclined, compared to island $\mathrm{B}$. The size-frequency distribution is steep but the orbital distribution lacks any evidence of a collisional cluster. These observational constraints are somewhat puzzling and therefore the origin of the long-lived asteroids has not been explained so far. With the aim to provide a viable explanation, we first update the resonant population and revisit its physical properties. Using an $N$-body model with seven planets and the Yarkovsky effect included, we demonstrate that the dynamical depletion of island $\mathrm{A}$ is faster, in comparison with island $\mathrm{B}$. Then we investigate (i) the survivability of primordial resonant asteroids and (ii) capture of the population during planetary migration, following a recently described scenario with an escaping fifth giant planet and a jumping-Jupiter instability. We also model the collisional evolution of the resonant population over past $4\,\mathrm{Gyr}$. Our conclusion is that the long-lived group was created by resonant capture from a narrow part of hypothetical outer main-belt family during planetary migration. Primordial asteroids surviving the migration were probably not numerous enough to substantially contribute to the observed population.

CHAOTIC DISINTEGRATION OF THE INNER SOLAR SYSTEM

On timescales that greatly exceed an orbital period, typical planetary orbits evolve in a stochastic yet stable fashion. On even longer timescales, however, planetary orbits can spontaneously transition from bounded to unbound chaotic states. Large-scale instabilities associated with such behavior appear to play a dominant role in shaping the architectures of planetary systems, including our own. Here we show how such transitions are possible, focusing on the specific case of the long-term evolution of Mercury. We develop a simple analytical model for Mercury's dynamics and elucidate the origins of its short term stochastic behavior as well as of its sudden progression to unbounded chaos. Our model allows us to estimate the timescale on which this transition is likely to be triggered, i.e. the dynamical lifetime of the Solar System as we know it. The formulated theory is consistent with the results of numerical simulations and is broadly applicable to extrasolar planetary systems dominated by secular interactions. These results constitute a significant advancement in our understanding of the processes responsible for sculpting of the dynamical structures of generic planetary systems.