Stability analysis of the martian obliquity during the Noachian era

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°. These zones occur at obliquities below 30° and above 60°; intermediate values show either resonant or chaotic behaviour depending on the primordial orbits of the terrestrial planets.     

A 1 Gyr climate model for Mars: new orbital statistics and the importance of seasonally resolved polar processes

New results from a 1 Gyr integration of the martian orbit are presented along with a seasonally resolved energy balance climate model employed to illuminate the gross characteristics of the long-term atmospheric pressure evolution. We present a new analysis of the statistical variation of the martian obliquity and precession prior to and subsequent to the formation of the Tharsis uplift, and explore the long term effects on the martian climate. We find that seasonal polar cycles have a critical influence on the ability for the regolith to release CO₂ at high obliquities, and find that the atmospheric CO₂ actually decreases at high obliquities due to the cooling effect of polar deposits at latitudes where seasonal caps form. At low obliquity, the formation of massive, permanent polar caps depends critically on the values of the frost albedo, A_frost, and frost emissivity, ?_frost. Using our model with values of A_frost=0.67 and ?_frost=0.55, matched to the NASA Ames General Circulation Model (GCM) results (Haberle et al., 1993, J. Geophys. Res. 98, 3093-3123, and Haberle et al., 2003, Icarus 161, 66-89), we find that permanent caps only form at low obliquities (<13°), suggesting that any permanent deposits on the surface of Mars today may be residuals left over from a period of very low obliquity, or are the result of mechanisms not represented by this model. Thus, contrary to expectations, the martian atmospheric pressure is remarkable static over time, and decreases both at high and low obliquity. Also, from our one billion year orbital model, we present new results on the fraction of time Mars is expected to experience periods of low obliquity and high obliquity.     

Large scale chaos and marginal stability in the solar system

Large scale chaos is present everywhere in the solar system. It plays a major role in the sculpting of the asteroid belt and in the diffusion of comets from the outer region of the solar system. All the inner planets probably experienced large scale chaotic behavior for their obliquities during their history. The Earth obliquity is presently stable only because of the presence of the Moon, and the tilt of Mars undergoes large chaotic variations from 0° to about 60°. On billion years time scale, the orbits of the planets themselves present strong chaotic variations which can lead to the escape of Mercury or collision with Venus in less than 3.5 Gyr. The organization of the planets in the solar system thus seems to be strongly related to this chaotic evolution, reaching at all time a state of marginal stability, that is practical stability on a time-scale comparable to its age.This lecture was given at the XIth International Congress of Mathematical Physics, Paris, july 1994     

The web of three-planet resonances in the outer Solar System: II. A source of orbital instability for Uranus and Neptune

The motion of the giant planets from Jupiter to Neptune is chaotic with Lyapunov time of approximately 10 Myr. A recent theory explains the presence of this chaos with three-planet mean-motion resonances, i.e. resonances among the orbital periods of at least three planets. We find that the distribution of these resonances with respect to the semi-major axes of all the planets is compatible with orbital instability. In particular, they overlap in a region of 10⁻³ AU with respect to the variation of the semi-major axes of Uranus and Neptune. Fictitious planetary systems with initial conditions in this region can undergo systematic variations of semi-major axes. The true Solar System is marginally in this region, and Uranus and Neptune undergo very slow systematic variations of semi-major axes with speed of order 10⁻⁴ AU/Gyr.     

Constraints on Europa’s rotational dynamics from modeling of tidally-driven fractures

Cycloids, arcuate features observed on Europa’s surface, have been interpreted as tensile cracks that form in response to diurnal tidal stress caused by Europa’s orbital eccentricity. Stress from non-synchronous rotation may also contribute to tidal stress, and its influence on cycloid shapes has been investigated as well. Obliquity, fast precession, and physical libration would contribute to tidal stress but have often been neglected because they were expected to be negligibly small. However, more sophisticated analyses that include the influence of Jupiter’s other large satellites and the state of Europa’s interior indicate that perhaps these rotational parameters are large enough to alter the tidal stress field and the formation of tidally-driven fractures. We test tidal models that include obliquity, fast precession, stress due to non-synchronous rotation, and physical libration by comparing how well each model reproduces observed cycloids. To do this, we have designed and implemented an automated parameter-searching algorithm that relies on a quantitative measure of fit quality, which we use to identify the best fits to observed cycloids. We then apply statistical techniques to determine the tidal model best supported by the data. By incorporating obliquity, fits to observed southern hemisphere cycloids improve, and we can reproduce equatorial and equator-crossing cycloids. Furthermore, we find that obliquity plus physical libration is the tidal model best supported by the data. With this model, the obliquities range from 0.32° to 1.35°. The libration amplitudes are 0.72–2.44°, and the libration phases are −6.04° to 17.72° with one outlier at 84.5°. The variability in obliquity is expected if Europa’s ice shell is mechanically decoupled from the interior, and the libration amplitudes are plausible in the presence of a subsurface ocean. Indeed, the presence of a decoupling ocean may result in feedbacks that cause all of these rotational parameters to become time-variable.     

Obliquity variations of a moonless Earth

We numerically explore the obliquity (axial tilt) variations of a hypothetical moonless Earth. Previous work has shown that the Earth’s Moon stabilizes Earth’s obliquity such that it remains within a narrow range, between 22.1° and 24.5°. Without lunar influence, a frequency map analysis by Laskar et al. (Laskar, J., Joutel, F., Robutel, P. [1993]. Nature 361, 615–617) showed that the obliquity could vary between 0° and 85°. This has left an impression in the astrobiology community that a big moon is necessary to maintain a habitable climate on an Earth-like planet. Using a modified version of the orbital integrator mercury, we calculate the obliquity evolution for moonless Earths with various initial conditions for up to 4 Gyr. We find that while obliquity varies significantly more than that of the actual Earth over 100,000 year timescales, the obliquity remains within a constrained range, typically 20–25° in extent, for timescales of hundreds of millions of years. None of our Solar System integrations in which planetary orbits behave in a typical manner show obliquity accessing more than 65% of the full range allowed by frequency-map analysis. The obliquities of moonless Earths that rotate in the retrograde direction are more stable than those of prograde rotators. The total obliquity range explored for moonless Earths with rotation periods less than 12 h is much less than that for slower-rotating moonless Earths. A large moon thus does not seem to be needed to stabilize the obliquity of an Earth-like planet on timescales relevant to the development of advanced life.     

Reconstructing the orbital history of the Veritas family

The family of (490) Veritas is a young, dynamically heterogeneous asteroid family, located in the outer main belt. As such, it represents a valuable example for studying the effects of chaotic diffusion on the shape of asteroid families. The Veritas family can be decomposed into several groups, in terms of the principal mechanisms that govern the local dynamics, which are analyzed here. A relatively large spread in proper eccentricity is observed, for the members of two chaotic groups. We show that different types of chaos govern the motion of bodies within each group, depending on the extent of overlap among the components of the corresponding resonant multiplets. In particular, one group appears to be strongly diffusive, while the other is not. Studying the evolution of the diffusive group and applying statistical methods, we estimate the age of the family to be τ=(8.7±1.7) Myr. This value is statistically compatible with that of 8.3 Myr previously derived by Nesvorný et al. [Nesvorný, D., Bottke, W.F., Levison, H.F., Dones, L., 2003. Astrophys. J. 591, 486-497], who analyzed the secular evolution of family members on regular orbits. Our methodology, applied here in the case of the Veritas family, can be used to reconstruct the orbital history of other, dynamically complex, asteroid families and derive approximate age estimates for young asteroid families, located in diffusive regions of the main belt. Possible refinements of the method are also discussed.     

The Mars 1:2 resonant population

An excess of around 400 asteroids in the distribution of the semimajor axes of the asteroids is identified by means of numerical integrations as generated by a population of approximately 1000 asteroids evolving inside the exterior resonance 1:2 with Mars. Approximately 200 asteroids are librating around the asymmetric libration centers and their evolution in a time-scale of 1 million years appears stable but with a strong influence of Mars' eccentricity. The biggest Mars 1:2 resonant asteroid is (142) Polana.     

Origin and sustainability of the population of asteroids captured in the exterior resonance 1:2 with Mars

At present, approximately 1500 asteroids are known to evolve inside or sticked to the exterior 1:2 resonance with Mars at a ? 2.418 AU, being (142) Polana the largest member of this group. The effect of the forced secular modes superposed to the resonance gives rise to a complex dynamical evolution. Chaotic diffusion, collisions, close encounters with massive asteroids and mainly orbital migration due to the Yarkovsky effect generate continuous captures to and losses from the resonance, with a fraction of asteroids remaining captured over long time scales and generating a concentration in the semimajor axis distribution that exceeds by 20% the population of background asteroids. The Yarkovsky effect induces different dynamics according to the asteroid size, producing an excess of small asteroids inside the resonance. The evolution in the resonance generates a signature on the orbits, mainly in eccentricity, that depends on the time the asteroid remains captured inside the resonance and on the magnitude of the Yarkovsky effect. The greater the asteroids, the larger the time they remain captured in the resonance, allowing greater diffusion in eccentricity and inclination. The resonance generates a discontinuity and mixing in the space of proper elements producing misidentification of dynamical family members, mainly for Vesta and Nysa-Polana families. The half-life of resonant asteroids large enough for not being affected by the Yarkovsky effect is about 1 Gyr. From the point of view of taxonomic classes, the resonant population does not differ from the background population and the excess of small asteroids is confirmed.     

Insolation patterns on synchronous exoplanets with obliquity

A previous paper [Dobrovolskis, A.R., 2007. Icarus 192, 1-23] showed that eccentricity can have profound effects on the climate, habitability, and detectability of extrasolar planets. This complementary study shows that obliquity can have comparable effects.The known exoplanets exhibit a wide range of orbital eccentricities, but those within several million kilometers of their suns are generally in near-circular orbits. This fact is widely attributed to the dissipation of tides in the planets. Tides in a planet affect its spin even more than its orbit, and such tidally evolved planets often are assumed to be in synchronous rotation, so that their rotation periods are identical to their orbital periods. The canonical example of synchronous spin is the way that our Moon always keeps nearly the same hemisphere facing the Earth.Tides also tend to reduce the planet’s obliquity (the angle between its spin and orbital angular velocities). However, orbit precession can cause the rotation to become locked in a “Cassini state”, where it retains a nearly constant non-zero obliquity. For example, our Moon maintains an obliquity of about 6.7° with respect to its orbit about the Earth. In comparison, stable Cassini states can exist for practically any obliquity up to ∼90° or more for planets of binary stars, or in multi-planet systems with high mutual inclinations, such as are produced by scattering or by the Kozai mechanism.This work considers planets in synchronous rotation with circular orbits, but arbitrary obliquity β; this affects the distribution of insolation over the planet’s surface, particularly near its poles. For β=0, one hemisphere bakes in perpetual sunshine, while the opposite hemisphere experiences eternal darkness. As β increases, the region of permanent daylight and the antipodal realm of endless night both shrink, while a more temperate area of alternating day and night spreads in longitude, and especially in latitude. The regions of permanent day or night disappear at β=90°. The insolation regime passes through several more transitions as β continues to increase toward 180°, but the surface distribution of insolation remains non-uniform in both latitude and longitude.Thus obliquity, like eccentricity, can protect certain areas of the planet from the worst extremes of temperature and solar radiation, and can improve the planet’s habitability. These results also have implications for the direct detectability of extrasolar planets, and for the interpretation of their thermal emissions.     

A preliminary analysis of the orbit of the Mars Trojan asteroid (5261) Eureka

Observations and results of orbit determination of the first known Mars Trojan asteroid (5261) Eureka are presented. We have numerically calculated the evolution of the orbital elements, and have analyzed the behavior of the motion during the next 2 Myr. Strong perturbations by planets other than Mars seem to stabilize the eccentricity of the asteroid by stirring the high order resonances present in the elliptic restricted problem. As a result, the orbit appears stable at least on megayear timescales. The difference of the mean longitudes of Mars and Eureka and the semimajor axis of the asteroid form a pair of variables that essentially behave in an adiabatic manner, while the evolution of the other orbital elements is largely determined by the perturbations due to other planets.     

Linking the collisional history of the main asteroid belt to its dynamical excitation and depletion

The main belt is believed to have originally contained an Earth mass or more of material, enough to allow the asteroids to accrete on relatively short timescales. The present-day main belt, however, only contains ∼5×¹⁰⁻⁴ Earth masses. Numerical simulations suggest that this mass loss can be explained by the dynamical depletion of main belt material via gravitational perturbations from planetary embryos and a newly-formed Jupiter. To explore this scenario, we combined dynamical results from Petit et al. [Petit, J. Morbidelli, A., Chambers, J., 2001. The primordial excitation and clearing of the asteroid belt. Icarus 153, 338-347] with a collisional evolution code capable of tracking how the main belt undergoes comminution and dynamical depletion over 4.6 Gyr [Bottke, W.F., Durda, D., Nesvorny, D., Jedicke, R., Morbidelli, A., Vokrouhlický, D., Levison, H., 2005. The fossilized size distribution of the main asteroid belt. Icarus 175, 111-140]. Our results were constrained by the main belt's size-frequency distribution, the number of asteroid families produced by disruption events from diameter D>100 km parent bodies over the last 3-4 Gyr, the presence of a single large impact crater on Vesta's intact basaltic crust, and the relatively constant lunar and terrestrial impactor flux over the last 3 Gyr. We used our model to set limits on the initial size of the main belt as well as Jupiter's formation time. We find the most likely formation time for Jupiter was 3.3±2.6 Myr after the onset of fragmentation in the main belt. These results are consistent with the estimated mean disk lifetime of 3 Myr predicted by Haisch et al. [Haisch, K.E., Lada, E.A., Lada, C.J., 2001. Disk frequencies and lifetimes in young clusters. Astrophys. J. 553, L153-L156]. The post-accretion main belt population, in the form of diameter D?1000 km planetesimals, was likely to have been 160±40 times the current main belt's mass. This corresponds to 0.06-0.1 Earth masses, only a small fraction of the total mass thought to have existed in the main belt zone during planet formation. The remaining mass was most likely taken up by planetary embryos formed in the same region. Our results suggest that numerous D>200 km planetesimals disrupted early in Solar System history, but only a small fraction of their fragments survived the dynamical depletion event described above. We believe this may explain the limited presence of iron-rich M-type, olivine-rich A-type, and non-Vesta V-type asteroids in the main belt today. The collisional lifetimes determined for main belt asteroids agree with the cosmic ray exposure ages of stony meteorites and are consistent with the limited collisional evolution detected among large Koronis family members. Using the same model, we investigated the near-Earth object (NEO) population. We show the shape of the NEO size distribution is a reflection of the main belt population, with main belt asteroids driven to resonances by Yarkovsky thermal forces. We used our model of the NEO population over the last 3 Gyr, which is consistent with the current population determined by telescopic and satellite data, to explore whether the majority of small craters (D<0.1-1 km) formed on Mercury, the Moon, and Mars were produced by primary impacts or by secondary impacts generated by ejecta from large craters. Our results suggest that most small craters formed on these worlds were a by-product of secondary rather than primary impacts.     

Modification of impact craters in the northern plains of Mars: Implications for Amazonian climate history

Abstract— We measured the depth, wall steepness, and ejecta roughness and surveyed the wall and floor morphology of all craters 10–25 km in diameter within the typical Vastitas Borealis Formation in the northern lowlands of Mars north of 52°N. Two of the 130 craters have unusually rough ejecta; they are deep, have steep walls, and are apparently the youngest in the population. Icy mantles filling the local subkilometer‐scale topographic lows is the main contribution to ejecta smoothing, which occurs at a time scale on the order of tens of Myr. Wall degradation and crater shallowing generally occur at longer time scales, comparable to the duration of the Amazonian period. Many craters are shallow due to filling of the crater with specific ice‐rich material of uncertain origin. We use our collected data to infer the nature of the past climate back through the Amazonian, a period prior to ?10–20 Myr ago, when orbital parameter solutions are chaotic and one must rely on geological data to infer climate conditions. We conclude that moderately high obliquity and wide obliquity variations were probable during the last 40–160 Myr. We tentatively conclude that high obliquity peaks (>40–45°) may have occurred episodically through the last 210–430 Myr. A sharp step in the frequency distribution of wall steepness at 20° may indicate a geologically long period prior to that time where obliquity never exceeded 40–45°.     

Dynamics of Mars Trojans

In this paper we explore the dynamical stability of the Mars Trojan region applying mainly Laskar's Frequency Map Analysis. This method yields the chaotic diffusion rate of orbits and allows to determine the most stable regions. It also gives the frequencies which are responsible for the instability of orbits. The most stable regions are found for inclinations between about 15° and 30°. For inclinations smaller than 15°, we confirm, by applying a synthetic secular theory, that the secular resonances ν₃, ν₄, ν₁₃, ν₁₄ rapidly excite asteroid orbits within a few Myrs, or even faster. The asteroids are removed from the Trojan region after a close encounter with Mars. For large inclinations, the secular resonance ν₅ clears a small region around 30° while the Kozai resonance rapidly removes bodies for inclinations larger than 35°. The dynamical lifetimes of the three L5 Trojans, (5261) Eureka, 1998 VF31, 2001 DH47, and the only L4 Trojan 1999 UJ7 are determined by numerically integrating clouds of corresponding clones over the age of the Solar System. All four Trojans reside in the most stable region with smallest diffusion coefficients. Their dynamical half-lifetime is of the order of the age of the Solar System. The Yarkovsky force has little effect on the known Trojans but for bodies smaller than about 1-5 m the drag is strong enough to destabilize Trojans on a timescale shorter than 4.5 Gyr.     

Yarkovsky/YORP chronology of asteroid families

Asteroid families are the byproducts of catastrophic collisions whose fragments form clusters in proper semimajor axis, eccentricity, and inclination space. Although many families have been observed in the main asteroid belt, only two very young families, Karin and Veritas, have well-determined ages. The ages of other families are needed, however, if we hope to infer information about their ejection velocity fields, space weathering processes, etc. In this paper, we developed a method that allows us to estimate the ages of moderately young asteroid families (approximately in between 0.1 and 1 Gyr). We apply it to four suitable cases—Erigone, Massalia, Merxia, and Astrid—and derive their likely ages and approximate ejection velocity fields. We find that Erigone and Merxia were produced by large catastrophic disruption events (i.e., parent body ?100 km) that occurred approximately 280 and 330 Myr ago, respectively. The Massalia family was likely produced by a cratering event on Asteroid (20) Massalia less than 200 Myr ago. Finally, the Astrid family, which was produced by the disruption of a 60-70 km asteroid, is 100-200 Myr old, though there is considerable uncertainty in this result. We estimate that the initial ejection velocities for these families were only a few tens of meters per second, consistent with numerical hydrocode models of asteroid impacts. Our results help to verify that asteroid families are constantly undergoing dynamical orbital evolution from thermal (Yarkovsky) forces and spin vector evolution from thermal (YORP) torques.     

On the stability of a planet between Mars and the asteroid belt: Implications for the Planet V hypothesis

The stability of an additional planet between the orbit of Mars and the asteroid belt is examined in the context of the Planet V hypothesis. In this model, the Solar System initially contained a fifth terrestrial planet, “Planet V,” which was removed after ∼700 Myr, a possible trigger for the late heavy bombardment on the inner planets. The model is investigated using 96 N-body integrations of the 8 major planets with an additional body between Mars and the asteroid belt. In more than 1/4 of simulations, Planet V survives for 1000 Myr. In most other cases, Planet V collides with the Sun or hits another planet after several hundred Myr, leaving 4 surviving terrestrial planets. In 24/96 simulations, Planet V is lost by ejection or collision with the Sun while the other four terrestrial planets survive without undergoing a collision. In 18 cases, Planet V is removed at least 200 Myr after the beginning of the simulation. The endstate depends sensitively on the mass of Planet V. Collision with the Sun is likely when Planet V's mass is 0.25 Mars masses or less. When Planet V is more massive than this, collisions involving it and/or other terrestrial planets become commonplace. In unstable systems, the times of first encounter and first collision/ejection depend on the initial aphelion distance of Mars. Reducing Mars's aphelion distance increases these times and also increases the fraction of systems surviving for 1000 Myr. When Mars's current orbit is used, the stability of Planet V increases when these two planets are widely separated initially. Planet V's aphelion distance Q typically begins to cross the asteroid belt within a few tens to a few hundred Myr, and its orbit last leaves the belt several hundred Myr later in most cases. The total time spent with Q>2.1 AU is typically less than 200 Myr.     

The Influence of the Orbital Evolution of Main Belt Asteroids on Their Spin Vectors

It was found that certain features in the observed spin vector distribution of main belt asteroids can be explained by the differences in the dynamical spin vector evolution between objects with high and low orbital inclinations. In particular, the deficiency of high-inclination objects whose spin vectors are close to the ecliptic plane can be accounted for.The present spin vector distribution of main belt asteroids is due to several factors connected with their collisional and dynamical evolution. In this paper, the influence of the orbital evolution on the spin axis of asteroids is examined in the case of 25 objects with typical main belt orbital evolution and 125 synthetic objects, during an integration over a time period of 1 Myr. This investigation produced the following general results:• The difference between maximum and minimum obliquity increases in an approximately linear fashion with increasing orbital inclination of the studied objects.• The inclination is the major factor influencing the magnitude of the obliquity variation. This variation is generally larger for asteroids with their initial spin vectors located close to the orbital plane.• In general, the regular obliquity differences are relatively insensitive to differences in the shape, composition, and spin rate of the asteroids.The result is compared with the properties of the observed spin vectors for 73 main belt asteroids and good agreement is found between the above results and the existing spin vector distribution.     

Non-gravitational force modeling of Comet 81P/Wild 2: II. Rotational evolution

In this paper, we have studied both the dynamical and the rotational evolution of an 81P/Wild 2-like comet under the effects of the outgassing-induced force and torque. The main aim is to study if it is possible to reproduce the non-gravitational orbital changes observed in this comet, and to establish the likely evolution of both orbital and rotational parameters. To perform this study, a simple thermophysical model has been used to estimate the torque acting on the nucleus. Once the torque is calculated, Euler equations are solved numerically considering a nucleus mass directly estimated from the changes in the orbital elements (as determined from astrometry). According to these simulations, when the water production rate and changes in orbital parameters for 1997, as well as observational rotational parameters for 2004 are imposed as constraints, the change in the orbital period of 81P/Wild 2, , will decrease so that to , which is similar to the actual tendency observed from 1988 up to 1997. This nearly constant decreasing can be explained as due to a slight drift of the spin axis orientation towards larger ecliptic longitudes. After studying the possible spin axis orientations proposed for 1997, simulations suggest that the spin obliquity and argument (I,Φ)=(56°,167°) is the most likely. As for rotational evolution, changes per orbit smaller than 10% of the actual spin velocity are probable, while the most likely value corresponds to a change between 2 and 7% of the spin velocity. Equally, net changes in the spin axis orientation of 4°-8° per orbit are highly expected.     

Eccentricity evolution of giant planet orbits due to circumstellar disk torques

The extrasolar planets discovered to date possess unexpected orbital elements. Most orbit their host stars with larger eccentricities and smaller semi-major axes than similarly sized planets in our own Solar System do. It is generally agreed that the interaction between giant planets and circumstellar disks (Type II migration) drives these planets inward to small radii, but the effect of these same disks on orbital eccentricity, ?, is controversial. Several recent analytic calculations suggest that disk-planet interactions can excite eccentricity, while numerical studies generally produce eccentricity damping. This paper addresses this controversy using a quasi-analytic approach, drawing on several preceding analytic studies. This work refines the current treatment of eccentricity evolution by removing several approximations from the calculation of disk torques. We encounter neither uniform damping nor uniform excitation of orbital eccentricity, but rather a function d?/dt that varies in both sign and magnitude depending on eccentricity and other Solar System properties. Most significantly, we find that for every combination of disk and planet properties investigated herein, corotation torques produce negative values of d?/dt for some range in ? within the interval [0.1, 0.5]. If corotation torques are saturated, this region of eccentricity damping disappears, and excitation occurs on a short timescale of less than 0.08 Myr. Thus, our study does not produce eccentricity excitation on a timescale of a few Myr—we obtain either eccentricity excitation on a short time scale, or eccentricity damping on a longer time scale. Finally, we discuss the implications of this result for producing the observed range in extrasolar planet eccentricity.     

The peculiar case of the Agnia asteroid family

The Agnia asteroid family, a cluster of asteroids located near semimajor axis a=2.79 AU, has experienced significant dynamical evolution over its lifetime. The family, which was likely created by the breakup of a diameter D∼50 km parent body, is almost entirely contained within the high-order secular resonance z₁. This means that unlike other families, Agnia's full extent in proper eccentricity and inclination is a byproduct of the large-amplitude resonant oscillations produced by this resonance. Using numerical integration methods, we found that the spread in orbital angles observed among Agnia family members would have taken at least 40 Myr to create; this sets a lower limit on the family's age. To determine the upper bound on Agnia's age, we used a Monte Carlo model to track how the small members in the family evolve in semimajor axis by Yarkovsky thermal forces. Our results indicate the family is no more than 140 Myr old, with a best-fit age of 100⁺³⁰₋₂₀ Myr. Using two independent methods, we also determined that the D∼5 km fragments were ejected from the family-forming event at a velocity near 15 m/s. This velocity is consistent with results from numerical hydrocode simulations of asteroid impacts and observations of other similarly sized asteroid families. Finally, we found that 57% of known Agnia fragments were initially prograde rotators. The reason for this limited asymmetry is unknown, though we suspect it is a fluke produced by the stochastic nature of asteroid disruption events.