arXiv subjects

Andrea Milani

Publications and source records attributed to Andrea Milani.

At least 19 recordsLinked to original sources

arXiv2019

Completeness of Impact Monitoring

The completeness limit is a key quantity to measure the reliability of an impact monitoring system. It is the impact probability threshold above which every virtual impactor has to be detected. A goal of this paper is to increase the completeness without increasing the computational load. We propose a new method to sample the Line Of Variations (LOV) with respect to the previously one used in NEODyS. The step-size of the sampling is not uniform in the LOV parameter, since the probability of each LOV segment between consecutive points is kept constant. Moreover, the sampling interval has been extended to the larger interval [-5,5] in the LOV parameter and a new decomposition scheme in sub-returns is provided to deal with the problem of duplicated points in the same return. The impact monitoring system CLOMON-2 has been upgraded with all these features, resulting in a decrease of the generic completeness limit IP* by a factor $\simeq 4$ and in an increase of the computational load by a factor $\simeq 2$. Moreover, we statistically investigate the completeness actually reached by the system with two different methods: a direct comparison with the results of the independent system Sentry at JPL and an empirical power-law to model the number of virtual impactors as a function of the impact probability. We found empirically that the number of detected virtual impactors with $IP>IP^*$ appears to grow according to a power-law, proportional to $IP^{-2/3}$. An analytical model explaining this power-law is currently an open problem, but we think it is related to the way the number of virtual impactors within a time $t_{rel}$ from the first observed close approach accumulates, for which we prove the existence of a power-law proportional to $t_{rel}^3$. The power-law allows us to detect a loss of efficiency in the virtual impactors search for impact probabilities near the generic completeness limit.

astro-ph.EP↗

arXiv2018

Asteroid cratering families: recognition and collisional interpretation

We continue our investigation of the bulk properties of asteroid dynamical families identified using only asteroid proper elements (Milani et al. 2014) to provide plausible collisional interpretations. We focus on cratering families consisting of a substantial parent body and many small fragments. We propose a quantitative definition of cratering families based on the fraction in volume of the fragments with respect to the parent body; fragmentation families are above this empirical boundary. We assess the compositional homogeneity of the families and their shape in proper element space by computing the differences of the proper elements of the fragments with respect to the ones of the major body, looking for anomalous asymmetries produced either by post-formation dynamical evolution, or by multiple collisional/cratering events, or by a failure of the Hierarchical Clustering Method (HCM) for family identification. We identified a total of 25 dynamical families with more than 100 members ranging from moderate to heavy cratering. For three families (4, 15 and 283) we confirm the occurrence of two separate cratering events. For family 20, we propose a double collision origin, not previously identified. In four cases (31, 480, 163 and 179) we performed a dedicated search for dynamical resonant transport mechanisms that could have substantially changed the shape of the family. By using a new synthetic method for computation of secular frequencies, we found possible solutions for families 31, 480, and 163, but not for family 179, for which we propose a new interpretation, based on a secular resonance contaminating this family: the family of 179 should be split into two separate clusters, one containing (179) itself and the other, family (9506) Telramund, of fragmentation type, for which we have computed an age.

astro-ph.EP↗

arXiv2018

Detecting the Yarkovsky effect among near-Earth asteroids from astrometric data

We present an updated set of near-Earth asteroids with a Yarkovsky-related semimajor axis drift detected from the orbital fit to the astrometry. We find 87 reliable detections after filtering for the signal-to-noise ratio of the Yarkovsky drift estimate and making sure the estimate is compatible with the physical properties of the analyzed object. Furthermore, we find a list of 24 marginally significant detections, for which future astrometry could result in a Yarkovsky detection. A further outcome of the filtering procedure is a list of detections that we consider spurious because unrealistic or not explicable with the Yarkovsky effect. Among the smallest asteroids of our sample, we determined four detections of solar radiation pressure, in addition to the Yarkovsky effect. As the data volume increases in the near future, our goal is to develop methods to generate very long lists of asteroids with reliably detected Yarkovsky effect, with limited amounts of case by case specific adjustments. Furthermore, we discuss the improvements this work could bring to impact monitoring. In particular, we exhibit two asteroids for which the adoption of a non-gravitational model is needed to make reliable impact predictions.

astro-ph.EP↗

arXiv2018

Addressing some critical aspects of the BepiColombo MORE relativity experiment

The Mercury Orbiter radio Science Experiment (MORE) is one of the experiments on-board the ESA/JAXA BepiColombo mission to Mercury, to be launched in October 2018. Thanks to full on-board and on-ground instrumentation performing very precise tracking from the Earth, MORE will have the chance to determine with very high accuracy the Mercury-centric orbit of the spacecraft and the heliocentric orbit of Mercury. This will allow to undertake an accurate test of relativistic theories of gravitation (relativity experiment), which consists in improving the knowledge of some post-Newtonian and related parameters, whose value is predicted by General Relativity. This paper focuses on two critical aspects of the BepiColombo relativity experiment. First of all, we address the delicate issue of determining the orbits of Mercury and the Earth-Moon barycenter at the level of accuracy required by the purposes of the experiment and we discuss a strategy to cure the rank deficiencies that appear in the problem. Secondly, we introduce and discuss the role of the solar Lense-Thirring effect in the Mercury orbit determination problem and in the relativistic parameters estimation.

physics.space-ph↗

arXiv2017

On the contribution of PRIDE-JUICE to Jovian system ephemerides

The JUICE mission will perform detailed measurements of the properties of the Galilean moons, with a nominal in-system science-mission duration of about 3.5 years. Using both the radio tracking data, and (Earth- and JUICE-based) optical astrometry, the dynamics of the Galilean moons will be measured to unprecedented accuracy. This will provide crucial input to the determination of the ephemerides and physical properties of the system, most notably the dissipation in Io and Jupiter. The data from Planetary Radio Interferometry and Doppler Experiment (PRIDE) will provide the lateral position of the spacecraft in the ICRF. In this article, we analyze the relative quantitative influence of the JUICE-PRIDE observables to the determination of the ephemerides of the Jovian system and the associated physical parameters. We perform a covariance analysis for a broad range of mission and system characteristics. We analyze the influence of VLBI data quality, observation planning, as well as the influence of JUICE orbit determination quality. This provides key input for the further development of the PRIDE observational planning and ground segment development. Our analysis indicates that the VLBI data are especially important for constraining the dynamics of Ganymede and Callisto perpendicular to their orbital planes. Also, the use of the VLBI data makes the uncertainty in the ephemerides less dependent on the error in the orbit determination of the JUICE spacecraft itself. Furthermore, we find that optical astrometry data of especially Io using the JANUS instrument will be crucial for stabilizing the solution of the normal equations. Knowledge of the dissipation in the Jupiter system cannot be improved using satellite dynamics obtained from JUICE data alone, the uncertainty in Io's dissipation obtained from our simulations is similar to the present level of uncertainty.

astro-ph.EP↗

arXiv2016

Constraining the Nordtvedt parameter with the BepiColombo Radioscience experiment

BepiColombo is a joint ESA/JAXA mission to Mercury with challenging objectives regarding geophysics, geodesy and fundamental physics. The Mercury Orbiter Radioscience Experiment (MORE) is one of the on-board experiments, including three different but linked experiments: gravimetry, rotation and relativity. The aim of the relativity experiment is the measurement of the post-Newtonian parameters. Thanks to accurate tracking between Earth and spacecraft, the results are expected to be very precise. However, the outcomes of the experiment strictly depends on our "knowledge" about solar system: ephemerides, number of bodies (planets, satellites and asteroids) and their masses. In this paper we describe a semi-analytic model used to perform a covariance analysis to quantify the effects, on the relativity experiment, due to the uncertainties of solar system bodies parameters. In particular, our attention is focused on the Nordtvedt parameter $η$ used to parametrize the strong equivalence principle violation. After our analysis we estimated $σ[η]\lessapprox 4.5\times 10^{-5}$ which is about 1~order of magnitude larger than the "ideal" case where masses of planets and asteroids have no errors. The current value, obtained from ground based experiments and lunar laser ranging measurements, is $σ[η]\approx 4.4\times 10^{-4}$. Therefore, we conclude that, even in presence of uncertainties on solar system parameters, the measurement of $η$ by MORE can improve the current precision of about 1~order of magnitude.

gr-qc↗

arXiv2016

Keplerian integrals, elimination theory and identification of very short arcs in a large database of optical observations

The modern optical telescopes produce a huge number of asteroid observations, that are grouped into very short arcs (VSAs), each containing a few observations of the same object in one single night. To decide whether two VSAs, collected in different nights, refer to the same observed object we can attempt to compute an orbit with the observations of both arcs: this is called the linkage problem. Since the number of orbit computations to be performed is very large, we need efficient methods of orbit determination. Using the first integrals of Kepler's motion we can write algebraic equations for the linkage problem, which can be put in polynomial form. The equations introduced in (Gronchi et al. 2015) can be reduced to a univariate polynomial of degree 9: the unknown is the topocentric distance $ρ$ of the observed body at the mean epoch of one of the VSAs. Using elimination theory we show an optimal property of this polynomial: it has the least degree among the univariate polynomials in the same variable that are consequence of the algebraic conservation laws and are obtained without squaring operations, that can be used to bring these algebraic equations in polynomial form. In this paper we also introduce a procedure to join three VSAs belonging to different nights: from the conservation of angular momentum at the three mean epochs of the VSAs, we obtain a univariate polynomial equation of degree 8 in the topocentric distance $ρ_2$ at the intermediate epoch. This algorithm has the same computational complexity as the classical method by Gauss, but uses more information, therefore we expect that it can produce more accurate results. For both methods, linking two and three VSAs, we also discuss how to select the solutions, making use of the full two-body dynamics, and show some numerical tests comparing the results with the ones obtained by Gauss' method.

astro-ph.EP↗

arXiv2015

Shadowing Lemma and Chaotic Orbit Determination

Orbit determination is possible for a chaotic orbit of a dynamical system, given a finite set of observations, provided the initial conditions are at the central time. In a simple discrete model, the standard map, we tackle the problem of chaotic orbit determination when observations extend beyond the predictability horizon. If the orbit is hyperbolic, a shadowing orbit is computed by the least squares orbit determination. We test both the convergence of the orbit determination iterative procedure and the behaviour of the uncertainties as a function of the maximum number $n$ of map iterations observed. When the initial conditions belong to a chaotic orbit, the orbit determination is made impossible by numerical instability beyond a computability horizon, which can be approximately predicted by a simple formula. Moreover, the uncertainty of the results is sharply increased if a dynamical parameter is added to the initial conditions as parameter to be estimated. The uncertainty of the dynamical parameter decreases like $n^a$ with $a<0$ but not large (of the order of unity). If only the initial conditions are estimated, their uncertainty decreases exponentially with $n$. If they belong to a non-chaotic orbit the computational horizon is much larger, if it exists at all, and the decrease of the uncertainty is polynomial in all parameters, like $n^a$ with $a\simeq 1/2$. The Shadowing Lemma does not dictate what the asymptotic behaviour of the uncertainties should be. These phenomena have significant implications, which remain to be studied, in practical problems of orbit determination involving chaos, such as the chaotic rotation state of a celestial body and a chaotic orbit of a planet-crossing asteroid undergoing many close approaches.

astro-ph.EP↗

arXiv2015

Asteroid family ages

A new family classification, based on a catalog of proper elements with $\sim 384,000$ numbered asteroids and on new methods is available. For the $45$ dynamical families with $>250$ members identified in this classification, we present an attempt to obtain statistically significant ages: we succeeded in computing ages for $37$ collisional families. We used a rigorous method, including a least squares fit of the two sides of a V-shape plot in the proper semimajor axis, inverse diameter plane to determine the corresponding slopes, an advanced error model for the uncertainties of asteroid diameters, an iterative outlier rejection scheme and quality control. The best available Yarkovsky measurement was used to estimate a calibration of the Yarkovsky effect for each family. The results are presented separately for the families originated in fragmentation or cratering events, for the young, compact families and for the truncated, one-sided families. For all the computed ages the corresponding uncertainties are provided. We found 2 cases where two separate dynamical families form together a single V-shape with compatible slopes, thus indicating a single collisional event. We have also found 3 examples of dynamical families containing multiple collisional families, plus a dubious case. We have found 2 cases of families containing a conspicuous subfamily, such that it is possible to measure the slope of a distinct V-shape, thus the age of the secondary collision. We also provide data on the central gaps appearing in some families. The ages computed in this paper are obtained with a single and uniform methodology, thus the ages of different families can be compared, providing a first example of collisional chronology of the asteroid main belt.

astro-ph.EP↗

arXiv2014

On the Juno Radio Science Experiment: models, algorithms and sensitivity analysis

Juno is a NASA mission launched in 2011 with the goal of studying Jupiter. The probe will arrive to the planet in 2016 and will be placed for one year in a polar high-eccentric orbit to study the composition of the planet, the gravity and the magnetic field. The Italian Space Agency (ASI) provided the radio science instrument KaT (Ka-Band Translator) used for the gravity experiment, which has the goal of studying the Jupiter's deep structure by mapping the planet's gravity: such instrument takes advantage of synergies with a similar tool in development for BepiColombo, the ESA cornerstone mission to Mercury. The Celestial Mechanics Group of the University of Pisa, being part of the Juno Italian team, is developing an orbit determination and parameters estimation software for processing the real data independently from NASA software ODP. This paper has a twofold goal: first, to tell about the development of this software highlighting the models used, second, to perform a sensitivity analysis on the parameters of interest to the mission.

physics.space-ph↗

arXiv2014

Orbit and Bulk Density of the OSIRIS-REx Target Asteroid (101955) Bennu

The target asteroid of the OSIRIS-REx asteroid sample return mission, (101955) Bennu (formerly 1999 RQ$_{36}$), is a half-kilometer near-Earth asteroid with an extraordinarily well constrained orbit. An extensive data set of optical astrometry from 1999--2013 and high-quality radar delay measurements to Bennu in 1999, 2005, and 2011 reveal the action of the Yarkovsky effect, with a mean semimajor axis drift rate $da/dt = (-19.0 \pm 0.1)\times 10^{-4}$ au/Myr or $284\pm 1.5\;\rm{m/yr}$. The accuracy of this result depends critically on the fidelity of the observational and dynamical model. As an example, neglecting the relativistic perturbations of the Earth during close approaches affects the orbit with $3σ$ significance in $da/dt$. The orbital deviations from purely gravitational dynamics allow us to deduce the acceleration of the Yarkovsky effect, while the known physical characterization of Bennu allows us to independently model the force due to thermal emissions. The combination of these two analyses yields a bulk density of $ρ= 1260\pm70\,\rm{kg/m^3}$, which indicates a macroporosity in the range $40\pm10$% for the bulk densities of likely analog meteorites, suggesting a rubble-pile internal structure. The associated mass estimate is $(7.8\pm0.9)\times 10^{10}\, \rm{kg}$ and $GM = 5.2\pm0.6\,\rm{m^3/s^2}$. Bennu's Earth close approaches are deterministic over the interval 1654--2135, beyond which the predictions are statistical in nature. In particular, the 2135 close approach is likely within the lunar distance and leads to strong scattering and therefore numerous potential impacts in subsequent years, from 2175--2196. The highest individual impact probability is $9.5\times 10^{-5}$ in 2196, and the cumulative impact probability is $3.7\times 10^{-4}$, leading to a cumulative Palermo Scale of -1.70.

astro-ph.EP↗

arXiv2014

Asteroid families classification: exploiting very large data sets

The number of asteroids with accurately determined orbits increases fast. The catalogs of asteroid physical observations have also increased, although the number of objects is still smaller than in the orbital catalogs. We developed a new approach to the asteroid family classification by combining the Hierarchical Clustering Method (HCM) with a method to add new members to existing families. This procedure makes use of the much larger amount of information contained in the proper elements catalogs, with respect to classifications using also physical observations for a smaller number of asteroids. Our work is based on the large catalog of the high accuracy synthetic proper elements (available from AstDyS). We first identify a number of core families; to these we attribute the next layer of smaller objects. Then, we remove all the family members from the catalog, and reapply the HCM to the rest. This gives both halo families which extend the core families and new independent families, consisting mainly of small asteroids. These two cases are discriminated by another step of attribution of new members and by merging intersecting families. By using information from absolute magnitudes, we take advantage of the larger size range in some families to analyze their shape in the proper semimajor axis vs. inverse diameter plane. This leads to a new method to estimate the family age (or ages). The results from the previous steps are then analyzed, using also auxiliary information on physical properties including WISE albedos and SDSS color indexes. This allows to solve some difficult cases of families overlapping in the proper elements space but generated by different collisional events. We analyze some examples of cratering families (Massalia, Vesta, Eunomia) which show internal structures, interpreted as multiple collisions. We also discuss why Ceres has no family.

astro-ph.EP↗

arXiv2013

The Pan-STARRS Moving Object Processing System

We describe the Pan-STARRS Moving Object Processing System (MOPS), a modern software package that produces automatic asteroid discoveries and identifications from catalogs of transient detections from next-generation astronomical survey telescopes. MOPS achieves > 99.5% efficiency in producing orbits from a synthetic but realistic population of asteroids whose measurements were simulated for a Pan-STARRS4-class telescope. Additionally, using a non-physical grid population, we demonstrate that MOPS can detect populations of currently unknown objects such as interstellar asteroids. MOPS has been adapted successfully to the prototype Pan-STARRS1 telescope despite differences in expected false detection rates, fill-factor loss and relatively sparse observing cadence compared to a hypothetical Pan-STARRS4 telescope and survey. MOPS remains >99.5% efficient at detecting objects on a single night but drops to 80% efficiency at producing orbits for objects detected on multiple nights. This loss is primarily due to configurable MOPS processing limits that are not yet tuned for the Pan-STARRS1 mission. The core MOPS software package is the product of more than 15 person-years of software development and incorporates countless additional years of effort in third-party software to perform lower-level functions such as spatial searching or orbit determination. We describe the high-level design of MOPS and essential subcomponents, the suitability of MOPS for other survey programs, and suggest a road map for future MOPS development.

astro-ph.IM↗

arXiv2012

Identification of known objects in solar system surveys

The discovery of new objects in modern wide-field asteroid and comet surveys can be enhanced by first identifying observations belonging to known solar system objects. The assignation of new observations to a known object is an attribution problem that occurs when a least squares orbit already exists for the object but a separate fit is not possible to just the set of new observations. In this work we explore the strongly asymmetric attribution problem in which the existing least squares orbit is very well constrained and the new data are sparse. We describe an attribution algorithm that introduces new quality control metrics in the presence of strong biases in the astrometric residuals. The main biases arise from the stellar catalogs used in the reduction of asteroid observations and we show that a simple debiasing with measured regional catalog biases significantly improves the results. We tested the attribution algorithm using data from the PS1 survey that used the 2MASS star catalog for the astrometric reduction. We found small but statistically significant biases in the data of up to 0.1 arcsec that are relevant only when the observations reach the level of accuracy made possible by instruments like PS1. The false attribution rate was measured to be < 1/1,000 with a simple additional condition that can reduce it to zero while the attribution efficiency is consistent with 100%.

astro-ph.EP↗

arXiv2012

Desaturation Maneuvers and Precise Orbit Determination for the BepiColombo Mission

The purpose of this work is the analysis of the consequences that desaturation maneuvers can have in the precise orbit determination corresponding to the Radio Science Experiment (MORE) of the BepiColombo mission to Mercury. This mission is an ESA/JAXA joint project with very challenging objectives regarding geodesy, geophysics and fundamental physics. In the neighborhood of Mercury, the s/c will experience strong solar radiation pressure torques; the s/c attitude is controlled by inertial wheels that after some time reach their maximum rotation state. Then they have to be slowed down by means of thruster pulses, inducing a residual acceleration on the s/c, with a desaturation (or off-loading) maneuver. In this paper, we will show how such maneuvers affect the orbit of the s/c and the radio science measurements and, also, how to include them in the orbit determination and parameter estimation procedure. The non linear least squares fit we consider is applied on a set of observational arcs separated by intervals of time where the probe is not visible. With the current baseline of two ground stations, two maneuvers are performed per day, one during the observing session, the other in the dark. To reach the scientific goals of the mission, they have to be treated as "solve for quantities". We have developed a specific methodology based on the deterministic propagation of the orbit, which is able to deal with these variables, by connecting subsequent observational arcs in a smooth way. The numerical simulations we will show demonstrate that this constrained multi-arc strategy is able to determine the maneuvers, including the ones in the dark, together with the other parameters of interest at a high level of accuracy. The future development consists in including accelerometer readings and calibrations in the method.

physics.space-ph↗

arXiv2012

Observational and Dynamical Characterization of Main-Belt Comet P/2010 R2 (La Sagra)

We present observations of comet-like main-belt object P/2010 R2 (La Sagra) obtained by Pan-STARRS 1 and the Faulkes Telescope-North on Haleakala in Hawaii, the University of Hawaii 2.2 m, Gemini-North, and Keck I telescopes on Mauna Kea, the Danish 1.54 m telescope at La Silla, and the Isaac Newton Telescope on La Palma. An antisolar dust tail is observed from August 2010 through February 2011, while a dust trail aligned with the object's orbit plane is also observed from December 2010 through August 2011. Assuming typical phase darkening behavior, P/La Sagra is seen to increase in brightness by >1 mag between August 2010 and December 2010, suggesting that dust production is ongoing over this period. These results strongly suggest that the observed activity is cometary in nature (i.e., driven by the sublimation of volatile material), and that P/La Sagra is therefore the most recent main-belt comet to be discovered. We find an approximate absolute magnitude for the nucleus of H_R=17.9+/-0.2 mag, corresponding to a nucleus radius of ~0.7 km, assuming an albedo of p=0.05. Using optical spectroscopy, we find no evidence of sublimation products (i.e., gas emission), finding an upper limit CN production rate of Q_CN<6x10^23 mol/s, from which we infer an H2O production rate of Q_H2O<10^26 mol/s. Numerical simulations indicate that P/La Sagra is dynamically stable for >100 Myr, suggesting that it is likely native to its current location and that its composition is likely representative of other objects in the same region of the main belt, though the relatively close proximity of the 13:6 mean-motion resonance with Jupiter and the (3,-2,-1) three-body mean-motion resonance with Jupiter and Saturn mean that dynamical instability on larger timescales cannot be ruled out.

astro-ph.EP↗

arXiv2012

Discovery of Main-Belt Comet P/2006 VW139 by Pan-STARRS1

Main belt asteroid (300163) 2006 VW139 (later designated P/2006 VW139) was discovered to exhibit comet-like activity by the Pan-STARRS1 survey telescope using automated point-spread-function analyses performed by PS1's Moving Object Processing System. Deep follow-up observations show both a short (\sim 10") antisolar dust tail and a longer (\sim 60") dust trail aligned with the object's orbit plane, similar to the morphology observed for another main-belt comet, P/2010 R2 (La Sagra), and other well-established comets, implying the action of a long-lived, sublimation-driven emission event. Photometry showing the brightness of the near-nucleus coma remaining constant over \sim 30 days provides further evidence for this object's cometary nature, suggesting it is in fact a main-belt comet, and not a disrupted asteroid. A spectroscopic search for CN emission was unsuccessful, though we find an upper limit CN production rate of Q_CN < 1.3x10^24 mol/s, from which we infer a water production rate of Q_H2O < 10^26 mol/s. We also find an approximately linear optical spectral slope of 7.2%/1000A, similar to other cometary dust comae. Numerical simulations indicate that P/2006 VW139 is dynamically stable for > 100 Myr, while a search for a potential asteroid family around the object reveals a cluster of 24 asteroids within a cutoff distance of 68 m/s. At 70 m/s, this cluster merges with the Themis family, suggesting that it could be similar to the Beagle family to which another main-belt comet, 133P/Elst-Pizarro, belongs.

astro-ph.EP↗

arXiv2011

Innovative observing strategy and orbit determination for Low Earth Orbit Space Debris

We present the results of a large scale simulation, reproducing the behavior of a data center for the build-up and maintenance of a complete catalog of space debris in the upper part of the low Earth orbits region (LEO). The purpose is to determine the performances of a network of advanced optical sensors, through the use of the newest orbit determination algorithms developed by the Department of Mathematics of Pisa (DM). Such a network has been proposed to ESA in the Space Situational Awareness (SSA) framework by Carlo Gavazzi Space SpA (CGS), Istituto Nazionale di Astrofisica (INAF), DM, and Istituto di Scienza e Tecnologie dell'Informazione (ISTI-CNR). The conclusion is that it is possible to use a network of optical sensors to build up a catalog containing more than 98% of the objects with perigee height between 1100 and 2000 km, which would be observable by a reference radar system selected as comparison. It is also possible to maintain such a catalog within the accuracy requirements motivated by collision avoidance, and to detect catastrophic fragmentation events. However, such results depend upon specific assumptions on the sensor and on the software technologies.

math.DS↗