898 research outputs found
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 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 with
but not large (of the order of unity). If only the initial conditions are
estimated, their uncertainty decreases exponentially with . 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 with . 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
Asteroid proper elements and secular resonances
In a series of papers (e.g., Knezevic, 1991; Milani and Knezevic, 1990; 1991) we reported on the progress we were making in computing asteroid proper elements, both as regards their accuracy and long-term stability. Additionally, we reported on the efficiency and 'intelligence' of our software. At the same time, we studied the associated problems of resonance effects, and we introduced the new class of 'nonlinear' secular resonances; we determined the locations of these secular resonances in proper-element phase space and analyzed their impact on the asteroid family classification. Here we would like to summarize the current status of our work and possible further developments
Asteroid family ages
A new family classification, based on a catalog of proper elements with numbered asteroids and on new methods is available. For the
dynamical families with members identified in this classification, we
present an attempt to obtain statistically significant ages: we succeeded in
computing ages for 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
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.Comment: Accepted for publication in MONTHLY NOTICES of the Royal Astronomical
Society 2014 October 31. Received 2014 July 28; in original form 2013 October
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 used to parametrize the
strong equivalence principle violation. After our analysis we estimated
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 .
Therefore, we conclude that, even in presence of uncertainties on solar system
parameters, the measurement of by MORE can improve the current precision
of about 1~order of magnitude
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
On-barn pig weight estimation based on body measurements by structure-from-motion (SfM)
Information on the body shape of pigs is a key indicator to monitor their performance and health and to control or predict their market weight. Manual measurements are among the most common ways to obtain an indication of animal growth. However, this approach is laborious and difficult, and it may be stressful for both the pigs and the stockman. The present paper proposes the implementation of a Structure from Motion (SfM) photogrammetry approach as a new tool for on-barn animal reconstruction applications. This is possible also to new software tools allowing automatic estimation of camera parameters during the reconstruction process even without a preliminary calibration phase. An analysis on pig body 3D SfM characterization is here proposed, carried out under different conditions in terms of number of camera poses and animal movements. The work takes advantage of the total reconstructed surface as reference index to quantify the quality of the achieved 3D reconstruction, showing how as much as 80% of the total animal area can be characterized
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