Papers by Giovanni Gronchi
Contemporary observational surveys provide a huge number of detections of small solar system bodi... more Contemporary observational surveys provide a huge number of detections of small solar system bodies, in particular of asteroids. These have to be reduced in real time in order to optimize the observational strategy and to select the targets for the follow-up and for the subsequent determination of an orbit. Typically, reported astrometry consists of few positions over a short time
Celestial Mechanics and Dynamical Astronomy, 2004
Most asteroid discoveries consist of a few astrometric observations over a short time span, and i... more Most asteroid discoveries consist of a few astrometric observations over a short time span, and in many cases the amount of information is not enough to compute a full orbit according to the least squares principle. We investigate whether such a Very Short Arc may nonetheless contain significant orbit information, with predictive value, e.g., allowing to compute useful ephemerides with a well defined uncertainty for some time in the future.
Proceedings of the International Astronomical Union, 2006
The distance between two confocal Keplerian orbits, called MOID in the literature, is a useful to... more The distance between two confocal Keplerian orbits, called MOID in the literature, is a useful tool to know if two celestial bodies can collide or undergo a very close approach. Two confocal orbits may get close at more than one pair of points, thus it is useful to compute not only the absolute minimum of the distance function d between
… on Space Debris
The number and performance of the sensors to be used for a survey is a function of the minimum nu... more The number and performance of the sensors to be used for a survey is a function of the minimum number of observations required to determine an orbit. This is critical for the definition of the sensor network and the observation planning.
Discrete and Continuous Dynamical Systems - Series B, 2007
We introduce a regularization for the minimal distance maps, giving the locally minimal values of... more We introduce a regularization for the minimal distance maps, giving the locally minimal values of the distance between two points on two confocal Keplerian orbits. This allows to define a meaningful uncertainty for the minimal distance also when orbit crossings are possible, and it is useful to detect the possibility of collisions or close approaches between two celestial bodies moving approximatively on these orbits, with important consequences in the study of their dynamics. An application to the orbit of a recently discovered near-Earth asteroid is also given.
Theory of Orbit Determination, 2009
Theory of Orbit Determination, 2009
Theory of Orbit Determination, 2009
Theory of Orbit Determination, 2009
Theory of Orbit Determination, 2009
Theory of Orbit Determination, 2009
Theory of Orbit Determination, 2009
Icarus, 2001
In this paper we test the accuracy of proper elements and proper frequencies computed for near-Ea... more In this paper we test the accuracy of proper elements and proper frequencies computed for near-Earth asteroids (NEAs) by a semianalytic method with the planets on circular and coplanar orbits. These elements are compared with the ones computed by pure numerical integrations in the same reference frame and in a more realistic planetary system that takes into account the eccentricity and the inclination of the planets. To check the validity of the semianalytic method for the different kinds of existing dynamical behaviors, a fairly representative sample of NEAs has been investigated. These objects have different dynamical behaviors and have been chosen among the two categories of ω-librating and ω-circulating asteroids, ω being the argument of perihelion; to give a general idea of the validity of the semianalytic theory, the mean orbit of a meteor stream is included in our tests. We have then developed a procedure which allows the comparison between the outputs of the two methods. Given the required accuracy, this comparison appears satisfying, apart from a few cases for which the theory is known not to be valid. Therefore, the semianalytic method can already be used to compute proper elements and frequencies of known NEAs in a reliable way, though some improvements will be needed to account for the eccentricities and inclinations of the planets in the planetary system used for the computation.
Icarus, 2012
We report on our search for genetically related asteroids amongst the near-Earth object (NEO) pop... more We report on our search for genetically related asteroids amongst the near-Earth object (NEO) population-families of NEOs akin to the well known main belt asteroid families. We used the technique proposed by . Icarus 178(2), 434-449) supplemented with a detailed analysis of the statistical significance of the detected clusters. Their significance was assessed by comparison to identical searches performed on 1000 'fuzzy-real' NEO orbit distribution models that we developed for this purpose. The family-free 'fuzzy-real' NEO models maintain both the micro and macro distribution of five orbital elements (ignoring the mean anomaly). Three clusters were identified that contain four or more NEOs but none of them are statistically significant at P 3r. The most statistically significant cluster at the $ 2r level contains four objects with H < 20 and all members have long observational arcs and concomitant good orbital elements. Despite the low statistical significance we performed several other tests on the cluster to determine if it is likely a genetic family. The tests included examining the cluster's taxonomy, size-frequency distribution, consistency with a familyforming event during tidal disruption in a close approach to Mars, and whether it is detectable in a proper element cluster search. None of these tests exclude the possibility that the cluster is a family but neither do they confirm the hypothesis. We conclude that we have not identified any NEO families.
Discrete and Continuous Dynamical Systems - Series B, 2007
We introduce a regularization for the minimal distance maps, giving the locally minimal values of... more We introduce a regularization for the minimal distance maps, giving the locally minimal values of the distance between two points on two confocal Keplerian orbits. This allows to define a meaningful uncertainty for the minimal distance also when orbit crossings are possible, and it is useful to detect the possibility of collisions or close approaches between two celestial bodies moving approximatively on these orbits, with important consequences in the study of their dynamics. An application to the orbit of a recently discovered near-Earth asteroid is also given.
Celestial Mechanics and Dynamical Astronomy, 2011
The first integrals of the Kepler problem are used to compute preliminary orbits starting from tw... more The first integrals of the Kepler problem are used to compute preliminary orbits starting from two short observed arcs of a celestial body, which may be obtained either by optical or radar observations. We write polynomial equations for this problem, that we can solve using the powerful tools of computational Algebra. An algorithm to decide if the linkage of two short arcs is successful, i.e. if they belong to the same observed body, is proposed and tested numerically. In this paper we continue the research started in , where the angular momentum and the energy integrals were used. A suitable component of the Laplace-Lenz vector in place of the energy turns out to be convenient, in fact the degree of the resulting system is reduced to less than half.
Given a set of astrometric observations of the same object, the problem of orbit determination is... more Given a set of astrometric observations of the same object, the problem of orbit determination is to compute the orbit and to assess its uncertainty and reliability. For the next generation surveys, with much larger number density of observed objects, new algorithms or substantial revisions of the classical ones are needed. The problem has three main steps, preliminary orbit, least
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Papers by Giovanni Gronchi