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Research Activity – Maro' Stefano ESR5


My research topic is asteroid orbit determination. The problem was formulated in modern terms at the beginning of the XIX century by Gauss. He dealt with the recovery of the asteroid Ceres, knowing the observations made by Piazzi.
To be more precise, the problem consists of completing the position and velocity vector of an asteroid, since optical observations only give informations on the angular coordinates (right ascension and declination, see figure).


Once we know position and velocity we have an orbit. Gauss was able to first compute a preliminary approximation of the orbit of Ceres and then improve it using the least square method.
Gauss' method is still valid and used nowadays. Anyway, the new technologies and the next generations sky surveys, provide a huge amount of observation so that we need to find new and more efficient methods to deal with very large databases.
Actually, in order to find the preliminary approximation, the method of Gauss uses the observations at three different times. Hence, to compute all the possible combinations, the computational complexity would be cubic and the computational time extremely large.
Therefore we are searching for new methods to compute preliminary orbits using the observations only at two different times. This is called the linkage problem.

On this line, it is proved that the linkage problem can be reduced to a polinomial equation, but the degree (20) was still too large so that we concentrate on the search for methods that could come out with a polinomial equation of lower degree. To compute the preliminary orbit it is generally assumed the Keplerian regime so that we can use the fact that energy, angular momentum and the Lenz vector are constant. In this way we found a polinomial system that could be reduced to a polinomial equation of degree 9. This allows to have more reasonable computational time and handle larger databases.  


REFERENCES




• G.F. Gronchi, G. Baù and S. Marò: Orbit determination with the two-body integrals. III. To appear in Celestial Mechanics & Dynamical Astronomy (2015)


• S. Marò and G.F. Gronchi: Orbit identification for large sets of data: preliminary results, Complex Planetary Systems - Proceedings IAU Symposium No.310, 2014 Z. Knezevic & A. Lemaitre, eds.    


 
 
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