Orbit determination with the two-body integrals |
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| Authors: | G F Gronchi L Dimare A Milani |
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| Institution: | 1.Dipartimento di Matematica,Università di Pisa,5 Pisa,Italy;2.Dipartimento di Matematica,Università di Roma ‘La Sapienza’,2 Roma,Italy |
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| Abstract: | We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of
the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where often
the information contained in the observations allows only to compute, by interpolation, two angular positions of the observed
body and their time derivatives at a given epoch; we call this set of data attributable. Given two attributables of the same body at two different epochs we can use the energy and angular momentum integrals of
the two-body problem to write a system of polynomial equations for the topocentric distance and the radial velocity at the
two epochs. We define two different algorithms for the computation of the solutions, based on different ways to perform elimination
of variables and obtain a univariate polynomial. Moreover we use the redundancy of the data to test the hypothesis that two
attributables belong to the same body (linkage problem). It is also possible to compute a covariance matrix, describing the uncertainty of the preliminary orbits which results
from the observation error statistics. The performance of this method has been investigated by using a large set of simulated
observations of the Pan-STARRS project. |
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