NDLI: Orbit determination with the two-body integrals

Content Provider	Springer Nature Link
Author	Gronchi, G. F. Dimare, L. Milani, A.
Copyright Year	2010
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.
Starting Page	299
Ending Page	318
Page Count	20
File Format	PDF
ISSN	09232958
Journal	Celestial Mechanics and Dynamical Astronomy
Volume Number	107
Issue Number	3
e-ISSN	15729478
Language	English
Publisher	Springer Netherlands
Publisher Date	2010-05-04
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Orbit determination Algebraic methods Attributables Linkage Covariance matrix Mathematics Astronomy, Observations and Techniques Astrophysics and Astroparticles Dynamical Systems and Ergodic Theory
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Mathematical Physics Astronomy and Astrophysics Modeling and Simulation Computational Mathematics Space and Planetary Science

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