Mathematics – Logic
Scientific paper
Oct 1991
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991aj....102.1539m&link_type=abstract
Astronomical Journal (ISSN 0004-6256), vol. 102, Oct. 1991, p. 1539-1552.
Mathematics
Logic
11
Asteroids, Orbit Calculation, Planetary Orbits, Celestial Mechanics, Gauss Equation
Scientific paper
Physically meaningful results are obtained in mathematically indeterminate cases via a modification of the Gauss-Enke-Merton (GEM) form of the Gaussian method of three-observation orbit determination. The modified procedure allows situations to be isolated where at least one observation is erroneous. A logical extension of the procedure provides a mechanism for using only two observations of a minor planet to identify additional data. Though analogous to the 'modified' Vaisala method, the new procedure is found to be more convenient for application in practice and to have distinct advantages in the case of Apollo objects, which in the Vaisala method must unrealistically be presumed at aphelion. It is also shown that the three-observation procedure can readily be extended to incorporate additional observations. The relative performance of the GEM method and traditional orbit-determination methods in cases of discrete nontrivial multiple solutions is discussed.
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