Computer Science – Numerical Analysis
Scientific paper
Apr 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994p%26ss...42..307m&link_type=abstract
Planetary and Space Science, vol. 42, no. 4, p. 307-313
Computer Science
Numerical Analysis
11
Accuracy, Asteroids, Error Analysis, Orbit Calculation, Two Body Problem, Approximation, Numerical Analysis, Orbital Elements, Semiempirical Equations, Time Dependence
Scientific paper
We have carried out a two-body orbital uncertainty analysis for more than 10,000 asteroids observed at single apparitions. Our working database included the epoch, number of observations, observational arc, orbital elements and their 1-sigma uncertainties, several orbital quality metrics (which we term the mean motion, leak and s leak metrics), the correlations among the orbital elements, and the 1-sigma sky-plane uncertainties one month after the last observation. The orbital quality metrics correlated clearly with the observational arc. We found semi-empirical power laws of the form Theta approximately equals 10 Tarc-2/square root of (N-3) and sigma psi approximately equals 6 x 104 Tarc-2/square root of (N-3)(leak metric Theta in radians, sky-plane uncertainty sigma psi in arcsec, observational arc Tarc in days, and number of observations N). The power laws are valid for single-apparition main-belt asteroids to within a factor of five. The s leak and leak metrics were often dominated by the uncertainty in the eccentricity or the uncertainty in the mean longitude. We outline two principal applications of the orbital quality estimates: assessment of whether an orbit is accurate enough for proper element calculation, and the establishment of simple criteria for judging how an asteroid's orbit and ephemeris prediction are likely to improve with further observation.
Bowell Edward
Muinonen Karri
Wasserman Larry H.
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