Asteroid orbits using phase-space volumes of variation

Abstract

We present a statistical orbit computation technique for asteroids with transitional observational data, that is, a moderate number of data points spanning a moderate observational time interval. With the help of local least-squares solutions in the phase space of the orbital elements, we map the volume of variation as a function of one or more of the elements. We sample the resulting volume using a Monte Carlo technique and, with proper weights for the sample orbital elements, characterize the six-dimensional orbital-element probability density function. The volume-ofvariation (VOV) technique complements the statistical ranging technique for asteroids with exiguous observational data (short time intervals and/or small numbers of observations) and the least-squares technique for extensive observational data. We show that, asymptotically, results using the new technique agree closely with those from ranging and least squares. We apply the technique to the near-Earth object 2004 HA 39 , the main-belt object 2004 QR and the transneptunian object 2002 CX 224 recently observed at the Nordic Optical Telescope on La Palma, illustrating the potential of the technique in ephemeris prediction. The VOV technique helps us assess the phase transition in orbital-element probability densities, that is, the nonlinear collapse of wide orbital-element distributions to narrow localized ones. For the three objects above, the transition takes place for observational time intervals of the order of 10 h, 5 d and 10 months, respectively, emphasizing the significance of the orbital-arc fraction covered by the observations.

Asteroid identification over apparitions

“…is critical to be able to link observation sets over long time intervals. For the inversion of the SASs for the orbital-element p.d.f.s, we use either statistical orbital ranging (Ranging; Virtanen et al 2001, or the phase-space Volumes-of-Variation method (VoV; Muinonen et al 2006). Typ-…”

“…ically, Ranging is used in the domain before the so-called phase transition in the orbital uncertainty , Muinonen et al 2006), whereas VoV is optimized for the phase-transition domain. Least squares with linearized covariances (LSL; see, for example, ) is used after the phase transition when the inverse problem can typically be treated with linearized methods.…”

Linking large-parallax Spitzer–CFHT–VLT astrometry of asteroids

“…is performed using either the sampling methods, that is, statistical orbital ranging (Ranging;Virtanen et al 2001, Muinonen et al 2001 or the new Volume-of-Variation method (VoV; Muinonen et al 2006a), or the pointestimate method of least-squares accompanied with linearized covariances (LSL; see, e.g., Danby 1992). Note that Ranging is applicable to astrometric observation sets with short observational time intervals (typically up to days) containing two or more observations, while VoV and LSL require more observations and, typically, longer observational time intervals.…”

Nonlinear methods of statistic simulation of virtual parameter values for investigating uncertainties in orbits determined from observations

“…With the advent of quick-operating and multiprocessor computers, recently one tends to employ statistic simulation of virtual parameter values for investigating uncertainties in orbits determined from observations (Chernitsov et al 1998;Virtanen et al 2001;Bordovitsyna et al 2001;Williams et al 2005;Muinonen et al 2006;Avdyushev and Banschikova 2007;Desmars et al 2009;Avdyushev 2009;Emel'yanov 2010), which is generally required when V. A. Avdyushev (B) Celestial Mechanics and Astrometry Department, Applied Mathematics and Mechanics Institute, 634050 Tomsk, Russia e-mail: sch@niipmm.tsu.ru planning future observations and identifying celestial bodies, and also in the problems of asteroid hazard.…”