# Development of an observational error model, and astrometric masses of 28 asteroids

Baer, James J. (2010) Development of an observational error model, and astrometric masses of 28 asteroids. PhD thesis, James Cook University.

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## Abstract

As a large asteroid encounters a smaller body, its gravitational attraction perturbs the trajectory of the smaller asteroid. The method of astrometric mass determination uses a least-square algorithm to simultaneously solve for both the orbit of the small asteroid, and the mass of the larger asteroid required to produce the observed perturbation. Since the perturbations are quite small, the observations of the smaller asteroid must be highly precise; and the perturbations of other asteroids must be accounted for.

Current practice, however, is to assume that all observations of a given era have the same uncertainty, and that the errors in these observations are uncorrelated. These assumptions are unrealistic; and they lead to sub-optimal masses and orbits. We therefore pursue development of an observational error model that provides realistic estimates of the uncertainties and correlations in asteroid observations.

In the course of our first attempt to construct the error model, we detected a significant bias in the observations of numbered asteroids, due to position-dependent errors in the star catalogs from which the observations were reduced. Before proceeding further, we developed a method to remove these biases, and undertook extensive calculations to validate its performance. Implementing this technique, we completed development of the error model, and demonstrated that it produces orbits that are both more accurate, and more precise. We then used the new error model to iteratively refine an integrated ephemeris of 300 large asteroids, which allowed us to deduce the masses of 28 main-belt asteroids. These include the first published masses of 5 Astraea (1.255±0.003 × 10⁻¹² M⊙) and 39 Laetitia (2.83±0.73 × 10⁻¹² M⊙).

After combining our mass estimates with those of other authors, we studied the bulk porosities of over 50 main-belt asteroids; and after reviewing the collisional evolution of main-belt asteroids, we concluded that asteroids as large as 300 km in diameter may be loose gravitational aggregates. This finding will place a specific constraint on models of main-belt collisional evolution. Additionally, we found that C-type asteroids tend to have significantly higher macroporosity than S-type asteroids; and after reviewing thermal models of asteroid accretion, we concluded that distant C-type asteroids likely have a cometary-type structure and composition that results from a lack of global heating following their initial accretion.

ID Code: 23904 Thesis (PhD) asteroid belt; asteroid observations; asteroids; astrometric mass determination; astrometric mass; astrometric masses; astrometry; celestial mechanics; main belt asteroids; mass calculation; orbit calculation; orbit determination; orbiting; orbits; perturbation theory; perturbations 02 PHYSICAL SCIENCES > 0201 Astronomical and Space Sciences > 020108 Planetary Science (excl Extraterrestrial Geology) @ 100% 97 EXPANDING KNOWLEDGE > 970102 Expanding Knowledge in the Physical Sciences @ 100% 15 Nov 2012 12:05 07 Jan 2013 16:29 Total: 101Last 12 Months: 96 More Statistics

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