Planetary Science belongs to the so-called fundamental sciences, which do not have to have immediate practical applications or implications. The recent decades have however shown that the study of asteroids may have direct implications on our life. Studies of asteroid dynamics have shown that some of those objects can collide with the Earth. Studies of asteroid mineralogy suggest that some of them contain minerals and elements important for industry. For both of those topics, determining physical and dynamical properties is crucial.
Markov-chain Monte Carlo methods and algorithms such as the Metropolis-Hastings algorithm are growing in popularity and becoming important tools in deriving model parameters in many branches of science today. In this thesis, Bayesian statistics along with the above-mentioned numerical methods have been used to infer dynamical and physical properties of asteroids.
First, a new Markov-chain Monte Carlo ranging method is developed for computing asteroid orbits. The method is applicable for asteroids with short observational time intervals and/or small number of observations. The method is particularly useful in deriving orbits for new asteroid discoveries and computing collision probabilities for such objects. The Markov-chain Monte Carlo ranging method is applied to a number of asteroids including a recent Earth impactor - asteroid 2008 TC3. Markov-chain Monte Carlo ranging is available through the open-source orbit-computation package called OpenOrb and is implemented into the Gaia satellite data processing pipeline, where it will be heavily used in the daily data processing.
Second, Markov-chain Monte Carlo and Monte Carlo methods are used to assess phase curve photometric parameters and their uncertainties. Absolute magnitudes and photometric parameters are derived for half a million asteroids by fitting phase curves to the Lowell Observatory photometric database. Asteroid phase curves depend on physical properties of regolith and absolute magnitudes are useful in computing sizes and albedos. Fitting the phase functions to a large number of asteroid families suggests homogeneity of photometric parameters in asteroid families. The derived photometric parameters are also found to correspond to asteroid taxonomic complexes and colors
