DETERMINATION OF VISUAL BINARIES’ ORBITAL ELEMENTS USING PARAMETRIC METHODS: CROSS ENTROPY (CE) AND DIFFERENTIAL EVOLUTION MARKOV CHAIN MONTE CARLO (DE-MCMC)

• Main Author: Agung Prabowo, Mohamad
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/39375
• Institution: Institut Teknologi Bandung

Binary stars are defined as a system containing two stars which are gravitationally bounded. Based on the observational methods, binary stars are grouped into visual, astrometric, spectroscopic, and eclipsing binaries. By studying binary stars, stellar mass can be determined. There are seven orbital elements in visual binaries, those are P (period), T (time of periastron passage), e (eccentricity), a (semi-major axis), i (inclination), ? (longitude of periastron) dan ? (position angle of the ascending node). Thiele-Innes constants A, B, F, dan G can be used to substitute orbital elements a, i, ? and ? (Lucy, 2014). The determination of orbital elements of visual binaries can be done using either empiric or parametric methods. However empiric method is considered as inefficient. In the other hand, determination of orbital elements of visual binaries using parametric method can be done by building model data from each orbital element, and then determine the fitted probability of observational data with the model data. This Bachelor Thesis use Cross Entropy (CE) method by Kroese (2006) and Differential Evolution Markov Chain Monte Carlo (DE-MCMC) method by Mendez (2017). Data which are used in this thesis is synthetic data made according Lucy (2014) and three binary stars: WDS18558+0327, WDS06451-1643 and WDS20514-0538 obtained from Washington Double Star Catalogue. Based on our result, orbital elements of visual binaries can be determined accurately with CE and DE-MCMC methods if the observational errors are known and the data has minimum 40% of orbital fraction.