MCMC Approach for Orbit Determination of Visual Binaries

A key component of astrophysics study is determining visual binary orbits, which allows for accurate measurements of star masses and provides information on the mass-luminosity relationship. Conventional orbit determination techniques like Kowalsky's method and Thiele-Innes elements sometimes have trouble processing sparse or noisy data. To tackle these issues, this work presents a Markov Chain Monte Carlo (MCMC) framework, which provides a reliable and probabilistic method for orbital parameter refinement. The process combines statistical probability assessments with iterative sampling to solve Kepler's equation and calculate ephemerides. Two test orbits with different eccentricities and inclinations were used to verify the framework, showing that it effectively lowered errors and closely matched observational data. The findings demonstrate the versatility of the MCMC approach, its accuracy in orbit refining, and possible use in more complex star systems, such as circumbinary planets and hierarchical triples.