Institution(s): 1. Lille 1 University, 2. Paris Observatory
Orbit determination from observations is one of the classical problems in celestial mechanics. Deriving the trajectory of binary asteroid with high precision is much more complicate than the trajectory of simple asteroid. Here we present a method of orbit determination based on the algorithm of Monte Carlo Markov Chain (MCMC). This method can be used for the preliminary orbit determination with relatively small number of observations, or for adjustment of orbit previously determined.
The problem consists on determination of a conditional a posteriori probability density with given observations. Applying the Bayesian statistics, the a posteriori probability density of the binary asteroid orbital parameters is proportional to the a priori and likelihood probability densities. The likelihood function is related to the noise probability density and can be calculated from O-C deviations (Observed minus Calculated positions). The optionally used a priori probability density takes into account information about the population of discovered asteroids. The a priori probability density is used to constrain the phase space of possible orbits.
As a MCMC method the Metropolis–Hastings algorithm has been applied, adding a globally convergent coefficient. The sequence of possible orbits derives through the sampling of each orbital parameter and acceptance criteria.
The method allows to determine the phase space of every possible orbit considering each parameter. It also can be used to derive one orbit with the biggest probability density of orbital elements.