Orbit of an Astrometric Binary System

Abstract

We present a new method to solve the problem of initial orbit determination of any binary system. This method is mainly based on the material available for an observer, for example relative positions at a given time of the couple in the ''plane of sky'', namely the tangent plane to the celestial sphere at the position of the primary component. The problem of orbit determination is solved by splitting in successive stages in order to decorrelate the parameters of each other as much as possible. On one hand, the geometric problem is solved using the first Kepler's law from a single observing run and, on the other hand, dynamical parameters are then inferred from the fit of the Kepler's equation. At last, the final stage consists in determining the main physical parameters involved in the secular evolution of the system, that is the spin axis and the J 2 parameter of the primary if we assume that it is a quasispherical body. As a matter of fact there is no need to make too restrictive initial assumptions (such as circular orbit or zero eccentricity) and initial guesses of parameters required by a nonlinear least-squares Levenberg-Marquardt algorithm are finally obtained after each stage. Such a protocol is very useful to study systems like binary asteroids for which all of the parameters should be considered a priori as unknowns. As an example of application, we used our method to estimate the set of the Pluto-Charon system parameters from observations collected in the literature since 1980.

Determination of binary asteroid orbits with a genetic-based algorithm

“…We have used several different algorithms to estimate the orbital elements of the asteroid satellites, including geometrical (Descamps 2005), statistical , and dynamical methods. Other groups have used similar types of algorithms to derive the orbits of a moon around the dwarf planet Pluto (Stern et al 2006), Binary TNOs (Grundy et al 2011), and Triple NEAs (Fang et al 2011).…”

“…In this case, several orbits with identical likelihoods can be found, and the search ranges for the orbital parameters are manually set (Noll et al 2004). We added non-gravitational effects, such as the precessions of the lines of nodes due to an irregularly shaped primary, to the geometrical model developed by Descamps (2005), giving us the possibility of deriving an estimate of the dynamical J 2 of the triple asteroid system (87) Sylvia (Marchis et al 2005).…”

Main belt binary asteroidal systems with eccentric mutual orbits

“…Descamps (2005) developed the Binary Orbit Fit (BOF) algorithm for this task based on the geometrical fitting of an apparent orbit and its dynamical evolution due to precession.…”

Triplicity and physical characteristics of Asteroid (216) Kleopatra

“…A preliminary orbit solution was derived assuming a simple Keplerian formalism (Descamps, 2005). The resulting orbital elements are listed in Table 2.…”