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Modeling of double asteroids with PIKAIA algorithm Przemysław Bartczak Astronomical Observatory of A. Mickiewicz University Idea of modelling Observation data Model of binary system simulation Model of system Body frame: The axes are directed along the principal moments of interia of the primary. Fixed frame: the axes are aligned with some suitably chosen astronomical coordinate system. Both system of axes are Cartesian, right-handed and share the same origin 0, located at the center of mass of the primary Cayley-Klein parameters: Euler angles: Rotation angle α Nutation angle β Precession angle γ Drawback: undetermined for β=0 or β=π Model of system When the primary rotates, the Cayley-Klein parameters change according to the differential equations where Ω is the angular rate vector in body frame. Model of system Dynamics equations describe the orbital motion of the satelite with respect to the primary and rotation of primary . Ω - Angular rate vector R - Satelite’s radius vector P - Momentum vector Γ - Angular momentum vector J1,J2,J3 – principal moments Model of system Constans of motion: Hamiltonian: Total angular momentum vector: Cayley-Klein parameters: Integrating the equations of motion by means of the Raudau-Everhart RA-15 procedure, we have obtained highly accurate results within a fairly short computation time. Model of shape The dynamical part of the model (free or forced precession) Primary: Satellite: Three-axial ellipsoid Spherical Model of shape The synchronous double asteroids Primary and satellite: Three-axial elipsoids plus two craters. Primary and satellite: Three-axial elipsoids Model of shape YORP Only one body: Triangular faces Input parameters Date of observation Position of asteroid (Orbital elements ) Position of Sun and Earth Orientation of binary system Model of shape and binary system Modelling of lightcurve Model of lightcurve • Ray tracing is a technique for generating an image by tracing the path of light through pixels in an image plane and simulating the effects of its encounters with virtual objects. Scattering : Lommel-Seeliger law Model of lightcurve • Ray tracing Modelling of lightcurve • Z-buffering is the management of image depth coordinates in three-dimensional (3-D) graphics. The depth of a generated pixel (z coordinate) is stored in a buffer (the z-buffer or depth buffer) Modelling of lightcurve • Z-buffering PIKAIA – genetic algorithm Genetic algorithms are a class of search techniques inspired from the biological process of evolution by means of natural selection. PIKAIA – genetic algorithm System: Determined parameters of model (blue): Shape: Period , density , Rotation angle α, Nutation angle β Precession angle γ primary: a, b/a, c/a secoundary: a, b/a, c/a Deformation: 2 craters: (8 parameters) Parallel computing SQL database PC PC System: Debian Compilator: gcc,c++ SQL database: MySql , oracleXe Librares: CORBA, POSIX Threads PC