1. Modeling of double asteroids with PIKAIA algorithm Przemysław Bartczak Astronomical Observatory of A. Mickiewicz University

2. Idea of modelling Observation data Model of binary system simulation

3. Model of system Cayley-Klein parameters:Euler angles: Rotation angle α Nutation angle β Precession angle γ 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 Drawback: undetermined for β=0 or β=π

4. Model of system When the primary rotates, the Cayley-Klein parameters change according to the differential equations where is the angular rate vector in body frame.

5. 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 - Satelites radius vector P - Momentum vector Γ - Angular momentum vector J 1,J 2,J 3 – principal moments

6. 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.

7. Model of shape The dynamical part of the model (free or forced precession) Primary: Three-axial ellipsoid Satellite: Spherical

8. Model of shape The synchronous double asteroids Primary and satellite: Three-axial elipsoids Primary and satellite: Three-axial elipsoids plus two craters.

9. Model of shape YORP Only one body: Triangular faces

10. Input parameters Date of observation Position of asteroid (Orbital elements ) Orientation of binary system Model of shape and binary system Modelling of lightcurve Position of Sun and Earth

11. 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

12. Model of lightcurve Ray tracing

13. 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)

14. Modelling of lightcurve Z-buffering

15. PIKAIA – genetic algorithm Genetic algorithms are a class of search techniques inspired from the biological process of evolution by means of natural selection.

16. PIKAIA – genetic algorithm Determined parameters of model (blue): System:Shape: Period, primary: a, b/a, c/a density, secoundary: a, b/a, c/a Rotation angle α, Nutation angle βDeformation: Precession angle γ2 craters: (8 parameters)

17. Parallel computing SQL database PC System: Debian Compilator: gcc,c++ SQL database: MySql, oracleXe Librares: CORBA, POSIX Threads