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Modeling of double asteroids with PIKAIA algorithm

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.

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Modeling of double asteroids with PIKAIA algorithm

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  1. Modeling of double asteroidswith PIKAIA algorithm Przemysław Bartczak AstronomicalObservatory of A. Mickiewicz University

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

  3. Model of system Body frame: Theaxesaredirectedalongthe principal moments of interia of theprimary. Fixedframe: theaxesarealignedwithsomesuitablychosenastronomicalcoordinate system. Both system of axesareCartesian, right-handed and sharethe same origin 0, locatedatthe center of mass of theprimary Cayley-Kleinparameters: Euler angles: Rotationangleα Nutationangleβ Precessionangleγ Drawback: undetermined for β=0 orβ=π

  4. Model of system Whentheprimaryrotates, theCayley-Kleinparameterschangeaccording to thedifferentialequations whereΩistheangularratevectorin body frame.

  5. Model of system Dynamics equationsdescribethe orbital motion of thesatelitewithrespect to theprimary and rotation of primary. Ω - Angularratevector R - Satelite’s radius vector P - Momentumvector Γ - Angularmomentumvector J1,J2,J3 – principal moments

  6. Model of system Constans of motion: Hamiltonian: Total angularmomentumvector: Cayley-Kleinparameters: Integratingtheequations of motion by means of theRaudau-Everhart RA-15 procedure, we haveobtainedhighlyaccurateresultswithin a fairlyshortcomputation time.

  7. Model of shape Thedynamical part of the model (freeorforcedprecession) Primary: Three-axialellipsoid Satellite: Spherical

  8. Model of shape Thesynchronous double asteroids Primary and satellite: Three-axialelipsoids plus twocraters. Primary and satellite: Three-axialelipsoids

  9. Model of shape YORP Only one body: Triangularfaces

  10. Inputparameters

  11. Model of lightcurve • Ray tracingis 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-bufferingis 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 – geneticalgorithm Genetic algorithms are a class of search techniques inspired from the biological process of evolution by means of natural selection.

  16. PIKAIA – geneticalgorithm Determinedparameters of model (blue): System: Shape: Period , primary: a, b/a, c/a density , secoundary: a, b/a, c/a Rotationangleα, NutationangleβDeformation: Precessionangleγ 2 craters: (8 parameters)

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

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