# Modeling of double asteroids with PIKAIA algorithm

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Modeling of double asteroids with PIKAIA algorithm

Modeling of double asteroids with PIKAIA algorithmPrzemysaw Bartczak

Astronomical Observatory of A. Mickiewicz University

Idea of modelling

Observation dataModel of binary systemsimulationModel of system

Cayley-Klein parameters:Euler angles:

Rotation angle Nutation angle Precession angle 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 primaryDrawback: undetermined for =0 or = 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.

Model of systemDynamics equations describe the orbital motion of the satelite with respect to the primary and rotation of primary .

- Angular rate vector R - Satelites radius vectorP - Momentum vector - Angular momentum vectorJ1,J2,J3 principal momentsModel 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 shapeThe dynamical part of the model (free or forced precession)

Primary:

Three-axial ellipsoidSatellite:

Spherical

Model of shapeThe synchronous double asteroids

Primary and satellite:Three-axial elipsoidsPrimary and satellite:Three-axial elipsoids plus two craters.Model of shape YORP

Only one body:

Triangular facesInput parametersModel of lightcurveRay 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 lightcurveRay tracing

Modelling of lightcurveZ-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 lightcurveZ-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 algorithmDetermined parameters of model (blue):System:Shape:

Period , primary: a, b/a, c/a density , secoundary: a, b/a, c/a Rotation angle , Nutation angle Deformation: Precession angle 2 craters: (8 parameters)

Parallel computingSystem: DebianCompilator: gcc,c++

SQL database: MySql , oracleXeLibrares: CORBA, POSIX Threads