Modeling of double asteroids with PIKAIA algorithm
Przemysław Bartczak
Astronomical Observatory of A. Mickiewicz University
Idea of modellingObservation data
Model of binary system
simulation
Model of system
Cayley-Klein parameters: Euler angles:
Rotation angle αNutation angle βPrecession 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
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 systemDynamics 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 vectorP - Momentum vectorΓ - Angular momentum vector
J1,J2,J3 – principal moments
Model of systemConstans 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 ellipsoid
Satellite:
Spherical
Model of shapeThe synchronous double asteroids
Primary and satellite:Three-axial elipsoids
Primary and satellite:Three-axial elipsoids plus
two craters.
Model of shape
YORP
Only one body:
Triangular faces
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
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
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 β Deformation: Precession angle γ 2 craters: (8 parameters)
Parallel computing
SQL database
PC PC PC
System: DebianCompilator: gcc,c++
SQL database: MySql , oracleXeLibrares: CORBA, POSIX Threads
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