Modeling of double asteroids with PIKAIA algorithm
description
Transcript of Modeling of double asteroids with PIKAIA algorithm
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