Download 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
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
Cayley-Klein parameters:
Euler angles:
Rotation angle α
Nutation angle β
Precession angle γ
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 system
Dynamics 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 vector
P - Momentum vector
Γ - Angular momentum vector
J1,J2,J3 – principal moments
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.
Model of shape
The dynamical part of the model
(free or forced precession)
Primary:
Satellite:
Three-axial ellipsoid
Spherical
Model of shape
The synchronous double asteroids
Primary and satellite:
Three-axial elipsoids plus
two craters.
Primary and satellite:
Three-axial elipsoids
Model of shape
YORP
Only one body:
Triangular faces
Input parameters
Date of observation
Position of asteroid
(Orbital elements )
Position of Sun and
Earth
Orientation of
binary system
Model of shape
and binary system
Modelling of lightcurve
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
System:
Determined parameters of model (blue):
Shape:
Period ,
density ,
Rotation angle α,
Nutation angle β
Precession angle γ
primary:
a, b/a, c/a
secoundary: a, b/a, c/a
Deformation:
2 craters: (8 parameters)
Parallel computing
SQL
database
PC
PC
System: Debian
Compilator: gcc,c++
SQL database: MySql , oracleXe
Librares: CORBA, POSIX Threads
PC