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