Instituto de Astrofísica de Andalucía Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial RETRIEVING ROTATIONAL PARAMETERS OF ROSETTA TARGET OBJECTS FROM OSIRIS IMAGES OSIRIS TEAM MEETING VENICE 2007 18 September 2007 The IAA-INTA Team

Rotation Analysis AIM: METHOD: Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial Rotation Analysis AIM: Development of a software for the analysis of the rotational parameters of a celestial body. The software would allow the determination of the rotational parameters of STEINS, LUTETIA and the COMET NUCLEUS METHOD: Proceeding from the study of the position of LANDMARKS on the body surface, fitting the values of the coordinates with the values predicted by the equations of rotational motion.

Instituto de Astrofísica de Andalucía Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial Rotation Analysis FIRST STEP: Analyze the motion with the equations of a rotating sphere (simple rotation) SECOND STEP: In the case of excited rotation, analysis is done with Euler equations of motion of a rigid body WHY THIS SECOND STEP?: The motion can be excited because the body can be affected by no gravitational forces Changes in rotational parameters can occur during comet orbit. We want to monitor them

Instituto de Astrofísica de Andalucía Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial Rotation Analysis

Rotation Analysis FIT PARAMETERS DUE TO ROTATION: I1,I2,I3 L E Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial Rotation Analysis FIT PARAMETERS DUE TO ROTATION: I1,I2,I3 principal moments of inertia (3 constant scalars, one of which is arbitrary) L modulus of angular momentum (L is constant vector along Z axe in an inertial system) E rotational energy (constant scalar)

Rotation Analysis FIT PARAMETERS DUE TO OBSERVER: LJ,Lf,Ly Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial Rotation Analysis FIT PARAMETERS DUE TO OBSERVER: LJ,Lf,Ly inertial system orientation (3 angles) FIT PARAMETERS DUE TO EQUATIONS: S initial time step FIT PARAMETERS DUE TO LANDMARKS: Rn, an, bn radius, longitude, latitude of every landmark in the body reference system (3*n variables)

Rotation Analysis REAL VALUES TO FIT: NECESSARY CONDITION FOR THE FIT: Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial Rotation Analysis REAL VALUES TO FIT: X and Y coordinates of every landmark in every image (2*n*m values) NECESSARY CONDITION FOR THE FIT: real values >= variables 2*n*m >= 3*n + 8 n = number of landmarks m = number of images   number of landmarks 1 2 3 4 5 6 7 8 9 10 -1 number of images

EXCITED ROTATION FIT VALUES Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial Results The software has been successfully tested using synthetic images of a rotating body REAL VALUES EXCITED ROTATION FIT VALUES RELATIVE ERROR L 2.688 E-4 2.715 E-4 +/- 0.025 E-4 0.99 % I1 0.687 0.775 +/- 0.035 12.8 % I3 2.019 2.084 +/- 0.044 3.22 % E 2.195 E-8 2.242 E-8 +/- 0.033 E-8 2.15 % Step 11 +/- 125 JL 0.615 0.611 +/- 0.023 jL 1.571 1.597 yL 3.927 3.897 +/- 0.019

Instituto de Astrofísica de Andalucía Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial Results For this fit 4 landmarks and 6 images were used. A larger number can lead to a better fit time [s] Third Euler angle [ rad +/- 1 sigma] Second Euler angle [ rad +/- 1 sigma] time [s] First Euler angle [ rad +/- 1 sigma] time [s]

Instituto de Astrofísica de Andalucía Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial Results From the fit done by this software it is possible to retrieve information on the physical parameters of the body: it is a first step to the reconstruction of the shape of the body it allows to track the rotational evolution of the body (if excited rotation) it can give information on the internal mass distribution

Instituto de Astrofísica de Andalucía Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial Future Work The analysis provided by the software must be improved overcoming the limitations it has by now, in particular: observer position does not change the origin of body system is considered known. If it should be considered unknown, then we would have to consider 3 more free variables for every image in the fit process

Thank You for Your Attention Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial Thank You for Your Attention the IAA-INTA Team