1. 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

2. 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.

3. 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

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

5. 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)

6. 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)

7. 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

8. 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
+/ E-4
0.99 % I1
0.687
0.775 +/
12.8 % I3
2.019
2.084 +/
3.22 % E
2.195 E-8
2.242 E-8
+/ E-8
2.15 %
Step 11
+/- 125 JL
0.615
0.611 +/ jL
1.571
1.597 yL
3.927
3.897 +/

9. 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]

10. 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

11. 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

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