1. Deeper insight in the Steins flyby geometry:
A new method of 3D reconstruction of the asteroid
Vazzola, E. Simioni, G. Cremonese, G. Naletto
Padova, September 2010
OSIRIS FBWG meeting

2. Problems in kernels and headers on Steins orbit
Ringberg Castle meeting revealed some incoherence around Steins-Rosetta relative position or pointing:
Simioni: “problem in automatic recostrunction, silhouettes are not centered”
Capaccioni: “large offset in VIRTIS and MIRO”
- Sabolo: “Optimal orbit determination on Rosetta is a long work with many improvement, we found offsets in kernels”
Deeper insight in the Steins flyby geometry: a new method of 3D reconstruction of the asteroid.

3. Non coherent re-projection using kernels
Our work reveals a non coherent kernel re-projection of Steins. This is shown by Steins centroid displacement with respect to the expected one:
variable offset, as large as 8 pixels, both positive and negative
no continuous trend of offsets
offset trend shows regular spikes along x axis
offset trend shows noise
Deeper insight in the Steins flyby geometry: a new method of 3D reconstruction of the asteroid.

4. Used method and surface covering
The method we used for the 3D reconstruction of the observed surface of Steins returns its visual hull.
With this method concave and shadow areas are undetermined, so the returned model has more mass than the real object.
In our case, all the projection cones have their axes in a plane, due to orbits conformations, so saddle points on equator cannot be determined.
WAC images cover an angle of 115°.
Deeper insight in the Steins flyby geometry: a new method of 3D reconstruction of the asteroid.

5. Offset problem analysis
The analysis of the kernel data showed the presence of non linearities in the drift of Steins image “centroid”.
These offsets could not be associated to relative displacement Steins-Rosetta, but to “internal” causes or problems in software data reduction.
To this end, we better analyzed the effects due to:
- Filter exchange (F)
- Terminator definition (T)
Deeper insight in the Steins flyby geometry: a new method of 3D reconstruction of the asteroid.

6. Analysis of the filter exchange effect
Filter exchanges cause periodic offsets in Steins image center position. These offsets were actually calibrated both on ground and in flight, but adding these corrections to the data did not totally solve the problem.
So various filtering on filters (as offset grouping, FFT and others) have been used to remove the residual errors.
Deeper insight in the Steins flyby geometry: a new method of 3D reconstruction of the asteroid.

7. Correction of filter exchange effect
Spikes are now removed, but noise remains.
NB: when filter wheels do not change position, e.g. when using filter 71, there is no noise.
Deeper insight in the Steins flyby geometry: a new method of 3D reconstruction of the asteroid.

8. Analysis of the terminator on Steins centroid
Terminator moves the actual asteroid center to the illuminated area center.
Calculations of center of dark side vs. total viewed area give us some usable results to minimize this effect.
On first Steins images, terminator is not the primary effect of offset.
But during last observations, phase angle increases a lot and terminator gives to center a wider offset, also where images are more detailed*.
*At closest approach, phase angle is ~52.2°
Deeper insight in the Steins flyby geometry: a new method of 3D reconstruction of the asteroid.

9. After filter and terminator effect corrections
The “target” zone identifies a maximum offset of 1 pixel at closest approach
Deeper insight in the Steins flyby geometry: a new method of 3D reconstruction of the asteroid.

10. Steins orbit segment correction
It is now possible to define a new Steins orbit segment based on image centers.
If we assume Rosetta position and attitude data as “nominal” in the J2000 reference system, we can reconstruct the optimal Steins orbit segment which minimizes the centroid offsets.
The new Steins orbital segment is optimized in velocity, rotation relative to WAC axis and shift along pointing axis. Calculated orbital parameter differences:
- Steins' velocities relative to J2000: cm/s
- Shift of Rosetta Steins id 180: 77 m
- WAC x axis parallel rotation on id 180: 2.6 nrad
- WAC z axis parallel rotation on id 180: 87 μrad
Deeper insight in the Steins flyby geometry: a new method of 3D reconstruction of the asteroid.

11. A “symmetrical” distribution of residual offsets remains
Steins centroid offset residuals
A “symmetrical” distribution of residual offsets remains
Deeper insight in the Steins flyby geometry: a new method of 3D reconstruction of the asteroid.

12. Single offset effect contributions
Deeper insight in the Steins flyby geometry: a new method of 3D reconstruction of the asteroid.

13. Centroid offsets and Rosetta attitude
Unfortunately, all these corrections do not completely remove the offset noise.
However, the residual offsets have some relationship with the Rosetta attitude, both when filters are exchanged and during the phase of the closest approach.
Deeper insight in the Steins flyby geometry: a new method of 3D reconstruction of the asteroid.

14. Rosetta attitude control
A reasonable cause of this symmetrical distribution can be the effect of the reaction wheels that try to compensate the rotation of filter wheels during the filter exchange.
In fact, at every filter change there is a noise in the z rotation velocity; then gyros’ momentum destabilize attitude values, by a symmetrical distribution on xy plane.
Moreover, some “drift” in the Rosetta attitude control seems to be present during the closest approach phase.
Deeper insight in the Steins flyby geometry: a new method of 3D reconstruction of the asteroid.

15. Re-projections of 3D Steins model
Using all these corrections, we realized a new 3D model of the Steins visible surface.
With the new slightly changed Steins orbital parameter, and with the compensation of all the described offset sources, Steins re-projections now are perfectly corresponding, giving a “consistent” model.
The model here shown is built using an image every degree of relative phase angle (when available), for a total of 64 images and 110° of covered angle. Range time is 406 s, corresponding to a 6.7° Steins rotation.
Deeper insight in the Steins flyby geometry: a new method of 3D reconstruction of the asteroid.

16. Comparison with previous results
A comparison between the sizes of Steins obtained with this analysis and the ones given in Science paper (“E-Type Asteroid (2867) Steins as Imaged by OSIRIS on Board Rosetta”), which also used the light curve information to reconstruct the asteroid hidden portion, shows some difference.
Bounding box are quite similar, 5.90×[N/A]×4.29 km3 vs. 5.81×6.67×4.47 km3 (+1.5%,[N/A],4.2%), but the equatorial shapes are not the same.
Mean sphere diameter is 5.1 km, with respect to 5.3 km (3.8%).
Deeper insight in the Steins flyby geometry: a new method of 3D reconstruction of the asteroid.

17. Additional images with new Steins model
Deeper insight in the Steins flyby geometry: a new method of 3D reconstruction of the asteroid.

18. Conclusions
We have been able to determine and to separate different contributions which allow to explain the difference between the Steins position foreseen by kernels and the measured one. The main contributions were the orbit slight correction and the terminator effect in defining the asteroid centroid. Also the filter exchange gave a contribution, even if less important.
By compensating these effects, a consistent model of Steins have been obtained, which differs by few percent with respect to the one previously determined.
This suggests that great care has to be taken when analyzing these data, because errors are possible. This should be considered also for Lutetia 3D reconstruction.
Deeper insight in the Steins flyby geometry: a new method of 3D reconstruction of the asteroid.