1. Investigation of different flyby geometries for asteroid Steins - Surface area, stereo and phase angle coverage
Sofie Spjuth
Max-Planck-Institut für Sonnensystemforschung
Katlenburg-Lindau, Germany
OSIRIS Team Meeting , November 7, 2006

2. Reference system/Steins‘ system
Opposite rotation
Along rotation
Z-axis – spin axis
X-axis towards the Sun’s projection onto Steins’ equatorial plane
Y-axis completes the right handed system
Latitude Sun: φ
The geometry of the flyby is equivalent to a fixed Steins and Rosetta approaching on a straight line with a constant relative velocity.

3. Assumptions/Constants/Constraints
Steins is a sphere with radius 2.3 km
Images taken at distances less than km
Two solutions of the rotation axis:
1. β = 265° ± 10°, λ = 8° ± 10°
2. β = 82° ± 10°, λ = 38° ± 10°
Rotational period: 6.06 hours
Constant relative velocity of 8.6 km/s
Minimum distance of 800 km without a problem with the slew angle
Cameras points towards Steins‘ center
Solar elongation: 24° NAC (< 2h)
45° WAC

4. Inputs Separation angle & min resolution for stereo coverage
Pole solution
Trajectory
direction
Minimum
distance
Interval between images

5. Outputs Examples Area fraction coverege (of total surface) 0.7
Stereo fraction coverage (of total surface)
Images resolution range (km/pixel) – 2.00
Phase angle coverage ° – 150°
Longitude/Latitude range

6. Area calculation
Steins‘ divided into a grid with optional spacing in longitude and latitude
Copied from:
Retrieve the part that is illuminated by the Sun

7. The total area  sum of the imaged, illuminated pieces
Longitude/Latitude
matrix
&
Area matrix
The total area  sum of the imaged, illuminated pieces
Area of first image

8. Stereo area calculation
Separation angle 5°
Copied from:
Resolution
> 0.2 km/pixel

9. FLYBY‘s (view from above).
800
800
100
800
Flyby‘s in a plane with
the Sun and Steins
1776
Flyby „above“ Steins

10. β = 265°, λ = 8°
Dir.
Min obs
A frac
< 200 m/pix
S frac
Phase angle
coverage
at closest
approach A
800
0.629
0.510
0.505
0° - 150°
61° O
0.639
0.470
0.426
29° - 156°
119°
1776
0.645
0.506
0.502
0° - 140°
62°
528
0.508
0.503
18° - 151° -
Sun’s latitude: -72°

11. 0° phase angle occurs 3 minutes before closest approach at a distance
of 1748 km.
Closest approach
Min phase angle

12. Longitude coverage: 357°
Latitude coverage: 108°
Steins

13. Area fraction of total surface: 0.629
Area fraction of total surface, res. < 0.2 km/pixel: 0.510
Stereo fraction of total surface, res. < 0.2 km/pixel: 0.505

14. β = 82°, λ = 38°
Dir.
Min obs
A frac
< 200 m/pix
S frac
Phase angle
coverage
at closest
approach A
800
0.757
0.501
0.497
0° - 150°
61° O
0.797
0.468
0.440
29° - 156°
119°
1776
0.785
0.505
0.500
0° - 140°
62°
528
0.756
0.495
0.491
18° - 151° -
Sun’s latitude: 53°

15. Flyby „above“ Steins A 800 0.629 0.474 0.467 28° - 151° 87° A 800
Flyby plane being offset relative to the Sun-Steins line by 800 km
Dir.
Min obs
A frac
< 200 m/pix
S frac
Phase angle
coverage
at closest
approach A
800
0.629
0.474
0.467
28° - 151°
87°
Compare with the trajectory in the Sun-Steins plane A
800
0.629
0.510
0.505
0° - 150°
61°
Sun’s latitude: -72°

16. Pole solutions with error barsβ λ
A frac
< 200
S frac
Sun
Lat.
265° ± 10°
8° ± 10°
0.54 – 0.72
~ 0.50
-58° – -85°
82° ± 10°
38° ± 10°
0.68 – 0.83
41° – 65°

17. Conclusions
Total area coverage between %, depending on pole solution (amount of polar night region)
Small differences of area fraction between cases of the same pole solution. But...
- The 100 km flyby has problem with the slew constraint, thus the zero phase angle and closest approach is lost.
- Trajectory opposite rotation (on the „back side“) performed at high phase angles
- The original flyby (1776 km) return less images at low resolution than a closer flyby
- Flyby „above“ Steins return no lower phase angles and have problem wtih solar panels rotation and illumination
- Thus, the closest trajectory possible, without suffering from the slew constraint, along rotation and in a plane with the Sun and Steins, is the optimal flyby for area coverage and phase angle coverage