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

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.

Assumptions/Constants/Constraints Steins is a sphere with radius 2.3 km Images taken at distances less than 100 000 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

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

Outputs Examples Area fraction coverege (of total surface) 0.7 Stereo fraction coverage (of total surface) 0.5 Images resolution range (km/pixel) 0.02 – 2.00 Phase angle coverage 0° – 150° Longitude/Latitude range

Area calculation Steins‘ divided into a grid with optional spacing in longitude and latitude Copied from: http://mitgcm.org/cubedsphere/latlongrid.html Retrieve the part that is illuminated by the Sun

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

Stereo area calculation Separation angle 5° Copied from: http://mitgcm.org/cubedsphere/latlongrid.html Resolution > 0.2 km/pixel

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

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°

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

Longitude coverage: 357° Latitude coverage: 108° Steins

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

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°

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°

Pole solutions with error bars β 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°

Conclusions Total area coverage between 54-83 %, 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