Computer Science – Databases
Scientific paper
Sep 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011amos.confe..11o&link_type=abstract
Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, held in Wailea, Maui, Hawaii, September
Computer Science
Databases
Scientific paper
Optical observations of rotating space debris near GEO contain important information on size, shape, composition, and rotational states, but these aspects are difficult to extract due to data limitations and the high number of degrees of freedom in the modeling process. For tri-axial rigid debris objects created by satellite fragmentations, the most likely initial rotation states have large components of angular velocity directed along the intermediate axis of inertia, leading to large reorientations of the body on the timescale of the rotation period. This lends some support to the simplest possible interpretation of light curves -- that they represent sets of random orientations of the objects of study, although such rotation states do not typically sample orientation space uniformly even over a large number of rotations. Furthermore, effects of solar radiation can cause significant modification of rotation states within timescales of hours, for cm-sized objects of irregular shape. In order to examine the rotational dynamics under solar influence, a set of seven firstorder coupled equations of motion were assembled in state form: three are Euler equations describing the rates of change of the components of angular velocity in the body frame, and four describe the rates of change of the components of the unit quaternion. Quaternions are four-dimensional extensions of complex numbers that form a seamless, singularity-free representation of body orientation on S3. The Euler equations contain explicit terms describing torque from solar radiation. Numerical integrations reveal widely varying rotation states, such that in general, light curves for small objects of irregular shape can be expected to radically change character between different observation epochs. Because the axis of maximum rotational inertia tends to be roughly coincident with the normal to the largest projected cross-sectional area, internal friction or magnetic damping, if significant, may lead to reduced variation of light curve amplitudes at a given phase angle, but a large dependence of the amplitudes on phase angle. At a given phase angle, databases are generated that show reflected intensities at all orientations simultaneously, within a semi-transparent 3D spherical projection of the quaternion intensity database. Simulated rotational sequences form trajectories through this space which may be conveniently visually examined relative to all possible orientations. Symmetries in the problem suggest that if internal friction or magnetic retarding torques are significant, preferred rotation states will be likely, defined relative to the object-sun direction and/or the magnetic field direction in inertial space and relative to the maximum principal axis of inertia in the body coordinate system. Such rotation states may greatly simplify the problem of light curve interpretation by reducing the number of degrees of freedom in the problem. Acknowledgements: This work was produced under NASA contract NNJ05HI05.
Hill Norman
Ojakangas G.
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