Other
Scientific paper
Dec 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999baas...31.1586k&link_type=abstract
American Astronomical Society, DPS Meeting #31, late abstracts, #59.14; Bulletin of the American Astronomical Society, Vol. 31,
Other
Scientific paper
We have developed new methods for determining the shapes (and albedo distributions), rotation periods, and pole directions of asteroids. In the order of increasing complexity, we search for: 1) a convex representation of a nonconvex original body, 2) the sidereal period and the pole direction simultaneously with the shape solution, and 3) a nonconvex description of the original object. The recovered shapes are general and not based on modifications of some prior shape model. We produce test lightcurves of various irregular bodies with a fast ray-tracing algorithm. In point 1) above, either smooth functions or polyhedra can be employed; the latter describe sharp features in lightcurves (and on surfaces) better, while the former enable fast inversion and provide a good initial guess for other optimization methods. No particular regularization methods are necessary: the problem is stabilized by a simple constraint that automatically restricts the result of inversion to feasible shapes. We have found that even when the original shape is strongly nonconvex, we can recover a solution that is similar to its convex hull. In point 2), we add period and pole as free parameters to the optimization procedure. This task is eased by the fact that the shape resolution can be coarse in this context, facilitating the use of smooth functions. In addition to locating the best minimum, a map describing the strength of the minimum is provided for error estimation. Point 3) is the most demanding one; however, suitable constraints and optimization algorithms make the reconstruction of nonconvex shapes possible. If the input lightcurves show `characteristic' features, the optimization procedure converges towards a good solution. Such features (typically at large solar phase angles) reveal the shape best: thus it is much better to have, e.g., ten 50-point lightcurves than 25 20-point ones. A feasible albedo distribution can be found by first optimizing the shape and then continuing to improve the fit by adjusting the albedo variegation.
Kaasalainen Mikko
Torppa Johanna
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