Determining the Shapes of Three-Dimensional Angle of Repose-limited Rubble Piles with Rotation.

Astronomy and Astrophysics – Astronomy

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Scientific paper

What would a self-gravitating, rotating rubble pile look like if every slope on the surface was at the angle of repose? A new numerical technique, called "seed growth," is demonstrated to solve the geometrical problem of constructing uniform density, three-dimensional objects for which the surface at every point is at a constant angle, φ, relative to the local horizontal. An implementation of the seed growth technique, called Sandyroid, was developed that generates angle of repose-limited bodies subject to certain simplifying constraints. Sandyroid produces three-dimensional objects iteratively by generating a finite number of constant-longitude, two-dimensional profiles that each maintain a constant slope relative to the sum of local gravitational and centripetal acceleration vectors. The gravitational acceleration vector is determined from a "seed" body, which is the solution body from the previous iteration. By altering the configuration of cusps, which are points along the profiles where φ changes sign but not magnitude, multiple solutions are possible. Five different cusp configurations are explored, and three of which yield solutions for 20°<φ<30°. The three solution shapes are called Donut, Top, and Hourglass. In the case of the Donut and Top configurations, when rotation is included the ratios of their shortest to longest dimensions, c/a, can fall outside the limits published in the literature for rotating cohesionless spheroidal bodies. This research was supported by NASA's Origins of Solar Systems Research Program under grant No. NNG05GI97G.

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