Speakers

• Prof. Barak Kol — Hebrew University of Jerusalem
• Dr Yogesh Dandekar — Bar-Ilan University
• Dr Manuel Pérez Molina — University of Alicante

Abstract

This seminar presents two distinct studies in celestial mechanics. The first investigates the distribution of regularized three-body phase-volume, essential for statistically predicting decay times in non-hierarchical three-body systems. The problem is reformulated into a three-degree-of-freedom triangle geometry space, applying a flux-based statistical theory. Divergence is addressed by a regularization method that subtracts a reference phase volume of asymptotically straight escape pipes. Analytical integrations enable numerical computation over S^3 (3D) or S^2 (2D). Results confirm accuracy for escape probabilities and demonstrate that σ̄(E,L) is positive, decreases with mass contrast, and approaches zero in limiting cases. The second study characterizes asteroid shapes and surface stability using super-ellipsoids, generalizing triaxial ellipsoids with exponent `n`. A Dynamically Equivalent Equal-Mass Super-Ellipsoid (DEEMSE) method minimizes surface deviation for optimal fitting. Application to bodies reveals best fits for Bennu and Ryugu as top-shapes (n ≈ 1.6), Vesta and Ceres as nearly ellipsoidal (n ≈ 2), and Eros as a rounded-corner orthohedron (n ≈ 2.5), improving characterization over standard ellipsoids. Surface stability on spinning super-ellipsoids is analyzed through derived detachment limits and slope angles. For fast rotations, top-shaped bodies exhibit more stable surfaces than ellipsoids. A parametric analysis of Didymos' primary suggests top-shaped configurations (n = 1.6–1.8) are more likely for stable surfaces consistent with dimensional estimates, implying a stable, nearly ellipsoidal Didymos is improbable.

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