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Register a new userCreating deterministic collisions between two orbiting bodies
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We aim to create deterministic collisions between orbiting bodies by applying a time-dependent external force to one or both bodies, whether the bodies are mutually repulsive, as in the two- or multi-electron atomic case or mutually attractive, as in the planetary-orbit case. Specifically, we have devised a mathematical framework for causing deterministic collisions by launching an inner orbiting body to a higher energy such that this inner body is guaranteed to collide with the outer body. Our method first expresses the problem mathematically as coupled nonlinear differential equations with a time-dependent driving force and solves to find a feasible solution for the force function. Although our calculation is based strictly on classical physics, our approach is suitable for the case of helium with two highly excited electrons and is also valid for creating collisions in the gravitational case such as for our solar system.
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We introduce and study the mechanical system which describes the dynamics and statics of rigid bodies of constant density floating in a calm incompressible fluid. Since much of the standard equilibrium theory, starting with Archimedes, allows bodies with vertices and edges, we assume the bodies to be convex and take care not to assume more regularity than that implied by convexity. One main result is the (Liapunoff) stability of equilibria satisfying a condition equivalent to the standard metacentric criterion.
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Collisions are the core agent of planet formation. In this work, we derive an analytic description of the dynamical outcome for any collision between gravity-dominated bodies. We conduct high-resolution simulations of collisions between planetesimals; the results are used to isolate the effects of different impact parameters on collision outcome. During growth from planetesimals to planets, collision outcomes span multiple regimes: cratering, merging, disruption, super-catastrophic disruption, and hit-and-run events. We derive equations (scaling laws) to demarcate the transition between collision regimes and to describe the size and velocity distributions of the post-collision bodies. The scaling laws are used to calculate maps of collision outcomes as a function of mass ratio, impact angle, and impact velocity, and we discuss the implications of the probability of each collision regime during planet formation. The analytic collision model presented in this work will significantly improve the physics of collisions in numerical simulations of planet formation and collisional evolution. (abstract abridged)
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