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The Proximities of Asteroids and Critical Points of the Distance FunctionKeywords: Celestial mechanics , Minor planets , Asteroids Abstract: The proximities are important for different purposes,for example to evaluate the risk of collisions of asteroids or comets with the Solar-System planets. We describe a simple and efficient method for finding the asteroid proximities in the case of elliptical orbits with a common focus. In several examples we have compared our method with the recent excellent algebraic and polynomial solutions of Gronchi (2002, 2005).
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