Dynamic method: Difference between revisions

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== Mathematical analysis ==

The simplest way to describe the deflection of the asteroids is in the case where one object is significantly more massive than the other. In this case the equations of motion are the same as for that of [[Rutherford scattering]] between oppositely charged objects (so that the force ifis attractive rather than repulsive). When rewritten in the more familiar notation used in celestial mechanics deflection angle can be related to the eccentricity of the hyperbolic orbit of the smaller object relative to the larger one by the following formula:<ref>{{Cite book | title = Classical Mechanics: A Modern Perspective | edition = 2nd. | last1 = Barger | first1 = Vernon D. | last2 = Olsson | first2 = Martin G. | year = 1995 | publisher = [[McGraw-Hill]] | isbn = 0-07-003734-5 | chapter = 5.6}}</ref>

:<math>\sin \left( \frac{\Theta}{2} \right) = \frac{1}{\epsilon}</math>