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Statement of a problem № 3341

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A particle is describing an ellipse of eccentricity 0.5 under the action of a force to a focus and when it arrives to an apse (turning point) the velocity is doubled. Show that the new orbit will be a parabola or hyperbola accordingly as the apse is the farther or nearer one.

Solution:
A particle is describing an ellipse of eccentricity 0.5 under the action of a fo

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