Trajectory of scattered alpha particle

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This is a famous experiment conducted by Rutherford, in this exprement, the alpha particle(+2e charge) repulsed from necleus by coulomb force, and eventually divert its trajectory by theta.

I want to show the trajectory of alpha particle has asympotes which means it go out along that asympote line after repulsed by neculeus.

Can anybody help me how to set up, how to start and what precedure should I follow.
 

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vanhees71
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Solve the Coulomb (Kepler) problem. In non-relativistic approximation the scattering (unbound) solutions are hyperbolae (or parabolae).
 

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