One question about Parabolic and Hyperbolic trajectory.

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    Hyperbolic Trajectory
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IPhO' 2008
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In the Parabolic and Hyperbolic trajectory.Is the sun in the focus point of parabola and hyperbola?
 
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To be more precise, the focus is at the center of mass (CM) of the two objects. If the body on a parabolic/hyperbolic trajectory had a mass comparable to that of the sun, the CM might be outside the surface of the sun.

It might interest you that the CM of the Sun-Jupiter system is outside the surface of the sun by about .12 solar radii = 83,500 km.