(a) For circular and parabolic orbits in an attractive 1/r potential having the same angul...

(a) For circular and parabolic orbits in an attractive 1/r potential having the same angular momentum, show that the perihelion distance of the parabola is one-half the radius of the circle.

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(b) Prove that in the same central force as in part (a) the speed of a particle at any point in a parabolic orbit is times the speed in a circular orbit passing through the same point.