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A planet of mass m revolves in elliptical orbit around the sun so that its maximum and minimum

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A planet of mass m revolves in elliptical orbit around the sun so that its maximum and minimum distances from the sun are equal to ra and rp respectively . Find the angular momentum of this planet relative to the sun.

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Using conservation of angular momentum

mvprp = mvara

As velocities are perpendicular to the radius vectors at apogee and perigee.

vprp = vara 

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