A planet A of mass m is in a circular orbit of radius "a" around a star ( M_star m ). Another planet B with the same mass m is in an elliptical orbit around the same star with its length of the semi-major axis equal to "a" . We have just learned that, in this case, the periods of revolution T and the mechanical energies of the two planets are the same. But, are the angular momenta of the planets with respect to the center of the star the same? Is the angular momentum of planet A equal to or different from the angular momentum of planet B, if so which one is greater ?

Question

A planet A  of mass m  is in a circular orbit of radius "a"  around a star ( M_star   >> m ). Another planet B  with the same mass m  is in an elliptical orbit around the same star with its length of the semi-major axis equal to "a" . We have just learned that, in this case, the periods of revolution  T and the mechanical energies of the two planets are the same. But, are the angular momenta of the planets with respect to the center of the star the same? Is the angular momentum of planet A  equal to or different from the angular momentum of planet B, if so which one is greater ?