Sei Mo.E.S. no Hakobune

Humanity has united into "Earth Federation." It seemed that men had finally found peace and happiness ...but a rain of comets brought misfortune. Fifty years after the fifteen Moena is worried about not being smart enough to go to a good high school. To her astonishment she's invited into the prestigious Institute of St. Moesu without any written or oral examinations. How is it possible? What link is there between the two events?