Into the Dark — J.A. Sutherland

At fifteen, Alexis Carew has to face an age old problem - she's a girl, and only a boy can inherit the family's vast holdings. Her options are few. She must marry and watch a stranger run the lands, or become a penniless tenant and see the lands she so dearly loves sold off. Yet there may be another option, one that involves becoming a midshipman on a shorthanded Navy spaceship with no other women.