This is book number 1986 in the Miles Vorkosigan Adventures series.
Miles Vorkosigan makes his debut in this frenetic coming-of-age tale. At age seventeen, Miles is allowed to take the entrance exams to the elite military academy; he passes the written but manages, through miscalculation in a moment of anger, to break both his legs on the obstacle course, washing out before he begins. His aged grandfather dies in his sleep shortly after, and Miles blames himself. He is sent to visit his grandmother Naismith on distant Beta Colony, accompanied by his bodyguard, Sergeant Bothari, and Bothari's daughter, Elena. Miles passes himself off as a mercenary leader as he picks up a ragtag crew, and soon his father Aral is under political attack back home as garbled rumors of Miles' mercenary operations trickle back. Miles must abandon his new fleet and dash back to Barrayar to stop the plot.