She was famous for a certain act that started her life of fame. She had found a comet and had named it Mitchells Comet. Because of this discovery she was accepted into the Academy of Arts and Science. She was also given a degree from Vassar college.  She later became a professor for Vassar College.  Her accomplishments was how she was appointed the first women to the faculty of Vassar, and how she was appointed president for the American Association for the Advancement of women.