At 10:50 pm on the night of October 1, 1847, Mitchell discovered Comet 1847 VI (modern designation C/1847 T1) using a Dollond refracting telescope with three inches of aperture and forty-six inch focal length. She had noticed the unknown object flying through the sky in an area where she previously had not noticed any other activity and believed it to be a comet. The comet later became known as “Miss Mitchell’s Comet”. Mitchell published a notice of her discovery in Silliman's Journal in January 1848 under her father's name. The following month, she submitted her calculation of the comet's orbit, ensuring her claim as the original discoverer. Mitchell was celebrated at the Seneca Falls Convention for the discovery and calculation later that year.
In 1848, Mitchell was awarded a gold medal prize for her discovery by King Christian VIII of Denmark. This award had been previously established by King Frederick VI of Denmark to honor the “first discoverer“ of each new telescopic comet, a comet too faint to be seen with the naked eye. A question of credit temporarily arose because Francesco de Vico had independently discovered the same comet two days after Mitchell but reported it to European authorities first. The question was resolved in Mitchell’s favor and she was awarded the prize. Her medal was inscribed with line 257 of Book I of Virgil’s Georgics: “Non Frustra Signorum Obitus Speculamur et Ortus” (English: Not in vain do we watch the setting and the rising [of the stars]). The only previous women to discover a comet were the astronomers Caroline Herschel and Maria Margarethe Kirch.
In 1848, Mitchell became the first woman elected Fellow of the American Academy of Arts and Sciences. She joined the American Association for the Advancement of Science in 1850 and befriended many of its members, including the director of the Smithsonian Institution, Joseph Henry. In 1869, Mitchell joined Mary Somerville and Elizabeth Cabot Agassiz in becoming some of the first women elected to the American Philosophical Society. Hanover College, Columbia University, and Rutgers Female College granted Mitchell honorary degrees.