martian moon phobos discovered august 17, 1877

Astronomer Asaph Hall discovered a "dim star" while observing Mars through a 26 inch refractor telescope at the US Naval Observatory, the largest telescope at that time. Hall had already discovered Deimos, the smaller Martian moon on August 11th. You can read more in a Universe Today article, "Finding Phobos: Discovery of a Martian Moon".