People usually think of William Herschel as a scientist. At one point he was even given the title Royal Astronomer by King George III. But Herschel hadn't always a professional. In fact, his most important discovery-- the identification of Uranus as a planet-- occurred when he was a young music teacher and self-taught astronomer who spent much of his spare time gazing at the stars. It was the Uranus discovery that brought him to the attention of the king.
Uranus - First described by William Herschel - 1781
Astronomy is not an exclusive field of science. To observe the stars doesn't require years of graduate school, nor is the night sky a reserved province of the credentialed or well heeled. The heavens are available to everyone, and the most basic and only necessary item of astronomy equipment consists essentially of mirrors or lenses. Today, Even hand figured telescopes of the finest quality can be acquired for less than the cost of a modest automobile.
Clyde Trombaugh's discovery of Pluto has probably been the most sensational find by an amateur astronomer.
By the time of his death in 1997 Clyde Tombaugh was not an amateur. He had just recently retired from New Mexico State University, where he taught astronomy for nearly twenty years. Before that he worked for the White Sands Missile Range in the early 1950s, not long after receiving astronomy degrees from the University of Kansas and Northern Arizona University.
But it was before his formal career as a scientist and teacher that Clyde Tombaugh made the discovery for which he is still famous. As a teenager Tombaugh corresponded with the Lowell Observatory and sent them telescopes and designs he had made. Impressed, they hired him as a researcher and he was given the task of systematically searching the same specific areas of the sky, night after night, taking and comparing images with a 13" astrograph in an attempt to find the "planet x" that Percival Lowell had predicted. What he found was Pluto.