After initial schooling, Trumpler entered the Universität Zürich but later transferred to the University of Göttingen where he earned his Ph.D. in 1910. In 1915, during World War I, he emigrated to the United States and joined the University of California. He took a position at Allegheny Observatory, and later went to Lick Observatory. In 1921, he became a naturalized citizen of the United States. He was elected a member of the United States National Academy of Sciences in 1932.
He is most noted for observing that the brightness of the more distant open clusters was lower than expected, and the stars appeared more red. This was explained by the interstellar dust scattered through the galaxy, resulting in the absorption (extinction) of light or interstellar extinction of light.
Trumpler further studied and catalogued open clusters in order to determine the size of the Milky Way galaxy. At first he thought his analysis placed an upper limit on the Milky Way's diameter of about 10,000 parsecs with the Sun located somewhat near the center although he later revised this. While cataloguing open clusters, he also devised a system for their classification according to the number of stars observed within them, how concentrated these stars are in the center of the cluster and the range of their apparent brightness. This system, known as the Trumpler classification, is still in use today.
The following celestial features are named after him:
... perhaps, among the high lights of 1935 the preliminary results announced by Trumpler (Dr. Robert Julius Trumpler) of the Lick Observatory on his test of ...