[2] The same year he became Professor of Mathematics at Delaware College and in 1856 Professor of Mathematics at Indiana University in Bloomington, Indiana, where he stayed until his retirement in 1886, with the exception of two years, 1865–1867, at Jefferson College in Canonsburg, Pennsylvania.

In the same paper, he was the first to correctly posit that the material in meteor showers is cometary debris.

This discovery earned Kirkwood an international reputation among astronomers; he was dubbed "the American Kepler" by Sears Cook Walker, who claimed that Kirkwood's Law proved the widely held Solar Nebula Theory.

The "Law" has since become discredited as new measurements of planetary rotation periods have shown that the pattern doesn't hold.

He is buried in the Rose Hill Cemetery in Bloomington, Indiana, where Kirkwood Avenue is named for him.