Kirkwood was born on a farm in Maryland and began teaching at the school at age 19. He learned self- algebra by he taught his students with the help of a textbook. Finally, he studied at the College York County, Pennsylvania, where he also taught after graduating in 1838.
In 1843 he became head of the Lancaster High School in Pennsylvania. Here he began to deal with astronomical topics. It created seven works, the second on the occasion of the discovery of the fifth asteroid ( Astrea ) dealt with the asteroid.
In August 1849, he achieved international attention when he discovered a relationship between the periods of the self-rotation of the planets and the radii of their orbits, which he called a mathematical analogy, and later became known as Kirkwood 's Analogy. Starting from the theory of Laplace on the formation of the solar system and looking for a similar law as the third Kepler law, only here for the rotation periods of the planets, he put the number n of revolutions of the planet per orbit around the sun with the diameter of its attraction sphere D in combination ( the distance between the points where each two neighboring planets exert same appeal when they are in conjunction, each of the outer and inner planetary neighbor ):
1849 presented the astronomer Sears Cook Walker from the U.S. Coastal Survey the formula at the annual meeting of the American Association for the Advancement of Science. The formula was tested on Earth, Venus and Saturn and showed good agreement. This also meant that the mists hypothesis of Laplace gained reputation back for more. At the same time supported the formula established already by Kepler theory that there had once been another planet between Mars and Jupiter ( the Walker Kirkwood called ), in the region of the asteroid belt, which form its remains. 1850 Kirkwood's discovery was celebrated in England at the meeting of the British Association for the Advancement of Science by David Brewster, by other astronomers as Charles Piazzi Smyth ( Royal Astronomer of Scotland, who saw a numerical coincidence as Bode 's law) and continental European astronomers such as Heinrich Christian Schumacher, which printed a message about it in the Astronomische Nachrichten, the reception was rather cool.
1851 Kirkwood became a professor of mathematics at Delaware College and served as president 1854-1856.
1856 Kirkwood went as professor of mathematics at Indiana University, Bloomington. Here continued to work in the asteroid research and made 1861 the proposal that the meteor shower could be the remains of a shattered comet.
His most significant achievement was the discovery of named after him gaps in the asteroid belt, which he made in 1866, the so-called Kirkwood gaps.