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Kirkwood, Daniel

Kirkwood, Daniel

(b. Harford County, Maryland, 27 September 1814; d. Riverside, California 11 June 1895)


Of Scots-Irish descent, Kirkwood was the son of John Kirkwood, a farmer, and Agnes Hope. He spent his formative years on his father’s farm, and his early education was limited to a nearby country school. In 1833, having little interest or aptitude in farming, he took a teaching post at a small school in Hopewell, Pennsylvania. There he encountered a student who wished to study algebra, and together they mastered Bonnycastle’s Algebra. In the spring of 1834, Kirkwood entered York County Academy, where he continued his mathematical studies; in 1838 he became first assistant and instructor in mathematics. In 1843 he was appointed principal of Lancaster High School, and two years later he married Sarah A. McNair, of Newtown, Pennsylvania. He became principal of Pottsville Academy in 1849. From 1851 to 1856 he was professor of mathematics at Delaware College, after 1854 also serving as college president.

Never one to relish public notice or the assumption of authority, Kirkwood preferred to devote his energies to teaching and research and eagerly accepted the chair of mathematics at Indiana University. Except for the interval 1865-1867 (when he was professor of mathematics and astronomy at Washington and Jefferson college in pennsylvania), he remained at Indian University for thirty years, retiring in 1886. He then moved to California and at the age of seventy-seven became nonresident lecturer on astronomy at Stanford University. Kirkwood was an immensely popular, enthusiastic, and inspiring teacher, He was a deeply religious and serene person who never found any conflict between his cosmogonical studies and his Presbyterian faith.

Kirkwood’s research and many writings were generally devoted to an understanding of the nature, origin, and evolution of the solar system; he studied, in particular, the role of the lesser members of the system—asteroids, comets, and meteoric and meteoritic bodies. His first publication (1849) consisted of a demonstration that the square of the number of rotations per orbital revolution of a planet is proportional to the cube of the radius of the sphere of attraction given by the Laplace nebular hypothesis. His subsequent research revealed that both this “Kepler-type” law and the nebular hypothesis required severe modification, although he never abandoned the hypothesis completely.

Kirkwood’s most important astronomical discovery was of the “gaps” or “chasms” in the distribution of the mean distances of the asteroids from the sun. He made this discovery as early as 1857, when only about fifty asteroids were known. He published two short lists of asteroidal resonances in the Astronomical Journal (1860); the lists revealed an obvious lack of asteroids in simple resonance with Jupiter, while asteroids in resonance with Mars were commonplace. His first formal publication of the discovery was not made until 1866, by which time the number of asteroids known had risen to eighty-seven. He remarked on discontinuities in the distribution at distances corresponding to periods of revolution of one-third, twofifths, and two-sevenths that of Jupiter. He later mentioned gaps at one-half, three-fifths, four-sevenths, five-eighths, three-sevenths, five-ninths, seven-elevenths, and four-ninths. Several more gaps have since been recognized. Kirkwood also pointed out in 1866 that the Cassini division between rings A and B of Saturn exhibits the same phenomenon, for any particles on the division would have periods of revolution one-third that of the satellite Enceladus. Soon afterwared he noted that the periods would also be close to one-half that of Mimas and that there were also resonances with Tethys and Dione; furthermore, the Encke division in ring A also corresponded to resonances with Saturn’s satellites.

A simple qualitative explanation of the Kirkwood gaps is that the repetitive gravitational action of Jupiter (or Mimas) would quickly remove any asteroid (or ring-particle) away from resonance. The effect would be most pronounced for the resonances of lowest order, where the difference between the numerators and denominators of the fractions is small. Some of Kirkwood’s contemporaries doubted that this was really an explanation. In addition Kirkwood himself consistently maintained that the regularly increasing orbital eccentricities of particles initially in resonance would lead to the possibility of collisions with nearby non-resonant particles, and that this was really the cause of the elimination. In the asteroid problem he felt that mutual collisions might be too infrequent, and elimination could be achieved instead by collisions with the sun: according to the nebular hypothesis, the radius of the sun would be only slightly smaller than the mean distance of a newly formed asteroid.

A completely satisfactory explanation of the gaps is still lacking. It is not clear whether they represent merely a statistical underpopulation, with the instantaneous mean distances of objects near resonance tending at any time to be near the extremes of longterm oscillations about the critical values, or whether the gaps still exist if one considers the distribution of mean distances averaged over a long period of time. Current thinking is that the latter is the case, and therefore that nongravitational effects such as collisions, even among the asteroids, play an important role. The problem was complicated for Kirkwood toward the end of his life by his realization that the only asteroids existing at large mean distances were in resonance, having periods two-thirds and three-fourths that of Jupiter; he therefore conjectured that these orbits were unstable. Asteroids are especially numerous at the two-thirds resonance—the Hilda group—and it is now known that they are stable, avoiding encounters with Jupiter precisely because they oscillate about exact resonance.

Kirkwood also anticipated the asteroid “families,” listing thirty-two groups with similar orbits (1892), and he surmised that the members of each group had separated from one another soon after their formation. Hirayama put the concept on a firmer basis with the use of “proper orbital elements.”

From about 1869 onward Kirkwood began to question Laplace’s nebular hypothesis . Although Kirkwood recognized that the existence of the asteroids and Saturn’s rings suggested that the contracting sun had thrown off a continuous succession of rings, he thought it curious that the orbits of the major planets should be so widely separated. He also objected to the nebular hypothesis because the planets would have to be nearly cold by the time they had formed; furthermore, the satellites could not be explained, and the time required for production of the planets would be much longer than what was then believed to be the age of the solar system. He concluded (1880-1885) that planets and satellites were formed not by accumulation from complete rings but from limited arcs expelled in the equatorial plane of the shrinking sun. In order to explain the revolution of the inner satellite of Mars in a period shorter than that of the rotation of Mars, he supposed that the satellite’s motion had been accelerated by passage through the resisting medium of the solar atmosphere. The possibility that the satellite’s motion was being accelerated was still under active discussion in the mid-twentieth century.

When discussing Saturn’s rings in 1884, Kirkwood remarked that “planets and comets have not formed from rings, but rings from planets and comets.” He had considered this possibility for comets alone as early as 1861, when he gave the first convincing demonstration of an association between meteors and comets; confirmation was provided during the following few years, with the realization that the orbits of several of the best-known meteor streams were virtually identical with those of particular comets. He discussed the consequences of collisions of comets with meteoric rings, and his idea that this could explain the nongravitational acceleration of Encke’s comet was subsequently adopted by Backlund. Kirkwood also seems to have been the first to suggest (1880) that there exists a genetically connected group of sun-grazing comets.

Kirkwood was the first to consider (1866-1867) the possible relationship of comets and asteroids and of shower meteors and stony meteorites. Although he was forced to withdraw his supposition that meteorites have a tendency to fall and bright fireballs to appear during meteor showers, the asteroidal versus cometary nature of bright fireballs is still an unresolved issue. As for the possible asteroid-comet relationship, more evidence in favor of this was forthcoming as Kirkwood’s life advanced; with the discovery in the twentieth century of the Apollo group of asteroids, Hidalgo, and to short-period comets of remarkably asteroidal appearance, connection in some cases seems to be assured.

Kirkwood received an honorary master of artsdegree from Washington (now Washington and Jefferson) College, Pennsylvania, in 1848 and that of doctor of laws from the University of Pennsylvania in 1852. His name has been appended to asteroid number 1578, which, approprately, is a member of the Hilda group.


I. Original Works. Kirkwood wrote three books: Meteoric Atronomy (Philadelphia, 1867), Comets and Meteors (Philadelphia, 1873), and The Asteroid (Philadelphia, 1888). His numerous papers include “On a New Analogy in the Periods of Rotation of the Primary Planets,” in Proceedings of the American Association for the Advancement of Science for 1849 (1850), 207; see also the letter from S. C. Walker communicating Kirkwood’s information to the editor of the Astronomische Nachrichten, 30 (1850), 11-14; “Instances of Nearly Commensurable Periods in the Solar System,” in Mathematical Monthly, 2 (1860), 126-132; “On the Nebular Hypothesis,” in American Journal of Science and Arts, 2nd ser.; 30 (1860), 161-181; the obscure article that first discussed the association of comets and meteors, in The Danville Quarterly Review (Dec. 1861); “On Certain Harmonics in the Solar System,” in American Journal of Science and Arts, 2nd ser., 38 (1864), 1-17.

See also “On the Theory of Meteors,” in Proceedings of the American Association for the Advancement of Science for 1866 (1867), pp. 8-14, for the first discussion of the gaps in the distribution of the asteroids and in Saturn’s rings; “On the Nebular Hypothesis, and the Approximate Commensurability of the Planetary Periods,” in Monthly Notices of the Royal Astronomical Society, 29 (1869), 96-102; “On the Periodicity of the Solar Spots,” in Proceedings of the American Philosophical Society, 11 (1871), 94-101; “On the Formation and Primi-Structure of the Solar System,” ibid., 12 (1872), 163-166; “The Asteroids Between Mars and Jupiter,” in Annual Report of the Smithsonian Institution for 1876, pp. 358-371; “On Some Remarkable Relations Between th Mean Motions of the Primary Planets,” in Astronomische Nachrichten, 88 (1876), 77-78; “The Satellites of Mars and the Nebular Hypotheses,” in The Observatory, 1 (1878), 280-282; “On Croll’s Hypothesis of the Origin of Solar and Sideral Heat,” ibid., 2 (1879), 116-118.

For further reference, see “On the Aerolitic Epoch of November 12th-13th,” ibid., 2 (1879), 118-121; “The Cosmogony of Laplace,” ibid., 3 (1880), 409-412; “On the Origin of the Planets,” ibid., 3 (1880), 446-447; “On the Great Southern Comet of 1880,” ibid., 3 (1880), 590-592; “The Divisions in Saturn’s Rings,” ibid., 6 (1883), 335-336; “The Limits of Stability of Nebulous Planets, and the Consequences Resulting From Their Mutual Relations,” in The Sidereal Messenger, 4 (1885), 65-77; “The Relation of short-Period Comets to the Zone of Asteroids,” ibid., 7 (1888), 177-181; “On the Age of Periodic Comets,” in Publications of the Astronomical Society of the Pacific, 2 (1890), 214-217; “Groups of Asteroids,” in The Sidereal Messenger, 11 (1892), 785-789; “On the Relations Which Obtain Between the Mean Motions of Jupiter, Saturn and Certain Minor Planets,” ibid., 12 (1893), 302-303.

II. Secondary Literature. Biographical information is contained in W. W. Payne, “Daniel Kirkwood,” in Popular Astronomy, 1 (1893), 167-169; and J. Swain, “Daniel Kirkwood,” in Publications of the Astronomical Society of the Pacifc, 13 (1901), 140-147.

For modern works on the Kirkwood gaps and related problems see D. Brouwer, “The Problem of the Kirkwood Gaps in the Asteroid Belt,” in Astronomical Journal, 68 (1963), 152-159; P. J. Message, “On Nearly-Commensurable Periods in the Restricted Problem of Three Bodies, With Calculations of the Long-Period Variations in the Interior 2:1 Case,” in G. Contopoulos, ed., International Astronomical Union Symposium No. 25: The Theory of Orbits in the Solar System and in Stellar Systems (London-New York, 1966), pp. 197-222.

W. H. Jeffreys, “Nongravitational Forces and Resonances in the Solar System,” in Astronomical Journal, 72 (1967), 872-875; J. Schubart, “Long-Period Effects in the Motion of Hilda-Type Planets,” ibid., 73 (1968), 99-103; G. Colombo, F. A. Franklin, and C. M. Munford, “On a Family of Periodic Orbits of the Restricted Three-Body Problem and the Question of the Gaps in the Asteroid Belt and in Saturn’s Rings,” ibid., 73 (1968), 111-123; F. Schweizer, “Resonant Asteroids in the Kirkwood Gaps and Statistical Explanations of the Gaps” ibid. 74 (1969), 779-788; A. T. Sinclair, “The Motions of Minor Planets Close to Commensurabilities with Jupiter,” in Monthly Notices of the Royal Astronomical Society, 142 (1969), 289-294; B. G. Marsden, “On the Relationship Between Comets and Minor Planets,” in Astronomical Journal, 75 (1970), 206-217; and F. A. Franklin and G. Colombo, “A Dynamical Model for the Radial Structure of Saturn’s Rings,” in Icarus, 12 (1970), 338-347.

Brian G. Marsden

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