Kirkwood_gap - Wikiparency

# Kirkwood gap  **Microsim — three.js (Wikitube framework):** *The asteroid belt in the Solar System explorer* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/solar/Solar_System.html?obj=belt&embed=1" data-title="The asteroid belt in the Solar System explorer"></div> *The Solar System explorer locked on this article's state (`?obj=belt`); every object and population of the [[PORTAL_Solar_System|Solar System portal]] has its own state in the same scene.*  *Try: under show, choose small bodies and look down on the belt from above to find the four thin empty lanes the explorer draws at the 3:1, 5:2, 7:3 and 2:1 resonances; drag to a low angle to see that the lanes cut through the whole thickness of the torus; then set show back to everything and the speed to 10 years/s, and watch Jupiter, whose 11.9-year period fixes where every lane falls, go round in a little over a second.* A **Kirkwood gap** is a dip or gap in the distribution of [[Asteroid|asteroids]] of the [[Asteroid_belt|main belt]] by semi-major axis, the average distance that fixes an asteroid's orbital period. Each gap lies where that period would be a simple fraction of [[Jupiter]]'s, a mean-motion resonance.[^fernie1999][^minton2009] Daniel Kirkwood identified the gaps in 1866 and correctly attributed them to Jupiter's repeated tugs at the same points of a resonant [[Orbit|orbit]].[^fernie1999] The clearest example lies near 2.50 [[Astronomical_unit|AU]], where an asteroid would take about 3.96 years (derived) to go round the [[Sun]] and so complete exactly three orbits for every one of Jupiter's; hardly any asteroids have that semi-major axis.[^minton2009][^jpl-t1] Resonance alone does not empty an orbit. In the main Kirkwood gaps the mean-motion resonances overlap with secular resonances, in which the slow turning of an asteroid's orbit keeps pace with that of Jupiter's or [[Saturn]]'s. The combination drives eccentricities up chaotically until asteroids cross the orbits of the planets, within a few million years.[^moons1995] Other resonances behave differently: Jupiter's 3:2 resonance, for example, holds on to the bodies captured in it, the [[Hilda_asteroid|Hilda asteroids]], instead of clearing them.[^minton2009][^ferrazmello1994] The explorer at the top of this page shows the main belt as ILLUSTRATIVE points, a random sample rather than real orbits, with empty lanes at the four main gaps, 3:1, 5:2, 7:3 and 2:1. The lanes mark where the gaps fall in semi-major axis; the named bodies in the belt are real objects on their catalogued orbits.[^jpl-sbdb] ## Main gaps The positions of the gaps follow from [[Kepler's_laws_of_planetary_motion|Kepler's third law]], which relates an orbit's period P to its semi-major axis a as P² ∝ a³. An asteroid that completes p orbits while Jupiter completes q has a period q/p times Jupiter's and therefore a semi-major axis a_J × (q/p)^(2/3). With Jupiter's semi-major axis of 5.203 AU and period of 11.86 years, this simple formula reproduces the resonance locations listed below to within about 0.001 AU (derived).[^jpl-t1][^openstax][^minton2009] | Resonance | Location | Period from Kepler (derived) | Notes | |---|---|---|---| | 5:1 | 1.780 AU | 2.37 yr | | | 4:1 | 2.065 AU | 2.97 yr | inner edge of the main belt | | 3:1 | 2.502 AU | 3.96 yr | Alinda group inside it | | 5:2 | 2.825 AU | 4.75 yr | | | 7:3 | 2.958 AU | 5.09 yr | | | 2:1 | 3.279 AU | 5.93 yr | Hecuba gap; Griqua group inside it | | 3:2 | 3.972 AU | 7.91 yr | populated: the Hilda asteroids | | 4:3 | 4.296 AU | 8.90 yr | populated: the Thule group | The locations in the table are those given by Minton and Malhotra.[^minton2009] Weaker or narrower dips occur at many higher-order resonances, among them 9:2 (1.909 AU), 7:2 (2.258 AU), 10:3 (2.332 AU), 8:3 (2.706 AU), 9:4 (3.031 AU), 11:5 (3.077 AU), 11:6 (3.474 AU), 9:5 (3.517 AU), 7:4 (3.584 AU) and 5:3 (3.702 AU).[^minton2009] These weaker resonances thin the population without clearing it.[^minton2009] The gaps are not all equally empty, and they did not all empty in the same way. Moons and Morbidelli showed that inside the 4:1, 3:1, 5:2 and 7:3 resonances the secular resonances ν5 and ν6, tied to the precession of Jupiter's and Saturn's orbits, overlap the mean-motion resonance, so that orbits become chaotic and reach planet-crossing eccentricities quickly.[^moons1995] The 2:1 resonance contains a few relatively stable islands, which leak slowly onto unstable orbits. That leakage is linked to Jupiter and Saturn lying near a 5:2 resonance of their own, and it may have been faster in the past, when the two planets' orbits lay closer together.[^moons1998] A small number of asteroids on highly eccentric orbits do sit in the gaps, including the Alinda group at 3:1 and the Griqua group at 2:1. Their eccentricities grow over tens of millions of years until close encounters with a planet remove them.[^moons1995][^moons1998] Asteroids keep arriving in the gaps too, because the Yarkovsky effect, a weak thrust from the uneven thermal emission of a rotating body, slowly changes their semi-major axes.[^demeo2015] The present gaps also record the history of the planets. Liou and Malhotra showed that sweeping resonances during the migration of the giant planets would have depleted the outer belt.[^liou1997] Minton and Malhotra compared the observed distribution with simulations and found that the belt is more depleted next to the gaps than the present planetary orbits can explain, a pattern consistent with Jupiter and Saturn having migrated.[^minton2009] The same sweeping appears in models of how the early belt lost most of its mass.[^petit2001] ## Asteroid zones A snapshot of asteroid positions at one moment does not show the gaps. Asteroid orbits are ellipses, so bodies with semi-major axes on either side of a gap pass through its radius at every point of their orbits, and the spatial density of asteroids in a gap's distance range is hardly different from that next to it.[^mcbride1990] The gaps appear only when asteroids are sorted by semi-major axis, or equivalently by orbital period. The explorer's empty lanes therefore show where the gaps lie in semi-major axis, a simplification that a real snapshot of positions would not reproduce. The main gaps divide the core of the belt into zones. The inner zone, zone I, runs from the 4:1 resonance at 2.06 AU to the 3:1 gap at 2.5 AU. The middle zone, zone II, runs from there to the 5:2 gap at 2.82 AU, and the outer zone, zone III, continues to the 2:1 gap at 3.28 AU.[^klacka1992] The zones also differ in composition: silicate-rich S types dominate the inner zone, and dark carbonaceous types become more common outward.[^demeo2015] [[4_Vesta|Vesta]] is the largest body in the inner zone, [[Ceres_(dwarf_planet)|Ceres]] and [[2_Pallas|Pallas]] are in the middle zone, and [[10_Hygiea|Hygiea]] is the largest in the outer zone.[^jpl-sbdb] In the explorer these four named bodies can be seen on either side of the lanes, and the lanes' positions can be checked against the table above. ## See also - [[Asteroid_belt]] - [[Hilda_asteroid]] · [[Jupiter_trojan]] - [[Kepler's_laws_of_planetary_motion]] - [[Resonance]] - Alinda group · Cybele group · Griqua group ## References [^fernie1999]: Fernie, J. D. (1999). "The American Kepler". *American Scientist* 87: 398. https://doi.org/10.1511/1999.5.398 [^minton2009]: Minton, D. A.; Malhotra, R. (2009). "A record of planet migration in the main asteroid belt". *Nature* 457: 1109–1111. https://doi.org/10.1038/nature07778 [^jpl-t1]: JPL Solar System Dynamics. "Approximate Positions of the Planets", Table 1. https://ssd.jpl.nasa.gov/planets/approx_pos.html [^moons1995]: Moons, M.; Morbidelli, A. (1995). "Secular resonances in mean motion commensurabilities: the 4/1, 3/1, 5/2, and 7/3 cases". *Icarus* 114: 33–50. https://doi.org/10.1006/icar.1995.1041 [^ferrazmello1994]: Ferraz-Mello, S. (1994). "Kirkwood gaps and resonant groups". In Milani, A.; Di Martino, M.; Cellino, A. (eds.), *Asteroids, Comets, Meteors 1993*, IAU Symposium 160. Kluwer Academic Publishers, pp. 175–188. Bibcode 1994IAUS..160..175F. [^jpl-sbdb]: JPL Solar System Dynamics. "Small-Body Database Lookup" (elements fetched 2026-09-18). https://ssd.jpl.nasa.gov/tools/sbdb_lookup.html [^openstax]: Ling, S. J.; Sanny, J.; Moebs, W. (2016). *University Physics Volume 1*, ch. 13 "Gravitation" (Kepler's laws). OpenStax. https://open.umn.edu/opentextbooks/textbooks/university-physics-volume-1 [^moons1998]: Moons, M.; Morbidelli, A.; Migliorini, F. (1998). "Dynamical structure of the 2/1 commensurability with Jupiter and the origin of the resonant asteroids". *Icarus* 135: 458–468. https://doi.org/10.1006/icar.1998.5963 [^demeo2015]: DeMeo, F. E.; Alexander, C. M. O'D.; Walsh, K. J.; Chapman, C. R.; Binzel, R. P. (2015). "The compositional structure of the asteroid belt". In Michel, P.; DeMeo, F. E.; Bottke, W. F. (eds.), *Asteroids IV*. University of Arizona Press, pp. 13–41. https://doi.org/10.2458/azu_uapress_9780816532131-ch002 [^liou1997]: Liou, J.-C.; Malhotra, R. (1997). "Depletion of the outer asteroid belt". *Science* 275: 375–377. https://doi.org/10.1126/science.275.5298.375 [^petit2001]: Petit, J.-M.; Morbidelli, A.; Chambers, J. (2001). "The primordial excitation and clearing of the asteroid belt". *Icarus* 153: 338–347. https://doi.org/10.1006/icar.2001.6702 [^mcbride1990]: McBride, N.; Hughes, D. W. (1990). "The spatial density of asteroids and its variation with asteroidal mass". *Monthly Notices of the Royal Astronomical Society* 244: 513–520. Bibcode 1990MNRAS.244..513M. [^klacka1992]: Klačka, J. (1992). "Mass distribution in the asteroid belt". *Earth, Moon, and Planets* 56: 47–52. https://doi.org/10.1007/BF00054599 ## External links - IAU Minor Planet Center. "Distribution of the minor planets" (semi-major axis plots showing the gaps). https://www.minorplanetcenter.net/iau/lists/MPDistribution.html - JPL Solar System Dynamics. "Small-Body Database query". https://ssd.jpl.nasa.gov/tools/sbdb_query.html ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Kirkwood_gap) : [Wikitube](https://en.wikitube.io/wiki/Kirkwood_gap) · pinned revision [1372351484](https://en.wikipedia.org/w/index.php?oldid=1372351484) · 2026-09-18 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Solar_System]]. --- *Solar System portal child articles, wave 1 · 2026-09-18 · drafted · row SOL-052 · explorer state `?obj=belt`.*