Histogram showing the four most prominent Kirkwood gaps and a possible division into inner, middle and outer main-belt asteroids: inner main-belt (a < 2.5 AU) intermediate main-belt (2.5 AU < a < 2.82 AU) outer main-belt (a > 2.82 AU)A plot of inner solar system asteroids and planets as of 2006 May 9, in a manner that exposes the Kirkwood gaps. Similar to the position plot, planets (with trajectories) are orange, Jupiter being the outer most in this view. Various asteroid classes are colour coded: 'generic' main-belt asteroids are white. Inside the main belt, there are the Atens (red), Apollos (green), and Amors (blue). Outside the main belt are the Hildas (blue) and the Trojans (green). All object position vectors have been normalized to the length of the object's semi-major axis. The Kirkwood gaps are visible in the main belt.
For example, there are very few asteroids with semimajor axis near 2.50 AU, period 3.95 years, which would make three orbits for each orbit of Jupiter (hence, called the 3:1 orbital resonance). Other orbital resonances correspond to orbital periods whose lengths are simple fractions of Jupiter's. The weaker resonances lead only to a depletion of asteroids, while spikes in the histogram are often due to the presence of a prominent asteroid family(see List of asteroid families).
Most of the Kirkwood gaps are depleted, unlike the mean-motion resonances (MMR) of Neptune or Jupiter's 3:2 resonance, that retain objects captured during the giant planet migration of the Nice model. The loss of objects from the Kirkwood gaps is due to the overlapping of the ν5 and ν6secular resonances within the mean-motion resonances. The orbital elements of the asteroids vary chaotically as a result and evolve onto planet-crossing orbits within a few million years.[2] The 2:1 MMR has a few relatively stable islands within the resonance, however. These islands are depleted due to slow diffusion onto less stable orbits. This process, which has been linked to Jupiter and Saturn being near a 5:2 resonance, may have been more rapid when Jupiter's and Saturn's orbits were closer together.[3]
More recently, a relatively small number of asteroids have been found to possess high eccentricity orbits which do lie within the Kirkwood gaps. Examples include the Alinda and Griqua groups. These orbits slowly increase their eccentricity on a timescale of tens of millions of years, and will eventually break out of the resonance due to close encounters with a major planet. This is why asteroids are rarely found in the Kirkwood gaps.
The gaps are not seen in a simple snapshot of the locations of the asteroids at any one time because asteroid orbits are elliptical, and many asteroids still cross through the radii corresponding to the gaps. The actual spatial density of asteroids in these gaps does not differ significantly from the neighboring regions.[5]
The main gaps occur at the 3:1, 5:2, 7:3, and 2:1 mean-motion resonances with Jupiter. An asteroid in the 3:1 Kirkwood gap would orbit the Sun three times for each Jovian orbit, for instance. Weaker resonances occur at other semi-major axis values, with fewer asteroids found than nearby. (For example, an 8:3 resonance for asteroids with a semi-major axis of 2.71 AU).[6]
The main or core population of the asteroid belt may be divided into the inner and outer zones, separated by the 3:1 Kirkwood gap at 2.5 AU, and the outer zone may be further divided into middle and outer zones by the 5:2 gap at 2.82 AU:[7]
4:1 resonance (2.06 AU)
Zone I population (inner zone)
3:1 resonance (2.5 AU)
Zone II population (middle zone)
5:2 resonance gap (2.82 AU)
Zone III population (outer zone)
2:1 resonance gap (3.28 AU)
4 Vesta is the largest asteroid in the inner zone, 1 Ceres and 2 Pallas in the middle zone, and 10 Hygiea in the outer zone. 87 Sylvia is probably the largest Main Belt asteroid beyond the outer zone.
^Coleman, Helen Turnbull Waite (1956). Banners in the Wilderness: The Early Years of Washington and Jefferson College. University of Pittsburgh Press. p. 158. OCLC 2191890.
^Moons, Michèle; Morbidelli, Alessandro; Migliorini, Fabio (1998). "Dynamical Structure of the 2/1 Commensurability with Jupiter and the Origin of the Resonant Asteroids". Icarus. 135 (2): 458–468. Bibcode:1998Icar..135..458M. doi:10.1006/icar.1998.5963.
^Minton, David A.; Malhotra, Renu (2009). "A record of planet migration in the main asteroid belt" (PDF). Nature. 457 (7233): 1109–1111. arXiv:0906.4574. Bibcode:2009Natur.457.1109M. doi:10.1038/nature07778. PMID 19242470. S2CID 2049956. Retrieved 13 December 2016.
^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.
^Ferraz-Mello, S. (June 14–18, 1993). "Kirkwood Gaps and Resonant Groups". proceedings of the 160th International Astronomical Union. Belgirate, Italy: Kluwer Academic Publishers. pp. 175–188. Bibcode:1994IAUS..160..175F.
^Klacka, Jozef (1992). "Mass distribution in the asteroid belt". Earth, Moon, and Planets. 56 (1): 47–52. Bibcode:1992EM&P...56...47K. doi:10.1007/BF00054599. S2CID 123074137.
External linksedit
Wikimedia Commons has media related to Kirkwood gap.
Article on Kirkwood gaps at Wolfram's scienceworld
May 03, 2024
kirkwood, distribution, semi, major, axes, equivalently, orbital, periods, orbits, main, belt, asteroids, they, correspond, locations, orbital, resonances, with, jupiter, histogram, showing, four, most, prominent, possible, division, into, inner, middle, outer. A Kirkwood gap is a gap or dip in the distribution of the semi major axes or equivalently of the orbital periods of the orbits of main belt asteroids They correspond to the locations of orbital resonances with Jupiter Histogram showing the four most prominent Kirkwood gaps and a possible division into inner middle and outer main belt asteroids inner main belt a lt 2 5 AU intermediate main belt 2 5 AU lt a lt 2 82 AU outer main belt a gt 2 82 AU A plot of inner solar system asteroids and planets as of 2006 May 9 in a manner that exposes the Kirkwood gaps Similar to the position plot planets with trajectories are orange Jupiter being the outer most in this view Various asteroid classes are colour coded generic main belt asteroids are white Inside the main belt there are the Atens red Apollos green and Amors blue Outside the main belt are the Hildas blue and the Trojans green All object position vectors have been normalized to the length of the object s semi major axis The Kirkwood gaps are visible in the main belt For example there are very few asteroids with semimajor axis near 2 50 AU period 3 95 years which would make three orbits for each orbit of Jupiter hence called the 3 1 orbital resonance Other orbital resonances correspond to orbital periods whose lengths are simple fractions of Jupiter s The weaker resonances lead only to a depletion of asteroids while spikes in the histogram are often due to the presence of a prominent asteroid family see List of asteroid families The gaps were first noticed in 1866 by Daniel Kirkwood who also correctly explained their origin in the orbital resonances with Jupiter while a professor at Jefferson College in Canonsburg Pennsylvania 1 Most of the Kirkwood gaps are depleted unlike the mean motion resonances MMR of Neptune or Jupiter s 3 2 resonance that retain objects captured during the giant planet migration of the Nice model The loss of objects from the Kirkwood gaps is due to the overlapping of the n5 and n6 secular resonances within the mean motion resonances The orbital elements of the asteroids vary chaotically as a result and evolve onto planet crossing orbits within a few million years 2 The 2 1 MMR has a few relatively stable islands within the resonance however These islands are depleted due to slow diffusion onto less stable orbits This process which has been linked to Jupiter and Saturn being near a 5 2 resonance may have been more rapid when Jupiter s and Saturn s orbits were closer together 3 More recently a relatively small number of asteroids have been found to possess high eccentricity orbits which do lie within the Kirkwood gaps Examples include the Alinda and Griqua groups These orbits slowly increase their eccentricity on a timescale of tens of millions of years and will eventually break out of the resonance due to close encounters with a major planet This is why asteroids are rarely found in the Kirkwood gaps Contents 1 Main gaps 2 Asteroid zones 3 See also 4 References 5 External linksMain gaps editThe most prominent Kirkwood gaps are located at mean orbital radii of 4 1 780 AU 5 1 resonance 2 065 AU 4 1 resonance 2 502 AU 3 1 resonance home to the Alinda group of asteroids 2 825 AU 5 2 resonance 2 958 AU 7 3 resonance 3 279 AU 2 1 resonance Hecuba gap home to the Griqua group of asteroids 3 972 AU 3 2 resonance home to the Hilda asteroids 4 296 AU 4 3 resonance home to the Thule group of asteroids Weaker and or narrower gaps are also found at 1 909 AU 9 2 resonance 2 258 AU 7 2 resonance 2 332 AU 10 3 resonance 2 706 AU 8 3 resonance 3 031 AU 9 4 resonance 3 077 AU 11 5 resonance 3 474 AU 11 6 resonance 3 517 AU 9 5 resonance 3 584 AU 7 4 resonance home to the Cybele asteroids 3 702 AU 5 3 resonance Asteroid zones editThe gaps are not seen in a simple snapshot of the locations of the asteroids at any one time because asteroid orbits are elliptical and many asteroids still cross through the radii corresponding to the gaps The actual spatial density of asteroids in these gaps does not differ significantly from the neighboring regions 5 The main gaps occur at the 3 1 5 2 7 3 and 2 1 mean motion resonances with Jupiter An asteroid in the 3 1 Kirkwood gap would orbit the Sun three times for each Jovian orbit for instance Weaker resonances occur at other semi major axis values with fewer asteroids found than nearby For example an 8 3 resonance for asteroids with a semi major axis of 2 71 AU 6 The main or core population of the asteroid belt may be divided into the inner and outer zones separated by the 3 1 Kirkwood gap at 2 5 AU and the outer zone may be further divided into middle and outer zones by the 5 2 gap at 2 82 AU 7 4 1 resonance 2 06 AU Zone I population inner zone 3 1 resonance 2 5 AU Zone II population middle zone 5 2 resonance gap 2 82 AU Zone III population outer zone 2 1 resonance gap 3 28 AU 4 Vesta is the largest asteroid in the inner zone 1 Ceres and 2 Pallas in the middle zone and 10 Hygiea in the outer zone 87 Sylvia is probably the largest Main Belt asteroid beyond the outer zone See also editOrbital resonance Alinda group Cybele group Griqua groupReferences edit Coleman Helen Turnbull Waite 1956 Banners in the Wilderness The Early Years of Washington and Jefferson College University of Pittsburgh Press p 158 OCLC 2191890 Moons Michele Morbidelli Alessandro 1995 Secular resonances inside mean motion commensurabilities the 4 1 3 1 5 2 and 7 3 cases Icarus 114 1 33 50 Bibcode 1995Icar 114 33M doi 10 1006 icar 1995 1041 Moons Michele Morbidelli Alessandro Migliorini Fabio 1998 Dynamical Structure of the 2 1 Commensurability with Jupiter and the Origin of the Resonant Asteroids Icarus 135 2 458 468 Bibcode 1998Icar 135 458M doi 10 1006 icar 1998 5963 Minton David A Malhotra Renu 2009 A record of planet migration in the main asteroid belt PDF Nature 457 7233 1109 1111 arXiv 0906 4574 Bibcode 2009Natur 457 1109M doi 10 1038 nature07778 PMID 19242470 S2CID 2049956 Retrieved 13 December 2016 McBride N amp 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 Ferraz Mello S June 14 18 1993 Kirkwood Gaps and Resonant Groups proceedings of the 160th International Astronomical Union Belgirate Italy Kluwer Academic Publishers pp 175 188 Bibcode 1994IAUS 160 175F Klacka Jozef 1992 Mass distribution in the asteroid belt Earth Moon and Planets 56 1 47 52 Bibcode 1992EM amp P 56 47K doi 10 1007 BF00054599 S2CID 123074137 External links edit nbsp Wikimedia Commons has media related to Kirkwood gap Article on Kirkwood gaps at Wolfram s scienceworld Retrieved from https en wikipedia org w index php title Kirkwood gap amp oldid 1198106129, wikipedia, wiki, book, books, library,
