In celestial mechanics, orbital resonance occurs when orbiting bodies exert regular, periodic gravitational influence on each other, usually because their orbital periods are related by a ratio of small integers. Most commonly, this relationship is found between a pair of objects. The physical principle behind orbital resonance is similar in concept to pushing a child on a swing, whereby the orbit and the swing both have a natural frequency, and the body doing the "pushing" will act in periodic repetition to have a cumulative effect on the motion. Orbital resonances greatly enhance the mutual gravitational influence of the bodies. In most cases, this results in an unstable interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists. Under some circumstances, a resonant system can be self-correcting and thus stable. Examples are the 1:2:4 resonance of Jupiter's moons Ganymede, Europa and Io, and the 2:3 resonance between Neptune and Pluto. Unstable resonances with Saturn's inner moons give rise to gaps in the rings of Saturn. The special case of 1:1 resonance between bodies with similar orbital radii causes large planetary system bodies to eject most other bodies sharing their orbits; this is part of the much more extensive process of clearing the neighbourhood, an effect that is used in the current definition of a planet.
The Jupiter trojans, commonly called trojan asteroids or simply trojans, are a large group of asteroids that share the planet Jupiter's orbit around the Sun. Relative to Jupiter, each trojan librates around one of Jupiter's stable Lagrange points: either L4, existing 60° ahead of the planet in its orbit, or L5, 60° behind. Jupiter trojans are distributed in two elongated, curved regions around these Lagrangian points with an average semi-major axis of about 5.2 AU.
The asteroid belt is a torus-shaped region in the Solar System, centered on the Sun and roughly spanning the space between the orbits of the planets Jupiter and Mars. It contains a great many solid, irregularly shaped bodies called asteroids or minor planets. The identified objects are of many sizes, but much smaller than planets, and, on average, are about one million kilometers apart. This asteroid belt is also called the main asteroid belt or main belt to distinguish it from other asteroid populations in the Solar System.
Commensurability is the property of two orbiting objects, such as planets, satellites, or asteroids, whose orbital periods are in a rational proportion.
The Hungaria asteroids, also known as the Hungaria group, are a dynamical group of asteroids in the asteroid belt which orbit the Sun with a semi-major axis between 1.78 and 2.00 astronomical units (AU). They are the innermost dense concentration of asteroids in the Solar System—the near-Earth asteroids are much more sparse—and derive their name from their largest member 434 Hungaria. The Hungaria group includes the Hungaria family, a collisional asteroid family which dominates its population.
A Hecuba-gap asteroid is a member of a dynamical group of resonant asteroids located in the Hecuba gap at 3.27 AU – one of the largest Kirkwood gaps in the asteroid belt, which is considered the borderline separating the outer main belt asteroids from the Cybeles. A Hecuba-gap asteroid stays in a 2:1 mean motion resonance with the gas giant Jupiter, which may gradually perturbe its orbits over a long period until it either intersect with the orbit of Mars or Jupiter itself. Depending on the dynamical stability of an asteroid's orbit in the Hecuba gap, three subgroups have been proposed. These are the marginally unstable Griqua asteroids, with an estimated lifetime of more than 100 million years, the stable Zhongguo asteroids, and an unnamed, strongly unstable population of asteroids with a dynamical lifetime of less than 70 million years.
11665 Dirichlet, provisional designation 1997 GL28, is a Griqua asteroid and a 2:1 Jupiter librator from the outermost regions of the asteroid belt, approximately 6.8 kilometers (4 miles) in diameter. It was discovered on 14 April 1997, by astronomer Paul Comba at the Prescott Observatory in Arizona, United States. The asteroid was named after German mathematician Peter Gustav Lejeune Dirichlet.
11573 Helmholtz, provisional designation 1993 SK3, is a Zhongguo asteroid from the outermost region of the asteroid belt, approximately 13 kilometers (8 miles) in diameter. It was discovered on 20 September 1993, by German astronomers Freimut Börngen and Lutz Schmadel at the Karl Schwarzschild Observatory in Tautenburg, Germany. It is one of few asteroids located in the 2:1 resonance with Jupiter. The asteroid was named for German physicist Hermann von Helmholtz.
4177 Kohman, provisional designation 1987 SS1, is a resonant Griqua asteroid from the outermost regions of the asteroid belt, approximately 11 kilometers (6.8 miles) in diameter. It was discovered on 21 September 1987, by American astronomer Edward Bowell at the Anderson Mesa Station of the Lowell Observatory near Flagstaff, Arizona, in the United States. The asteroid was named for American nuclear chemist Truman Kohman.
7604 Kridsadaporn, provisional designation 1995 QY2, is an unusual, carbonaceous asteroid and Mars-crosser on a highly eccentric orbit from the outer regions of the asteroid belt, approximately 12 kilometers (7.5 miles) in diameter. It was discovered on 31 August 1995, by Australian astronomer Robert McNaught at Siding Spring Observatory near Coonabarabran, Australia. Due to its particular orbit, the C-type asteroid belongs to MPC's list of "other" unusual objects, and has been classified as an "asteroid in cometary orbit", or ACO. The asteroid was named in memory of Thai astronomer Kridsadaporn Ritsmitchai.
22740 Rayleigh (provisional designation 1998 SX146) is a Zhongguo asteroid from the outermost region of the asteroid belt, approximately 10 kilometers (6 miles) in diameter. It was discovered on 20 September 1998, by Belgian astronomer Eric Elst at the La Silla Observatory in Chile. It is one of few asteroids located in the 2 : 1 resonance with Jupiter. The asteroid was named for English physicist and Nobel laureate Lord Rayleigh.
3789 Zhongguo, provisional designation 1928 UF, is a resonant asteroid from outermost region of the asteroid belt, approximately 14 kilometers in diameter. It was discovered in 1928 by Chinese astronomer Zhang Yuzhe at the Yerkes Observatory in Williams Bay, Wisconsin, in the United States. Originally named "China", the asteroid became lost and its name was transferred to another asteroid. After its re-discovery in 1986, it was named Zhongguo, which is the Chinese word for "China". The T/Xk-type asteroid is the namesake of the resonant Zhongguo group, located in the asteroid belt's Hecuba gap. It has a short rotation period of 3.8 hours.
1922 Zulu, provisional designation 1949 HC, is a carbonaceous asteroid in a strongly unstable resonance with Jupiter, located in the outermost regions of the asteroid belt, and approximately 20 kilometers in diameter. It was discovered on 25 April 1949, by South African astronomer Ernest Johnson at Union Observatory in Johannesburg, and named for the South African Zulu people.
The Nicemodel is a scenario for the dynamical evolution of the Solar System. It is named for the location of the Côte d'Azur Observatory—where it was initially developed in 2005—in Nice, France. It proposes the migration of the giant planets from an initial compact configuration into their present positions, long after the dissipation of the initial protoplanetary disk. In this way, it differs from earlier models of the Solar System's formation. This planetary migration is used in dynamical simulations of the Solar System to explain historical events including the Late Heavy Bombardment of the inner Solar System, the formation of the Oort cloud, and the existence of populations of small Solar System bodies such as the Kuiper belt, the Neptune and Jupiter trojans, and the numerous resonant trans-Neptunian objects dominated by Neptune.
The five-planet Nice model is a numerical model of the early Solar System that is a revised variation of the Nice model. It begins with five giant planets, the four that exist today plus an additional ice giant between Saturn and Uranus in a chain of mean-motion resonances.
The jumping-Jupiter scenario specifies an evolution of giant-planet migration described by the Nice model, in which an ice giant is scattered inward by Saturn and outward by Jupiter, causing their semi-major axes to jump, and thereby quickly separating their orbits. The jumping-Jupiter scenario was proposed by Ramon Brasser, Alessandro Morbidelli, Rodney Gomes, Kleomenis Tsiganis, and Harold Levison after their studies revealed that the smooth divergent migration of Jupiter and Saturn resulted in an inner Solar System significantly different from the current Solar System. During this migration secular resonances swept through the inner Solar System exciting the orbits of the terrestrial planets and the asteroids, leaving the planets' orbits too eccentric, and the asteroid belt with too many high-inclination objects. The jumps in the semi-major axes of Jupiter and Saturn described in the jumping-Jupiter scenario can allow these resonances to quickly cross the inner Solar System without altering orbits excessively, although the terrestrial planets remain sensitive to its passage.
The Nice 2 model is a model of the early evolution of the Solar System. The Nice 2 model resembles the original Nice model in that a late instability of the outer Solar System results in gravitational encounters between planets, the disruption of an outer planetesimal disk, and the migrations of the outer planets to new orbits. However, the Nice 2 model differs in its initial conditions and in the mechanism for triggering the late instability. These changes reflect the analysis of the orbital evolution of the outer Solar System during the gas disk phase and the inclusion of gravitational interactions between planetesimals in the outer disk into the model.
In planetary astronomy, the grand tack hypothesis proposes that Jupiter formed at a distance of 3.5 AU from the Sun, then migrated inward to 1.5 AU, before reversing course due to capturing Saturn in an orbital resonance, eventually halting near its current orbit at 5.2 AU. The reversal of Jupiter's planetary migration is likened to the path of a sailboat changing directions (tacking) as it travels against the wind.
(16882) 1998 BO13 (provisional designation 1998 BO13) is a dark Zhongguo asteroid from the background population in the outermost region of the asteroid belt, approximately 10 kilometers (6 miles) in diameter. It was discovered on 24 January 1998, by astronomers with the Lincoln Near-Earth Asteroid Research at the Lincoln Laboratory's Experimental Test Site near Socorro, New Mexico, in the United States.
