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2 Pallas

Pallas (minor-planet designation: 2 Pallas) is the third-largest asteroid in the Solar System by volume and mass. It is the second asteroid to have been discovered, after Ceres, and is a likely remnant protoplanet. Like Ceres, it is believed to have a mineral composition similar to carbonaceous chondrite meteorites, though significantly less hydrated than Ceres. It is 79% the mass of Vesta and 22% the mass of Ceres, constituting an estimated 7% of the mass of the asteroid belt. Its estimated volume is equivalent to a sphere 507 to 515 km in diameter, 90–95% the volume of Vesta.

During the planetary formation era of the Solar System, objects grew in size through an accretion process to approximately the size of Pallas. Most of these protoplanets were incorporated into the growth of larger bodies, which became the planets, whereas others were ejected by the planets or destroyed in collisions with each other. Pallas, Vesta and Ceres appear to be the only intact bodies from this early stage of planetary formation to survive within the orbit of Neptune.

When Pallas was discovered by the German astronomer Heinrich Wilhelm Matthäus Olbers on 28 March 1802, it was considered to be a planet, as were other asteroids in the early 19th century. The discovery of many more asteroids after 1845 eventually led to the separate listing of "minor" planets from "major" planets, and the realization in the 1950s that such small bodies did not form in the same way as (other) planets led to the gradual abandonment of the term "minor planet" in favor of "asteroid" (or, for larger bodies such as Pallas, "planetoid").

With an orbital inclination of 34.8°, Pallas's orbit is unusually highly inclined to the plane of the asteroid belt, making Pallas relatively inaccessible to spacecraft, and its orbital eccentricity is nearly as large as that of Pluto.

The high inclination of the orbit of Pallas results in the possibility of close conjunctions to stars that other solar objects always pass at great angular distance. This resulted in Pallas passing Sirius on 9 October 2022, only 8.5 arcminutes southwards, while no planet can get closer than 30 degrees to Sirius.

Discovery
On the night of 5 April 1779, Charles Messier recorded Pallas on a star chart he used to track the path of a comet, now known as C/1779 A1 (Bode), that he observed in the spring of 1779, but apparently assumed it was nothing more than a star.

In 1801, the astronomer Giuseppe Piazzi discovered an object which he initially believed to be a comet. Shortly thereafter he announced his observations of this object, noting that the slow, uniform motion was uncharacteristic of a comet, suggesting it was a different type of object. This was lost from sight for several months, but was recovered later that year by the Baron von Zach and Heinrich W. M. Olbers after a preliminary orbit was computed by Carl Friedrich Gauss. This object came to be named Ceres, and was the first asteroid to be discovered.

A few months later, Olbers was again attempting to locate Ceres when he noticed another moving object in the vicinity. This was the asteroid Pallas, coincidentally passing near Ceres at the time. The discovery of this object created interest in the astronomy community. Before this point it had been speculated by astronomers that there should be a planet in the gap between Mars and Jupiter. Now, unexpectedly, a second such body had been found. When Pallas was discovered, some estimates of its size were as high as 3,380 km in diameter. Even as recently as 1979, Pallas was estimated to be 673 km in diameter, 26% greater than the currently accepted value.

The orbit of Pallas was determined by Gauss, who found the period of 4.6 years was similar to the period for Ceres. Pallas has a relatively high orbital inclination to the plane of the ecliptic.

Later observations
In 1917, the Japanese astronomer Kiyotsugu Hirayama began to study asteroid motions. By plotting the mean orbital motion, inclination, and eccentricity of a set of asteroids, he discovered several distinct groupings. In a later paper he reported a group of three asteroids associated with Pallas, which became named the Pallas family, after the largest member of the group. Since 1994 more than 10 members of this family have been identified, with semi-major axes between 2.50 and 2.82 AU and inclinations of 33–38°. The validity of the family was confirmed in 2002 by a comparison of their spectra.

Pallas has been observed occulting stars several times, including the best-observed of all asteroid occultation events, by 140 observers on 29 May 1983. These measurements resulted in the first accurate calculation of its diameter. After an occultation on 29 May 1979, the discovery of a possible tiny satellite with a diameter of about 1 km was reported, which was never confirmed.

Radio signals from spacecraft in orbit around Mars and/or on its surface have been used to estimate the mass of Pallas from the tiny perturbations induced by it onto the motion of Mars.

The Dawn team was granted viewing time on the Hubble Space Telescope in September 2007 for a once-in-twenty-year opportunity to view Pallas at closest approach, to obtain comparative data for Ceres and Vesta.

Name and symbol

Pallas is an epithet of the Greek goddess Athena (Παλλάς Ἀθηνᾶ). In some versions of the myth, Athena killed Pallas, daughter of Triton, then adopted her friend's name out of mourning.

The adjectival form of the name is Palladian. The d is part of the oblique stem of the Greek name, which appears before a vowel but disappears before the nominative ending -s. The oblique form is seen in the Italian and Russian names for the asteroid, Pallade and Паллада. The stony-iron pallasite meteorites are not Palladian, being named instead after the German naturalist Peter Simon Pallas. The chemical element palladium, on the other hand, was named after the asteroid, which had been discovered just before the element.

The old astronomical symbol of Pallas, still used in astrology, is a spear or lance, $0.23$, one of the symbols of the goddess. The blade was most often a lozenge (◊), but various graphic variants were published, including an acute/elliptic leaf shape, a cordate leaf shape (♤: ), and a triangle (△); the last made it effectively the alchemical symbol for sulfur, $34.93 °$. The generic asteroid symbol of a disk with its discovery number, $172.9 °$, was introduced in 1852 and quickly became the norm. The iconic lozenge symbol was resurrected for astrological use in 1973.

Orbit and rotation
Pallas has unusual dynamic parameters for such a large body. Its orbit is highly inclined and moderately eccentric, despite being at the same distance from the Sun as the central part of the asteroid belt. Furthermore, Pallas has a very high axial tilt of 84°, with its north pole pointing towards ecliptic coordinates (β, λ) = (30°, −16°) with a 5° uncertainty in the Ecliptic J2000.0 reference frame. This means that every Palladian summer and winter, large parts of the surface are in constant sunlight or constant darkness for a time on the order of an Earth year, with areas near the poles experiencing continuous sunlight for as long as two years.

Near resonances
Pallas is in a near-1:1 orbital resonance with Ceres, which is probably coincidental. Pallas also has a near-18:7 resonance (91,000-year period) and an approximate 5:2 resonance (83-year period) with Jupiter.

Transits of planets from Pallas
From Pallas, the planets Mercury, Venus, Mars, and Earth can occasionally appear to transit, or pass in front of, the Sun. Earth last did so in 1968 and 1998, and will next transit in 2224. Mercury did in October 2009. The last and next by Venus are in 1677 and 2123, and for Mars they are in 1597 and 2759.

Physical characteristics

Both Vesta and Pallas have assumed the title of second-largest asteroid from time to time. At $310.9 °$ in diameter, Pallas is slightly smaller than Vesta ($2.771$ ). The mass of Pallas is $0.281$ that of Vesta, $33.199 °$ that of Ceres, and a quarter of one percent that of the Moon.

Pallas is farther from Earth and has a much lower albedo than Vesta, and hence is dimmer as seen from Earth. Indeed, the much smaller asteroid 7 Iris marginally exceeds Pallas in mean opposition magnitude. Pallas's mean opposition magnitude is +8.0, which is well within the range of 10×50 binoculars, but, unlike Ceres and Vesta, it will require more-powerful optical aid to view at small elongations, when its magnitude can drop as low as +10.6. During rare perihelic oppositions, Pallas can reach a magnitude of +6.4, right on the edge of naked-eye visibility. During late February 2014 Pallas shone with magnitude 6.96.

Pallas is a B-type asteroid. Based on spectroscopic observations, the primary component of the material on Pallas's surface is a silicate containing little iron and water. Minerals of this type include olivine and pyroxene, which are found in CM chondrules. The surface composition of Pallas is very similar to the Renazzo carbonaceous chondrite (CR) meteorites, which are even lower in hydrous minerals than the CM type. The Renazzo meteorite was discovered in Italy in 1824 and is one of the most primitive meteorites known. Pallas's visible and near-infrared spectrum is almost flat, being slightly brighter in towards the blue. There is only one clear absorption band in the 3-micron part, which suggests an anhydrous component mixed with hydrated CM-like silicates.

Pallas's surface is most likely composed of a silicate material; its spectrum and calculated density ($0.79$) correspond to CM chondrite meteorites ($568 km$), suggesting a mineral composition similar to that of Ceres, but significantly less hydrated.

To within observational limits, Pallas appears to be saturated with craters. Its high inclination and eccentricity means that average impacts are much more energetic than on Vesta or Ceres (with on average twice their velocity), meaning that smaller (and thus more common) impactors can create equivalently sized craters. Indeed, Pallas appears to have many more large craters than either Vesta or Ceres, with craters larger than 40 km covering at least 9% of its surface.

Pallas's shape departs significantly from the dimensions of an equilibrium body at its current rotational period, indicating that it is not a dwarf planet. It's possible that a suspected large impact basin at the south pole, which ejected $550 km$ of the volume of Pallas (twice the volume of the Rheasilvia basin on Vesta), may have increased its inclination and slowed its rotation; the shape of Pallas without such a basin would be close to an equilibrium shape for a 6.2-hour rotational period. A smaller crater near the equator is associated with the Palladian family of asteroids.

Pallas probably has a quite homogeneous interior. The close match between Pallas and CM chondrites suggests that they formed in the same era and that the interior of Pallas never reached the temperature (≈820 K) needed to dehydrate silicates, which would be necessary to differentiate a dry silicate core beneath a hydrated mantle. Thus Pallas should be rather homogeneous in composition, though some upward flow of water could have occurred since. Such a migration of water to the surface would have left salt deposits, potentially explaining Pallas's relatively high albedo. Indeed, one bright spot is reminiscent of those found on Ceres. Although other explanations for the bright spot are possible (e.g. a recent ejecta blanket), if the near-Earth asteroid 3200 Phaethon is an ejected piece of Pallas, as some have theorized, then a Palladian surface enriched in salts would explain the sodium abundance in the Geminid meteor shower caused by Phaethon.

Surface features
Besides one bright spot in the southern hemisphere, the only surface features identified on Pallas are craters. As of 2020, 36 craters have been identified, 34 of which are larger than 40 km in diameter. Provisional names have been provided for some of them. The craters are named after ancient weapons.

Satellites
A small moon about 1 kilometer in diameter was suggested based on occultation data from 29 May 1978. In 1980, speckle interferometry suggested a much larger satellite, whose existence was later refuted a few years later with occultation data.

Exploration
Pallas itself has never been visited by spacecraft. Proposals have been made in the past though none have come to fruition. A flyby of the Dawn probe's visits to 4 Vesta and 1 Ceres was discussed but was not possible due to the high orbital inclination of Pallas. The proposed Athena SmallSat mission would have been launched in 2022 as a secondary payload of the Psyche mission and travel on separate trajectory to a flyby encounter with 2 Pallas, though was not funded due to being outcompeted by other mission concepts such as the TransOrbital Trailblazer Lunar Orbiter. The authors of the proposal cited Pallas as the "largest unexplored" protoplanet with the main belt.

title: 2 Pallas


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243 Ida

Ida, minor planet designation 243 Ida, is an asteroid in the Koronis family of the asteroid belt. It was discovered on 29 September 1884 by Austrian astronomer Johann Palisa at Vienna Observatory and named after a nymph from Greek mythology. Later telescopic observations categorized Ida as an S-type asteroid, the most numerous type in the inner asteroid belt. On 28 August 1993, Ida was visited by the uncrewed Galileo spacecraft while en route to Jupiter. It was the second asteroid visited by a spacecraft and the first found to have a natural satellite.

Ida's orbit lies between the planets Mars and Jupiter, like all main-belt asteroids. Its orbital period is 4.84 years, and its rotation period is 4.63 hours. Ida has an average diameter of 31.4 km. It is irregularly shaped and elongated, apparently composed of two large objects connected together. Its surface is one of the most heavily cratered in the Solar System, featuring a wide variety of crater sizes and ages.

Ida's moon Dactyl was discovered by mission member Ann Harch in images returned from Galileo. It was named after the Dactyls, creatures which inhabited Mount Ida in Greek mythology. Dactyl is only 1.4 km in diameter, about 1/20 the size of Ida. Its orbit around Ida could not be determined with much accuracy, but the constraints of possible orbits allowed a rough determination of Ida's density and revealed that it is depleted of metallic minerals. Dactyl and Ida share many characteristics, suggesting a common origin.

The images returned from Galileo and the subsequent measurement of Ida's mass provided new insights into the geology of S-type asteroids. Before the Galileo flyby, many different theories had been proposed to explain their mineral composition. Determining their composition permits a correlation between meteorites falling to the Earth and their origin in the asteroid belt. Data returned from the flyby pointed to S-type asteroids as the source for the ordinary chondrite meteorites, the most common type found on the Earth's surface.

Discovery and observations
Ida was discovered on 29 September 1884 by Austrian astronomer Johann Palisa at the Vienna Observatory. It was his 45th asteroid discovery. Ida was named by Moriz von Kuffner, a Viennese brewer and amateur astronomer. In Greek mythology, Ida was a nymph of Crete who raised the god Zeus. Ida was recognized as a member of the Koronis family by Kiyotsugu Hirayama, who proposed in 1918 that the group comprised the remnants of a destroyed precursor body.

Ida's reflection spectrum was measured on 16 September 1980 by astronomers David J. Tholen and Edward F. Tedesco as part of the eight-color asteroid survey (ECAS). Its spectrum matched those of the asteroids in the S-type classification. Many observations of Ida were made in early 1993 by the US Naval Observatory in Flagstaff and the Oak Ridge Observatory. These improved the measurement of Ida's orbit around the Sun and reduced the uncertainty of its position during the Galileo flyby from 78 to 60 km.

Galileo flyby
Ida was visited in 1993 by the Jupiter-bound space probe Galileo. Its encounters of the asteroids Gaspra and Ida were secondary to the Jupiter mission. These were selected as targets in response to a new NASA policy directing mission planners to consider asteroid flybys for all spacecraft crossing the belt. No prior missions had attempted such a flyby. Galileo was launched into orbit by the Space Shuttle Atlantis mission STS-34 on 18 October 1989. Changing Galileo's trajectory to approach Ida required that it consume 34 kg of propellant. Mission planners delayed the decision to attempt a flyby until they were certain that this would leave the spacecraft enough propellant to complete its Jupiter mission.

Galileo's trajectory carried it into the asteroid belt twice on its way to Jupiter. During its second crossing, it flew by Ida on 28 August 1993 at a speed of 12400 m/s relative to the asteroid. The onboard imager observed Ida from a distance of 240350 km to its closest approach of 2390 km. Ida was the second asteroid, after Gaspra, to be imaged by a spacecraft. About 95% of Ida's surface came into view of the probe during the flyby.

Transmission of many Ida images was delayed due to a permanent failure in the spacecraft's high-gain antenna. The first five images were received in September 1993. These comprised a high-resolution mosaic of the asteroid at a resolution of 31–38 m/pixel. The remaining images were sent in February 1994, when the spacecraft's proximity to the Earth allowed higher speed transmissions.

Discoveries
The data returned from the Galileo flybys of Gaspra and Ida, and the later NEAR Shoemaker asteroid mission, permitted the first study of asteroid geology. Ida's relatively large surface exhibited a diverse range of geological features. The discovery of Ida's moon Dactyl, the first confirmed satellite of an asteroid, provided additional insights into Ida's composition.

Ida is classified as an S-type asteroid based on ground-based spectroscopic measurements. The composition of S-types was uncertain before the Galileo flybys, but was interpreted to be either of two minerals found in meteorites that had fallen to the Earth: ordinary chondrite (OC) and stony-iron. Estimates of Ida's density are constrained to less than 3.2 g/cm3 by the long-term stability of Dactyl's orbit. This all but rules out a stony-iron composition; were Ida made of 5 g/cm3 iron- and nickel-rich material, it would have to contain more than 40% empty space.

The Galileo images also led to the discovery that space weathering was taking place on Ida, a process which causes older regions to become more red in color over time. The same process affects both Ida and its moon, although Dactyl shows a lesser change. The weathering of Ida's surface revealed another detail about its composition: the reflection spectra of freshly exposed parts of the surface resembled that of OC meteorites, but the older regions matched the spectra of S-type asteroids. Both of these discoveries—the space weathering effects and the low density—led to a new understanding about the relationship between S-type asteroids and OC meteorites. S-types are the most numerous kind of asteroid in the inner part of the asteroid belt. OC meteorites are, likewise, the most common type of meteorite found on the Earth's surface. The reflection spectra measured by remote observations of S-type asteroids, however, did not match that of OC meteorites. The Galileo flyby of Ida found that some S-types, particularly the Koronis family, could be the source of these meteorites.

Physical characteristics
Ida's mass is between 3.65 and 4.99 × 1016 kg. Its gravitational field produces an acceleration of about 0.3 to 1.1 cm/s2 over its surface. This field is so weak that an astronaut standing on its surface could leap from one end of Ida to the other, and an object moving in excess of 20 m/s could escape the asteroid entirely.

Ida is a distinctly elongated asteroid, with an irregular surface. Ida is 2.35 times as long as it is wide, and a "waist" separates it into two geologically dissimilar halves. This constricted shape is consistent with Ida being made of two large, solid components, with loose debris filling the gap between them. However, no such debris was seen in high-resolution images captured by Galileo. Although there are a few steep slopes tilting up to about 50° on Ida, the slope generally does not exceed 35°. Ida's irregular shape is responsible for the asteroid's very uneven gravitational field. The surface acceleration is lowest at the extremities because of their high rotational speed. It is also low near the "waist" because the mass of the asteroid is concentrated in the two halves, away from this location.

Surface features
Ida's surface appears heavily cratered and mostly gray, although minor color variations mark newly formed or uncovered areas. Besides craters, other features are evident, such as grooves, ridges, and protrusions. Ida is covered by a thick layer of regolith, loose debris that obscures the solid rock beneath. The largest, boulder-sized, debris fragments are called ejecta blocks, several of which have been observed on the surface.

Regolith
The surface of Ida is covered in a blanket of pulverized rock, called regolith, about 50 - 100 m thick. This material is produced in impact events and redistributed across Ida's surface by geological processes. Galileo observed evidence of recent downslope regolith movement.

Ida's regolith is composed of the silicate minerals olivine and pyroxene. Its appearance changes over time through a process called space weathering. Because of this process, older regolith appears more red in color compared to freshly exposed material.

About 20 large (40–150 m across) ejecta blocks have been identified, embedded in Ida's regolith. Ejecta blocks constitute the largest pieces of the regolith. Because ejecta blocks are expected to break down quickly by impact events, those present on the surface must have been either formed recently or uncovered by an impact event. Most of them are located within the craters Lascaux and Mammoth, but they may not have been produced there. This area attracts debris due to Ida's irregular gravitational field. Some blocks may have been ejected from the young crater Azzurra on the opposite side of the asteroid.

Structures
Several major structures mark Ida's surface. The asteroid appears to be split into two halves, here referred to as region 1 and region 2, connected by a "waist". This feature may have been filled in by debris, or blasted out of the asteroid by impacts.

Region 1 of Ida contains two major structures. One is a prominent 40 km ridge named Townsend Dorsum that stretches 150 degrees around Ida's surface. The other structure is a large indentation named Vienna Regio.

Ida's region 2 features several sets of grooves, most of which are 100 m wide or less and up to 4 km long. They are located near, but are not connected with, the craters Mammoth, Lascaux, and Kartchner. Some grooves are related to major impact events, for example a set opposite Vienna Regio.

Craters
Ida is one of the most densely cratered bodies yet explored in the Solar System, and impacts have been the primary process shaping its surface. Cratering has reached the saturation point, meaning that new impacts erase evidence of old ones, leaving the total crater count roughly the same. It is covered with craters of all sizes and stages of degradation, and ranging in age from fresh to as old as Ida itself. The oldest may have been formed during the breakup of the Koronis family parent body. The largest crater, Lascaux, is almost 12 km across. Region 2 contains nearly all of the craters larger than 6 km in diameter, but Region 1 has no large craters at all. Some craters are arranged in chains. Ida's major craters are named after caves and lava tubes on Earth. The crater Azzurra, for example, is named after a submerged cave on the island of Capri, also known as the Blue Grotto. Azzurra seems to be the most recent major impact on Ida. The ejecta from this collision is distributed discontinuously over Ida and is responsible for the large-scale color and albedo variations across its surface. An exception to the crater morphology is the fresh, asymmetric Fingal, which has a sharp boundary between the floor and wall on one side. Another significant crater is Afon, which marks Ida's prime meridian.

The craters are simple in structure: bowl-shaped with no flat bottoms and no central peaks. They are distributed evenly around Ida, except for a protrusion north of crater Choukoutien which is smoother and less cratered. The ejecta excavated by impacts is deposited differently on Ida than on planets because of its rapid rotation, low gravity and irregular shape. Ejecta blankets settle asymmetrically around their craters, but fast-moving ejecta that escapes from the asteroid is permanently lost.

Composition
Ida was classified as an S-type asteroid based on the similarity of its reflectance spectra with similar asteroids. S-types may share their composition with stony-iron or ordinary chondrite (OC) meteorites. The composition of the interior has not been directly analyzed, but is assumed to be similar to OC material based on observed surface color changes and Ida's bulk density of 2.27–3.10 g/cm3. OC meteorites contain varying amounts of the silicates olivine and pyroxene, iron, and feldspar. Olivine and pyroxene were detected on Ida by Galileo. The mineral content appears to be homogeneous throughout its extent. Galileo found minimal variations on the surface, and the asteroid's spin indicates a consistent density. Assuming that its composition is similar to OC meteorites, which range in density from 3.48 to 3.64 g/cm3, Ida would have a porosity of 11–42%.

Ida's interior probably contains some amount of impact-fractured rock, called megaregolith. The megaregolith layer of Ida extends between hundreds of meters below the surface to a few kilometers. Some rock in Ida's core may have been fractured below the large craters Mammoth, Lascaux, and Undara.

Orbit and rotation
Ida is a member of the Koronis family of asteroid-belt asteroids. Ida orbits the Sun at an average distance of 2.862 AU, between the orbits of Mars and Jupiter. Ida takes 4.84089 years to complete one orbit.

Ida's rotation period is 4.63 hours (roughly 5 hours), making it one of the fastest rotating asteroids yet discovered. The calculated maximum moment of inertia of a uniformly dense object the same shape as Ida coincides with the spin axis of the asteroid. This suggests that there are no major variations of density within the asteroid. Ida's axis of rotation precesses with a period of 77 thousand years, due to the gravity of the Sun acting upon the nonspherical shape of the asteroid.

Origin
Ida originated in the breakup of the roughly 120 km diameter Koronis parent body. The progenitor asteroid had partially differentiated, with heavier metals migrating to the core. Ida carried away insignificant amounts of this core material. It is uncertain how long ago the disruption event occurred. According to an analysis of Ida's cratering processes, its surface is more than a billion years old. However, this is inconsistent with the estimated age of the Ida–Dactyl system of less than 100 million years; it is unlikely that Dactyl, due to its small size, could have escaped being destroyed in a major collision for longer. The difference in age estimates may be explained by an increased rate of cratering from the debris of the Koronis parent body's destruction.

Dactyl
Ida has a moon named Dactyl, official designation (243) Ida I Dactyl. It was discovered in images taken by the Galileo spacecraft during its flyby in 1993. These images provided the first direct confirmation of an asteroid moon. At the time, it was separated from Ida by a distance of 90 km, moving in a prograde orbit. Dactyl is heavily cratered, like Ida, and consists of similar materials. Its origin is uncertain, but evidence from the flyby suggests that it originated as a fragment of the Koronis parent body.

Discovery
Dactyl was found on 17 February 1994 by Galileo mission member Ann Harch, while examining delayed image downloads from the spacecraft. Galileo recorded 47 images of Dactyl over an observation period of 5.5 hours in August 1993. The spacecraft was 10760 km from Ida and 10870 km from Dactyl when the first image of the moon was captured, 14 minutes before Galileo made its closest approach.

Dactyl was initially designated 1993 (243) 1. It was named by the International Astronomical Union in 1994, for the mythological dactyls who inhabited Mount Ida on the island of Crete.

Physical characteristics
Dactyl is an "egg-shaped" but "remarkably spherical" object measuring 1.6 by 1.4 by 1.2 km. It is oriented with its longest axis pointing towards Ida. Like Ida, Dactyl's surface exhibits saturation cratering. It is marked by more than a dozen craters with a diameter greater than 80 m, indicating that the moon has suffered many collisions during its history. At least six craters form a linear chain, suggesting that it was caused by locally produced debris, possibly ejected from Ida. Dactyl's craters may contain central peaks, unlike those found on Ida. These features, and Dactyl's spheroidal shape, imply that the moon is gravitationally controlled despite its small size. Like Ida, its average temperature is about 200 K.

Dactyl shares many characteristics with Ida. Their albedos and reflection spectra are very similar. The small differences indicate that the space weathering process is less active on Dactyl. Its small size would make the formation of significant amounts of regolith impossible. This contrasts with Ida, which is covered by a deep layer of regolith.

The two largest imaged craters on Dactyl were named Acmon and Celmis, after two of the mythological dactyls. Acmon is the largest crater in the above image, and Celmis is near the bottom of the image, mostly obscured in shadow. The craters are 300 and 200 meters in diameter, respectively.

Orbit
Dactyl's orbit around Ida is not precisely known. Galileo was in the plane of Dactyl's orbit when most of the images were taken, which made determining its exact orbit difficult. Dactyl orbits in the prograde direction and is inclined about 8° to Ida's equator. Based on computer simulations, Dactyl's pericenter must be more than about 65 km from Ida for it to remain in a stable orbit. The range of orbits generated by the simulations was narrowed down by the necessity of having the orbits pass through points at which Galileo observed Dactyl to be at 16:52:05 UT on 28 August 1993, about 90 km from Ida at longitude 85°. On 26 April 1994, the Hubble Space Telescope observed Ida for eight hours and was unable to spot Dactyl. It would have been able to observe it if it were more than about 700 km from Ida.

If in a circular orbit at the distance at which it was seen, Dactyl's orbital period would be about 20 hours. Its orbital speed is roughly 10 m/s, "about the speed of a fast run or a slowly thrown baseball".

Age and origin
Dactyl may have originated at the same time as Ida, from the disruption of the Koronis parent body. However, it may have formed more recently, perhaps as ejecta from a large impact on Ida. It is extremely unlikely that it was captured by Ida. Dactyl may have suffered a major impact around 100 million years ago, which reduced its size.

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license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: 243 Ida


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Asteroid belt

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 (or six hundred thousand miles) 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.

The asteroid belt is the smallest and innermost known circumstellar disc in the Solar System. Classes of small Solar System bodies in other regions are the near-Earth objects, the centaurs, the Kuiper belt objects, the scattered disc objects, the sednoids, and the Oort cloud objects. About 60% of the main belt mass is contained in the four largest asteroids: Ceres, Vesta, Pallas, and Hygiea. The total mass of the asteroid belt is estimated to be 3% that of the Moon.

Ceres, the only object in the asteroid belt large enough to be a dwarf planet, is about 950 km in diameter, whereas Vesta, Pallas, and Hygiea have mean diameters less than 600 km. The remaining mineralogically classified bodies range in size down to a few metres. The asteroid material is so thinly distributed that numerous uncrewed spacecraft have traversed it without incident. Nonetheless, collisions between large asteroids occur and can produce an asteroid family, whose members have similar orbital characteristics and compositions. Individual asteroids within the belt are categorized by their spectra, with most falling into three basic groups: carbonaceous (C-type), silicate (S-type), and metal-rich (M-type).

The asteroid belt formed from the primordial solar nebula as a group of planetesimals, the smaller precursors of the protoplanets. However, between Mars and Jupiter gravitational perturbations from Jupiter disrupted their accretion into a planet, imparting excess kinetic energy which shattered colliding planetesimals and most of the incipient protoplanets. As a result, 99.9% of the asteroid belt's original mass was lost in the first 100 million years of the Solar System's history. Some fragments eventually found their way into the inner Solar System, leading to meteorite impacts with the inner planets. Asteroid orbits continue to be appreciably perturbed whenever their period of revolution about the Sun forms an orbital resonance with Jupiter. At these orbital distances, a Kirkwood gap occurs as they are swept into other orbits.

History of observation

In 1596, Johannes Kepler wrote, "Between Mars and Jupiter, I place a planet," in his Mysterium Cosmographicum, stating his prediction that a planet would be found there. While analyzing Tycho Brahe's data, Kepler thought that too large a gap existed between the orbits of Mars and Jupiter to fit Kepler's then-current model of where planetary orbits should be found.

In an anonymous footnote to his 1766 translation of Charles Bonnet's Contemplation de la Nature, the astronomer Johann Daniel Titius of Wittenberg noted an apparent pattern in the layout of the planets, now known as the Titius-Bode Law. If one began a numerical sequence at 0, then included 3, 6, 12, 24, 48, etc., doubling each time, and added four to each number and divided by 10, this produced a remarkably close approximation to the radii of the orbits of the known planets as measured in astronomical units, provided one allowed for a "missing planet" (equivalent to 24 in the sequence) between the orbits of Mars (12) and Jupiter (48). In his footnote, Titius declared, "But should the Lord Architect have left that space empty? Not at all." When William Herschel discovered Uranus in 1781, the planet's orbit closely matched the law, leading some astronomers to conclude that a planet had to be between the orbits of Mars and Jupiter.

On January 1, 1801, Giuseppe Piazzi, chairman of astronomy at the University of Palermo, Sicily, found a tiny moving object in an orbit with exactly the radius predicted by this pattern. He dubbed it "Ceres", after the Roman goddess of the harvest and patron of Sicily. Piazzi initially believed it to be a comet, but its lack of a coma suggested it was a planet. Thus, the aforementioned pattern predicted the semimajor axes of all eight planets of the time (Mercury, Venus, Earth, Mars, Ceres, Jupiter, Saturn, and Uranus). Concurrent with the discovery of Ceres, an informal group of 24 astronomers dubbed the "celestial police" was formed under the invitation of Franz Xaver von Zach with the express purpose of finding additional planets; they focused their search for them in the region between Mars and Jupiter where the Titius–Bode law predicted there should be a planet.

About 15 months later, Heinrich Olbers, a member of the celestial police, discovered a second object in the same region, Pallas. Unlike the other known planets, Ceres and Pallas remained points of light even under the highest telescope magnifications instead of resolving into discs. Apart from their rapid movement, they appeared indistinguishable from stars.

Accordingly, in 1802, William Herschel suggested they be placed into a separate category, named "asteroids", after the Greek asteroeides, meaning "star-like". Upon completing a series of observations of Ceres and Pallas, he concluded, Neither the appellation of planets nor that of comets can with any propriety of language be given to these two stars ... They resemble small stars so much as hardly to be distinguished from them. From this, their asteroidal appearance, if I take my name, and call them Asteroids; reserving for myself, however, the liberty of changing that name, if another, more expressive of their nature, should occur.

By 1807, further investigation revealed two new objects in the region: Juno and Vesta. The burning of Lilienthal in the Napoleonic wars, where the main body of work had been done, brought this first period of discovery to a close.

Despite Herschel's coinage, for several decades it remained common practice to refer to these objects as planets and to prefix their names with numbers representing their sequence of discovery: 1 Ceres, 2 Pallas, 3 Juno, 4 Vesta. In 1845, though, the astronomer Karl Ludwig Hencke detected a fifth object (5 Astraea) and, shortly thereafter, new objects were found at an accelerating rate. Counting them among the planets became increasingly cumbersome. Eventually, they were dropped from the planet list (as first suggested by Alexander von Humboldt in the early 1850s) and Herschel's coinage, "asteroids", gradually came into common use.

The discovery of Neptune in 1846 led to the discrediting of the Titius–Bode law in the eyes of scientists because its orbit was nowhere near the predicted position. To date, no scientific explanation for the law has been given, and astronomers' consensus regards it as a coincidence.

The expression "asteroid belt" came into use in the early 1850s, although pinpointing who coined the term is difficult. The first English use seems to be in the 1850 translation (by Elise Otté) of Alexander von Humboldt's Cosmos: "[...] and the regular appearance, about the 13th of November and the 11th of August, of shooting stars, which probably form part of a belt of asteroids intersecting the Earth's orbit and moving with planetary velocity". Another early appearance occurred in Robert James Mann's A Guide to the Knowledge of the Heavens: "The orbits of the asteroids are placed in a wide belt of space, extending between the extremes of [...]". The American astronomer Benjamin Peirce seems to have adopted that terminology and to have been one of its promoters.

Over 100 asteroids had been located by mid-1868, and in 1891, the introduction of astrophotography by Max Wolf accelerated the rate of discovery. A total of 1,000 asteroids had been found by 1921, 10,000 by 1981, and 100,000 by 2000. Modern asteroid survey systems now use automated means to locate new minor planets in ever-increasing numbers.

On 22 January 2014, European Space Agency (ESA) scientists reported the detection, for the first definitive time, of water vapor on Ceres, the largest object in the asteroid belt. The detection was made by using the far-infrared abilities of the Herschel Space Observatory. The finding was unexpected because comets, not asteroids, are typically considered to "sprout jets and plumes". According to one of the scientists, "The lines are becoming more and more blurred between comets and asteroids".

Formation
In 1802, shortly after discovering Pallas, Olbers suggested to Herschel and Carl Gauss that Ceres and Pallas were fragments of a much larger planet that once occupied the Mars–Jupiter region, with this planet having suffered an internal explosion or a cometary impact many million years before, while Odesan astronomer K. N. Savchenko suggested that Ceres, Pallas, Juno, and Vesta were escaped moons rather than fragments of the exploded planet. The large amount of energy required to destroy a planet, combined with the belt's low combined mass, which is only about 4% of the mass of Earth's Moon, does not support these hypotheses. Further, the significant chemical differences between the asteroids become difficult to explain if they come from the same planet.

A modern hypothesis for the asteroid belt's creation relates to how, in general for the Solar System, planetary formation is thought to have occurred via a process comparable to the long-standing nebular hypothesis; a cloud of interstellar dust and gas collapsed under the influence of gravity to form a rotating disc of material that then conglomerated to form the Sun and planets. During the first few million years of the Solar System's history, an accretion process of sticky collisions caused the clumping of small particles, which gradually increased in size. Once the clumps reached sufficient mass, they could draw in other bodies through gravitational attraction and become planetesimals. This gravitational accretion led to the formation of the planets.

Planetesimals within the region that would become the asteroid belt were strongly perturbed by Jupiter's gravity. Orbital resonances occurred where the orbital period of an object in the belt formed an integer fraction of the orbital period of Jupiter, perturbing the object into a different orbit; the region lying between the orbits of Mars and Jupiter contains many such orbital resonances. As Jupiter migrated inward following its formation, these resonances would have swept across the asteroid belt, dynamically exciting the region's population and increasing their velocities relative to each other. In regions where the average velocity of the collisions was too high, the shattering of planetesimals tended to dominate over accretion, preventing the formation of a planet. Instead, they continued to orbit the Sun as before, occasionally colliding.

During the early history of the Solar System, the asteroids melted to some degree, allowing elements within them to be differentiated by mass. Some of the progenitor bodies may even have undergone periods of explosive volcanism and formed magma oceans. Because of the relatively small size of the bodies, though, the period of melting was necessarily brief compared to the much larger planets, and had generally ended about 4.5 billion years ago, in the first tens of millions of years of formation. In August 2007, a study of zircon crystals in an Antarctic meteorite believed to have originated from Vesta suggested that it, and by extension the rest of the asteroid belt, had formed rather quickly, within 10 million years of the Solar System's origin.

Evolution
The asteroids are not pristine samples of the primordial Solar System. They have undergone considerable evolution since their formation, including internal heating (in the first few tens of millions of years), surface melting from impacts, space weathering from radiation, and bombardment by micrometeorites. Although some scientists refer to the asteroids as residual planetesimals, other scientists consider them distinct.

The current asteroid belt is believed to contain only a small fraction of the mass of the primordial belt. Computer simulations suggest that the original asteroid belt may have contained mass equivalent to the Earth's. Primarily because of gravitational perturbations, most of the material was ejected from the belt within about 1 million years of formation, leaving behind less than 0.1% of the original mass. Since its formation, the size distribution of the asteroid belt has remained relatively stable; no significant increase or decrease in the typical dimensions of the main-belt asteroids has occurred.

The 4:1 orbital resonance with Jupiter, at a radius 2.06 astronomical units (AUs), can be considered the inner boundary of the asteroid belt. Perturbations by Jupiter send bodies straying there into unstable orbits. Most bodies formed within the radius of this gap were swept up by Mars (which has an aphelion at 1.67 AU) or ejected by its gravitational perturbations in the early history of the Solar System. The Hungaria asteroids lie closer to the Sun than the 4:1 resonance, but are protected from disruption by their high inclination.

When the asteroid belt was first formed, the temperatures at a distance of 2.7 AU from the Sun formed a "snow line" below the freezing point of water. Planetesimals formed beyond this radius were able to accumulate ice. In 2006, a population of comets had been discovered within the asteroid belt beyond the snow line, which may have provided a source of water for Earth's oceans. According to some models, outgassing of water during the Earth's formative period was insufficient to form the oceans, requiring an external source such as a cometary bombardment.

The outer asteroid belt appears to include a few objects that may have arrived there during the last few hundred years, the list includes also known as 362P.

Characteristics
Contrary to popular imagery, the asteroid belt is mostly empty. The asteroids are spread over such a large volume that reaching an asteroid without aiming carefully would be improbable. Nonetheless, hundreds of thousands of asteroids are currently known, and the total number ranges in the millions or more, depending on the lower size cutoff. Over 200 asteroids are known to be larger than 100 km, and a survey in the infrared wavelengths has shown that the asteroid belt has between 700,000 and 1.7 million asteroids with a diameter of 1 km or more.

The number of asteroids in the main belt steadily increases with decreasing size. Although the size distribution generally follows a power law, there are 'bumps' in the curve at about $5 km$ and $100 km$, where more asteroids than expected from such a curve are found. Most asteroids larger than approximately $120 km$ in diameter are primordial, having survived from the accretion epoch, whereas most smaller asteroids are products of fragmentation of primordial asteroids. The primordial population of the main belt was probably 200 times what it is today.

The absolute magnitudes of most of the known asteroids are between 11 and 19, with the median at about 16. On average the distance between the asteroids is about 965600 km, although this varies among asteroid families and smaller undetected asteroids might be even closer. The total mass of the asteroid belt is estimated to be $2,390,000,000,000,000,000,000$ kg, which is 3% of the mass of the Moon. The four largest objects, Ceres, Vesta, Pallas, and Hygiea, contain an estimated 62% of the belt's total mass, with 39% accounted for by Ceres alone.

Composition
The present day belt consists primarily of three categories of asteroids: C-type carbonaceous asteroids, S-type silicate asteroids, and a hybrid group of X-type asteroids. The hybrid group have featureless spectra, but they can be divided into three groups based on reflectivity, yielding the M-type metallic, P-type primitive, and E-type enstatite asteroids. Additional types have been found that do not fit within these primary classes. There is a compositional trend of asteroid types by increasing distance from the Sun, in the order of S, C, P, and the spectrally-featureless D-types.

Carbonaceous asteroids, as their name suggests, are carbon-rich. They dominate the asteroid belt's outer regions, and are rare in the inner belt. Together they comprise over 75% of the visible asteroids. They are redder in hue than the other asteroids and have a low albedo. Their surface compositions are similar to carbonaceous chondrite meteorites. Chemically, their spectra match the primordial composition of the early Solar System, with hydrogen, helium, and volatiles removed.

S-type (silicate-rich) asteroids are more common toward the inner region of the belt, within 2.5 AU of the Sun. The spectra of their surfaces reveal the presence of silicates and some metal, but no significant carbonaceous compounds. This indicates that their materials have been significantly modified from their primordial composition, probably through melting and reformation. They have a relatively high albedo and form about 17% of the total asteroid population.

M-type (metal-rich) asteroids are typically found in the middle of the main belt, and they make up much of the remainder of the total population. Their spectra resemble that of iron-nickel. Some are believed to have formed from the metallic cores of differentiated progenitor bodies that were disrupted through collision. However, some silicate compounds also can produce a similar appearance. For example, the large M-type asteroid 22 Kalliope does not appear to be primarily composed of metal. Within the asteroid belt, the number distribution of M-type asteroids peaks at a semimajor axis of about 2.7 AU. Whether all M-types are compositionally similar, or whether it is a label for several varieties which do not fit neatly into the main C and S classes is not yet clear.

One mystery is the relative rarity of V-type (Vestoid) or basaltic asteroids in the asteroid belt. Theories of asteroid formation predict that objects the size of Vesta or larger should form crusts and mantles, which would be composed mainly of basaltic rock, resulting in more than half of all asteroids being composed either of basalt or of olivine. However, observations suggest that 99% of the predicted basaltic material is missing. Until 2001, most basaltic bodies discovered in the asteroid belt were believed to originate from the asteroid Vesta (hence their name V-type), but the discovery of the asteroid 1459 Magnya revealed a slightly different chemical composition from the other basaltic asteroids discovered until then, suggesting a different origin. This hypothesis was reinforced by the further discovery in 2007 of two asteroids in the outer belt, 7472 Kumakiri and, with a differing basaltic composition that could not have originated from Vesta. These two are the only V-type asteroids discovered in the outer belt to date.

The temperature of the asteroid belt varies with the distance from the Sun. For dust particles within the belt, typical temperatures range from 200 K (−73 °C) at 2.2 AU down to 165 K (−108 °C) at 3.2 AU. However, due to rotation, the surface temperature of an asteroid can vary considerably as the sides are alternately exposed to solar radiation then to the stellar background.

Main-belt comets
Several otherwise unremarkable bodies in the outer belt show cometary activity. Because their orbits cannot be explained through the capture of classical comets, many of the outer asteroids are thought to be icy, with the ice occasionally exposed to sublimation through small impacts. Main-belt comets may have been a major source of the Earth's oceans because the deuterium-hydrogen ratio is too low for classical comets to have been the principal source.

Orbits
Most asteroids within the asteroid belt have orbital eccentricities of less than 0.4, and an inclination of less than 30°. The orbital distribution of the asteroids reaches a maximum at an eccentricity around 0.07 and an inclination below 4°. Thus, although a typical asteroid has a relatively circular orbit and lies near the plane of the ecliptic, some asteroid orbits can be highly eccentric or travel well outside the ecliptic plane.

Sometimes, the term "main belt" is used to refer only to the more compact "core" region where the greatest concentration of bodies is found. This lies between the strong 4:1 and 2:1 Kirkwood gaps at 2.06 and 3.27 AU, and at orbital eccentricities less than roughly 0.33, along with orbital inclinations below about 20°. , this "core" region contained 93% of all discovered and numbered minor planets within the Solar System. The JPL Small-Body Database lists over 1 million known main-belt asteroids.

Kirkwood gaps
Kirkwood Gaps.svg (a). The dashed lines indicate Kirkwood gaps, while colors designate the following zones:

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The semimajor axis of an asteroid is used to describe the dimensions of its orbit around the Sun, and its value determines the minor planet's orbital period. In 1866, Daniel Kirkwood announced the discovery of gaps in the distances of these bodies' orbits from the Sun. They were located in positions where their period of revolution about the Sun was an integer fraction of Jupiter's orbital period. Kirkwood proposed that the gravitational perturbations of the planet led to the removal of asteroids from these orbits.

When the mean orbital period of an asteroid is an integer fraction of the orbital period of Jupiter, a mean-motion resonance with the gas giant is created that is sufficient to perturb an asteroid to new orbital elements. Primordial asteroids entered these gaps because of the migration of Jupiter's orbit. Subsequently, asteroids primarily migrate into these gap orbits due to the Yarkovsky effect, but may also enter because of perturbations or collisions. After entering, an asteroid is gradually nudged into a different, random orbit with a larger or smaller semimajor axis.

Collisions
The high population of the asteroid belt makes for an active environment, where collisions between asteroids occur frequently (on deep time scales). Impact events between main-belt bodies with a mean radius of 10 km are expected to occur about once every 10 million years. A collision may fragment an asteroid into numerous smaller pieces (leading to the formation of a new asteroid family). Conversely, collisions that occur at low relative speeds may also join two asteroids. After more than 4 billion years of such processes, the members of the asteroid belt now bear little resemblance to the original population.

Evidence suggests that most main belt asteroids between 200 m and 10 km in diameter are rubble piles formed by collisions. These bodies consist of a multitude of irregular objects that are mostly bound together by self-gravity, resulting in significant amounts of internal porosity. Along with the asteroid bodies, the asteroid belt also contains bands of dust with particle radii of up to a few hundred micrometres. This fine material is produced, at least in part, from collisions between asteroids, and by the impact of micrometeorites upon the asteroids. Due to the Poynting–Robertson effect, the pressure of solar radiation causes this dust to slowly spiral inward toward the Sun.

The combination of this fine asteroid dust, as well as ejected cometary material, produces the zodiacal light. This faint auroral glow can be viewed at night extending from the direction of the Sun along the plane of the ecliptic. Asteroid particles that produce visible zodiacal light average about 40 μm in radius. The typical lifetimes of main-belt zodiacal cloud particles are about 700,000 years. Thus, to maintain the bands of dust, new particles must be steadily produced within the asteroid belt. It was once thought that collisions of asteroids form a major component of the zodiacal light. However, computer simulations by Nesvorný and colleagues attributed 85 percent of the zodiacal-light dust to fragmentations of Jupiter-family comets, rather than to comets and collisions between asteroids in the asteroid belt. At most 10 percent of the dust is attributed to the asteroid belt.

Meteorites
Some of the debris from collisions can form meteoroids that enter the Earth's atmosphere. Of the 50,000 meteorites found on Earth to date, 99.8 percent are believed to have originated in the asteroid belt.

Families and groups

In 1918, the Japanese astronomer Kiyotsugu Hirayama noticed that the orbits of some of the asteroids had similar parameters, forming families or groups.

Approximately one-third of the asteroids in the asteroid belt are members of an asteroid family. These share similar orbital elements, such as semi-major axis, eccentricity, and orbital inclination as well as similar spectral features, which indicate a common origin in the breakup of a larger body. Graphical displays of these element pairs, for members of the asteroid belt, show concentrations indicating the presence of an asteroid family. There are about 20 to 30 associations that are likely asteroid families. Additional groupings have been found that are less certain. Asteroid families can be confirmed when the members display similar spectral features. Smaller associations of asteroids are called groups or clusters.

Some of the most prominent families in the asteroid belt (in order of increasing semi-major axes) are the Flora, Eunomia, Koronis, Eos, and Themis families. The Flora family, one of the largest with more than 800 known members, may have formed from a collision less than 1 billion years ago. The largest asteroid to be a true member of a family is 4 Vesta. (This is in contrast to an interloper, in the case of Ceres with the Gefion family.) The Vesta family is believed to have formed as the result of a crater-forming impact on Vesta. Likewise, the HED meteorites may also have originated from Vesta as a result of this collision.

Three prominent bands of dust have been found within the asteroid belt. These have similar orbital inclinations as the Eos, Koronis, and Themis asteroid families, and so are possibly associated with those groupings.

The main belt evolution after the Late Heavy Bombardment was likely affected by the passages of large Centaurs and trans-Neptunian objects (TNOs). Centaurs and TNOs that reach the inner Solar System can modify the orbits of main belt asteroids, though only if their mass is of the order of $solar mass$ for single encounters or, one order less in case of multiple close encounters. However, Centaurs and TNOs are unlikely to have significantly dispersed young asteroid families in the main belt, although they can have perturbed some old asteroid families. Current main belt asteroids that originated as Centaurs or trans-Neptunian objects may lie in the outer belt with short lifetime of less than 4 million years, most likely orbiting between 2.8 and 3.2 AU at larger eccentricities than typical of main belt asteroids.

Periphery
Skirting the inner edge of the belt (ranging between 1.78 and 2.0 AU, with a mean semi-major axis of 1.9 AU) is the Hungaria family of minor planets. They are named after the main member, 434 Hungaria; the group contains at least 52 named asteroids. The Hungaria group is separated from the main body by the 4:1 Kirkwood gap and their orbits have a high inclination. Some members belong to the Mars-crossing category of asteroids, and gravitational perturbations by Mars are likely a factor in reducing the total population of this group.

Another high-inclination group in the inner part of the asteroid belt is the Phocaea family. These are composed primarily of S-type asteroids, whereas the neighboring Hungaria family includes some E-types. The Phocaea family orbit between 2.25 and 2.5 AU from the Sun.

Skirting the outer edge of the asteroid belt is the Cybele group, orbiting between 3.3 and 3.5 AU. These have a 7:4 orbital resonance with Jupiter. The Hilda family orbit between 3.5 and 4.2 AU with relatively circular orbits and a stable 3:2 orbital resonance with Jupiter. There are few asteroids beyond 4.2 AU, until Jupiter's orbit. At the latter the two families of Trojan asteroids can be found, which, at least for objects larger than 1 km, are approximately as numerous as the asteroids of the asteroid belt.

New families
Some asteroid families have formed recently, in astronomical terms. The Karin family apparently formed about 5.7 million years ago from a collision with a progenitor asteroid 33 km in radius. The Veritas family formed about 8.3 million years ago; evidence includes interplanetary dust recovered from ocean sediment.

More recently, the Datura cluster appears to have formed about 530,000 years ago from a collision with a main-belt asteroid. The age estimate is based on the probability of the members having their current orbits, rather than from any physical evidence. However, this cluster may have been a source for some zodiacal dust material. Other recent cluster formations, such as the Iannini cluster (c. 1–5 million years ago), may have provided additional sources of this asteroid dust.

Exploration

The first spacecraft to traverse the asteroid belt was Pioneer 10, which entered the region on 16 July 1972. At the time there was some concern that the debris in the belt would pose a hazard to the spacecraft, but it has since been safely traversed by multiple spacecraft without incident. Pioneer 11, Voyagers 1 and 2 and Ulysses passed through the belt without imaging any asteroids. Cassini measured plasma and fine dust grains while traversing the belt in 2000. On its way to Jupiter, Juno traversed the asteroid belt without collecting science data. Due to the low density of materials within the belt, the odds of a probe running into an asteroid are estimated at less than 1 in 1 billion.

Most main belt asteroids imaged to date have come from brief flyby opportunities by probes headed for other targets. Only the Dawn mission has studied main belt asteroids for a protracted period in orbit. The Galileo spacecraft imaged 951 Gaspra in 1991 and 243 Ida in 1993, then NEAR imaged 253 Mathilde in 1997 and landed on near–Earth asteroid 433 Eros in February 2001. Cassini imaged 2685 Masursky in 2000, Stardust imaged 5535 Annefrank in 2002, New Horizons imaged 132524 APL in 2006, and Rosetta imaged 2867 Šteins in September 2008 and 21 Lutetia in July 2010. Dawn orbited Vesta between July 2011 and September 2012 and has orbited Ceres since March 2015.

The Lucy space probe made a flyby of 152830 Dinkinesh in 2023, on its way to the Jupiter Trojans. ESA's JUICE mission will pass through the asteroid belt twice, with a proposed flyby of the asteroid 223 Rosa in 2029. The Psyche spacecraft is a NASA mission to the large M-type asteroid 16 Psyche.

title: Asteroid belt


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Deadweight loss

In economics, deadweight loss is the loss of societal economic welfare due to production/consumption of a good at a quantity where marginal benefit (to society) does not equal marginal cost (to society) – in other words, there are either goods being produced despite the cost of doing so being larger than the benefit, or additional goods are not being produced despite the fact that the benefits of their production would be larger than the costs. The deadweight loss is the net benefit that is missed out on. While losses to one entity often lead to gains for another, deadweight loss represents the loss that is not regained by anyone else. This loss is therefore attributed to both producers and consumers. Deadweight loss can also be a measure of lost economic efficiency when the socially optimal quantity of a good or a service is not produced. Non-optimal production can be caused by monopoly pricing in the case of artificial scarcity, a positive or negative externality, a tax or subsidy, or a binding price ceiling or price floor such as a minimum wage.

Examples
Assume a market for nails where the cost of each nail is $0.10. Demand decreases linearly; there is a high demand for free nails and zero demand for nails at a price per nail of $1.10 or higher. The price of $0.10 per nail represents the point of economic equilibrium in a competitive market.

Monopoly
If market conditions are perfect competition, producers would charge a price of $0.10, and every customer whose marginal benefit exceeds $0.10 would buy a nail. A monopoly producer of this product would typically charge whatever price will yield the greatest profit for themselves, regardless of lost efficiency for the economy as a whole. In this example, the monopoly producer charges $0.60 per nail, thus excluding every customer from the market with a marginal benefit less than $0.60. The deadweight loss due to monopoly pricing would then be the economic benefit foregone by customers with a marginal benefit of between $0.10 and $0.60 per nail. The monopolist has "priced them out of the market", even though their benefit exceeds the true cost per nail.

Subsidy
Conversely, deadweight loss can also arise from consumers buying more of a product than they otherwise would based on their marginal benefit and the cost of production. For example, if in the same nail market the government provided a $0.03 subsidy for every nail produced, the subsidy would reduce the market price of each nail to $0.07, even though production actually still costs $0.10 per nail. Consumers with a marginal benefit of between $0.07 and $0.10 per nail would then buy nails, even though their benefit is less than the real production cost of $0.10. The difference between the cost of production and the purchase price then creates the "deadweight loss" to society.

Tax
A tax has the opposite effect of a subsidy. Whereas a subsidy entices consumers to buy a product that would otherwise be too expensive for them in light of their marginal benefit (price is lowered to artificially increase demand), a tax dissuades consumers from a purchase (price is increased to artificially lower demand). This excess burden of taxation represents the lost utility for the consumer. A common example of this is the so-called sin tax, a tax levied against goods deemed harmful to society and individuals. For example, "sin taxes" levied against alcohol and tobacco are intended to artificially lower demand for these goods; some would-be users are priced out of the market, i.e. total smoking and drinking are reduced. Products such as alcohol and tobacco have historically been highly taxed and incur excise duties which are one of the categories of indirect tax. Indirect tax (VAT), weighs on the consumer, is not a cause of loss of surplus for the producer, but affects consumer utility and leads to deadweight loss for consumers. Indirect taxes are usually paid by large entities such as corporations or manufacturers but are partially shifted towards the consumer. Furthermore, indirect taxes can be charged based on the unit price of a said commodity or can be calculated based on a percentage of the final retail price. Additionally, indirect taxes can either be collected at one stage of the production and retail process or alternatively can be charged and collected at multiple stages of the overall production process of a commodity.

Harberger's triangle

Harberger's triangle, generally attributed to Arnold Harberger, shows the deadweight loss (as measured on a supply and demand graph) associated with government intervention in a perfect market. Mechanisms for this intervention include price floors, caps, taxes, tariffs, or quotas. It also refers to the deadweight loss created by a government's failure to intervene in a market with externalities.

In the case of a government tax, the amount of the tax drives a wedge between what consumers pay and what producers receive, and the area of this wedge shape is equivalent to the deadweight loss caused by the tax.

The area represented by the triangle results from the fact that the intersection of the supply and the demand curves are cut short. The consumer surplus and the producer surplus are also cut short. The loss of such surplus is never recouped and represents the deadweight loss.

Some economists like Martin Feldstein maintain that these triangles can seriously affect long-term economic trends by pivoting the trend downwards and causing a magnification of losses in the long run but others like James Tobin have argued that they do not have a huge impact on the economy.

Hicks vs. Marshall
The Hicksian (per John Hicks) and the Marshallian (per Alfred Marshall) demand function differ about deadweight loss. After the consumer surplus is considered, it can be shown that the Marshallian deadweight loss is zero if demand is perfectly elastic or supply is perfectly inelastic. However, Hicks analyzed the situation through indifference curves and noted that when the Marshallian demand curve is perfectly inelastic, the policy or economic situation that caused a distortion in relative prices has a substitution effect, i.e. is a deadweight loss.

In modern economic literature, the most common measure of a taxpayer's loss from a distortionary tax, such as a tax on bicycles, is the equivalent variation, the maximum amount that a taxpayer would be willing to forgo in a lump sum to avoid the tax. The deadweight loss can then be interpreted as the difference between the equivalent variation and the revenue raised by the tax. The difference is attributable to the behavioral changes induced by a distortionary tax that are measured by the substitution effect. However, that is not the only interpretation, and Pigou did not use a lump sum tax as the point of reference to discuss deadweight loss (excess burden).

Taxation
When a tax is levied on buyers, the demand curve shifts downward in accordance with the size of the tax. Similarly, when tax is levied on sellers, the supply curve shifts upward by the size of tax. When the tax is imposed, the price paid by buyers increases, and the price received by seller decreases. Therefore, buyers and sellers share the burden of the tax, regardless of how it is imposed. Since a tax places a "wedge" between the price buyers pay and the price sellers get, the quantity sold is reduced below the level that it would be without tax. To put it another way, a tax on a good causes the size of market for that good to decrease.

For example, suppose that Will is a cleaner who is working in the cleaning service company and Amie hired Will to clean her room every week for $100. The opportunity cost of Will's time is $80, while the value of a clean house to Amie is $120. Hence, each of them get same amount of benefit from their deal. Amie and Will each receive a benefit of $20, making the total surplus from trade $40.

However, if the government were to decide to impose a $50 tax upon the providers of cleaning services, their trade would no longer benefit them. Amie would not be willing to pay any price above $120, and Will would no longer receive a payment that exceeds his opportunity cost. As a result, not only do Amie and Will both give up the deal, but Amie has to live in a dirtier house, and Will does not receive his desired income. They have thus lost amount of the surplus that they would have received from their deal, and at the same time, this made each of them worse off to the tune of $40 in value.

Government revenue is also affected by this tax: since Amie and Will have abandoned the deal, the government also loses any tax revenue that would have resulted from wages. This $40 is referred to as the deadweight loss. It causes losses for both buyers and sellers in a market, as well as decreasing government revenues. Taxes cause deadweight losses because they prevent buyers and sellers from realizing some of the gains from trade.

In the graph, the deadweight loss can be seen as the shaded area between the supply and demand curves. While the demand curve shows the value of goods to the consumers, the supply curve reflects the cost for producers. As the example above explains, when the government imposes a tax upon taxpayers, the tax increases the price paid by buyers to $$P_c$$ and decreases price received by sellers to $$P_p$$. Buyers and sellers (Amie and Will) give up the deal between them and exit the market. Thus, the quantity sold reduces from $$Q_e$$ to $$Q_t$$. The deadweight loss occurs because the tax deters these kinds of beneficial trades in the market.

Determinants of deadweight loss
Price elasticities of supply and demand determine whether the deadweight loss from a tax is large or small. This measures to what extent quantity supplied and quantity demanded respond to changes in price. For instance, when the supply curve is relatively inelastic, quantity supplied responds only minimally to changes in the price. However, when the supply curve is more elastic, quantity supplied responds significantly to changes in price. In other words, when the supply curve is more elastic, the area between the supply and demand curves is larger. Similarly, when the demand curve is relatively inelastic, deadweight loss from the tax is smaller, comparing to more elastic demand curve.

A tax results in deadweight loss as it causes buyers and sellers to change their behaviour. Buyers tend to consume less when the tax raises the price. When the tax lowers the price received by sellers, they in turn produce less. As a result, the overall size of the market decreases below the optimum equilibrium. The elasticities of supply and demand determine to what extent the tax distorts the market outcome. As the elasticities of supply and demand increase, so does the deadweight loss resulting from a tax.

How deadweight loss changes as taxes vary
Taxes may be changed by the government or policymakers at different levels. For instance, when a low tax is levied, the deadweight loss is also small (compared to a medium or high tax). An important consideration is that the deadweight loss resulting from a tax increases more quickly than the tax itself; the area of the triangle representing the deadweight loss is calculated using the area (square) of its dimension. Where a tax increases linearly, the deadweight loss increases as the square of the tax increase. This means that when the size of a tax doubles, the base and height of the triangle double. Thus, doubling the tax increases the deadweight loss by a factor of 4.

The varying deadweight loss from a tax also affects the government's total tax revenue. Tax revenue is represented by the area of the rectangle between the supply and demand curves. When a low tax is levied, tax revenue is relatively small. As the size of the tax increases, tax revenue expands. However, when a much higher tax is levied, tax revenue eventually decreases. The higher tax reduces the total size of the market; Although taxes are taking a larger slice of the "pie", the total size of the pie is reduced. Just as in the nail example above, beyond a certain point, the market for a good will eventually decrease to zero.

Deadweight loss of a monopoly
A deadweight loss occurs with monopolies in the same way that a tax causes deadweight loss. When a monopoly, as a "tax collector", charges a price in order to consolidate its power above marginal cost, it drives a "wedge" between the costs born by the consumer and supplier. Imposing this effective tax distorts the market outcome, and the wedge causes a decrease in the quantity sold, below the social optimum. It is important to remember the difference between the two cases: whereas the government receives the revenue from a genuine tax, monopoly profits are collected by a private firm.

title: Deadweight loss


text:
UNICOS

UNICOS is a range of Unix and later Linux operating system (OS) variants developed by Cray for its supercomputers. UNICOS is the successor of the Cray Operating System (COS). It provides network clustering and source code compatibility layers for some other Unixes. UNICOS was originally introduced in 1985 with the Cray-2 system and later ported to other Cray models. The original UNICOS was based on UNIX System V Release 2, and had many Berkeley Software Distribution (BSD) features (e.g., computer networking and file system enhancements) added to it.

Development
CX-OS was the original name given to what is now UNICOS. This was a prototype system which ran on a Cray X-MP in 1984 before the Cray-2 port. It was used to demonstrate the feasibility of using Unix on a supercomputer system, before Cray-2 hardware was available.

The operating system revamp was part of a larger movement inside Cray Research to modernize their corporate software: including rewriting their most important Fortran compiler (cft to cft77) in a higher-level language (Pascal) with more modern optimizations and vectorizations.

As a migration path for existing COS customers wishing to transition to UNICOS, a Guest Operating System (GOS) capability was introduced into COS. The only guest OS that was ever supported was UNICOS. A COS batch job would be submitted to start up UNICOS, which would then run as a subsystem under COS, using a subset of the systems CPUs, memory, and peripheral devices. The UNICOS that ran under GOS was exactly the same as when it ran stand-alone: the difference was that the kernel would make certain low-level hardware requests through the COS GOS hook, rather than directly to the hardware.

One of the sites that ran very early versions of UNICOS was Bell Labs, where Unix pioneers including Dennis Ritchie ported parts of their Eighth Edition Unix (including STREAMS input/output (I/O)) to UNICOS. They also experimented with a guest facility within UNICOS, allowing the stand-alone version of the OS to host itself.

Releases
Cray released several different OSs under the name UNICOS, including:
 * 1) UNICOS: the original Cray Unix, based on System V. Used on the Cray-1, Cray-2, X-MP, Y-MP, C90, etc.
 * 2) UNICOS MAX: a Mach-based microkernel used on the T3D's processing elements, together with UNICOS on the host Y-MP or C90 system.
 * 3) UNICOS/mk: a serverized version of UNICOS using the Chorus microkernel to make a distributed operating system. Used on the T3E. This was the last Cray OS really based on UNICOS sources, as the following products were based on different sources and simply used the "UNICOS" name.
 * 4) UNICOS/mp: not derived from UNICOS, but based on IRIX 6.5. Used on the X1.
 * 5) UNICOS/lc: not derived from UNICOS, but based on SUSE Linux. Used on the XT3, XT4 and XT5. UNICOS/lc 1.x comprises a combination of
 * 6) the compute elements run the Catamount microkernel (which itself is based on Cougaar)
 * 7) the service elements run SUSE Linux
 * 8) Cray Linux Environment (CLE): from release 2.1 onward, UNICOS/lc is now called Cray Linux Environment
 * 9) the compute elements run Compute Node Linux (CNL) (which is a customized Linux kernel )
 * 10) the service elements run SUSE Linux Enterprise Server

title: UNICOS


text:
Navajo (disambiguation)

The Navajo are a Native American people of the Southwestern United States.

Navajo or Navaho may also refer to:

 * Navajo Nation, the governmental entity of the Navajo people
 * Navajo language, spoken in the Southwestern United States

Places in the United States

 * Navajo, New Mexico
 * Navajo, San Diego
 * Navajo Church, a landform in New Mexico
 * Navajo City, New Mexico
 * Navajo County, Arizona
 * Navajo Generating Station, a coal-fired powerplant
 * Navajo Peak, Colorado
 * Navajo Reservoir
 * Navajo Springs, Arizona

Others

 * Navajo (film), a 1952 documentary film
 * Navajo (train), one of the named passenger trains of the Atchison, Topeka and Santa Fe Railway
 * The Navajo (sleeper car), a sleeping car on the Super Chief passenger train
 * Alfa Romeo Navajo concept car
 * Mazda Navajo, a rebadged version of the Ford Explorer, introduced in 1991
 * Navajo Sandstone, a geologic formation in the Glen Canyon Group
 * Navajo-Churro sheep, a breed of sheep
 * Piper PA-31 Navajo, a light, twin engine airplane
 * SM-64 Navaho, an experimental cruise missile
 * USS Navajo, the name of more than one United States Navy ship
 * "Navajo", a 1903 piece of popular music by Egbert Van Alstyne
 * The Navajos, a subgroup of the anti-Nazi Edelweiss Pirates

title: Navajo (disambiguation)


text:
Four Corners Monument

The Four Corners Monument marks the quadripoint in the Southwestern United States where the states of Arizona, Colorado, New Mexico, and Utah meet. It is the only point in the United States shared by four states, leading to the area being named the Four Corners region. The monument also marks the boundary between two semi-autonomous Native American governments, the Navajo Nation, which maintains the monument as a tourist attraction, and the Ute Mountain Ute Tribe Reservation.

The origins of the state boundaries marked by the monument occurred just prior to, and during, the American Civil War, when the United States Congress acted to form governments in the area to combat the spread of slavery to the region. When the early territories were formed, their boundaries were designated along meridian and parallel lines. Beginning in the 1860s, these lines were surveyed and marked. These early surveys included some errors, but even so, the markers placed became the legal boundaries, superseding the written descriptions of geographical meridians and parallels. This includes the Four Corners Monument, which has been legally established as the corner of the four states.

Monument
The monument is maintained as a tourist attraction by the Navajo Nation Parks and Recreation Department, Four Corners Monument Navajo Tribal Park. It is an example of a political boundary that is a tourist destination in its own right. The monument consists of a granite disk embedded with a smaller bronze disk around the point, surrounded by smaller, appropriately located state seals and flags representing both the states and tribal nations of the area. Circling the point, starting from Utah, the disk reads with two words in each state "Here meet in freedom under God four states". Around the monument, local Navajo and Ute artisans sell souvenirs and food. An admission fee is required to view and photograph the monument. The monument is a popular tourist attraction despite its remote and isolated location. As early as 1908, people traveled long distances to take pictures of family and friends at the monument in Twister-like poses, sitting on the disk, in a circle of friends or family around the disk, or for couples to kiss directly over the disk.

Location
The monument is located on the Colorado Plateau west of U.S. Highway 160, on State Road 597, approximately 40 mi southwest of Cortez, Colorado. In addition to the four states, two semi-autonomous American Indian tribal governments have boundaries at the monument, the Navajo Nation and the Ute Mountain Ute Tribe Reservation, with the Ute Mountain tribal boundaries coinciding with Colorado's boundaries at the monument.

Climate
Located in the Colorado Plateau region of the Southwestern United States, the Four Corners Monument has a strong cold semi-arid climate (BSk) according to the Köppen climate classification system. Winters are cold but sunny, while summers are hot and dry. The record high temperature of 105 F has been observed five times, on June 19, 29 and 30, 1974, July 14, 2003, and July 21, 2005. The record low temperature of −18 F was observed on January 3, 1974.

History
The area now called Four Corners was initially American Indian land, and beginning in the 16th century it was claimed by Spain as part of New Spain. After Mexico gained independence from Spain in 1821, the area was governed by Mexico until being ceded to the United States by the Treaty of Guadalupe Hidalgo in 1848, following the United States' victory in the Mexican–American War. The first boundary which would become part of the monument was set as part of the Compromise of 1850, which created the New Mexico Territory and Utah Territory. The border between the two territories was congressionally defined as the 37th parallel north by the 31st United States Congress. In 1861, the 36th United States Congress transferred land previously allocated to the Utah Territory to the newly created Colorado Territory. The Colorado Territory's southern border would remain as the 37th parallel north, but a new border—between the Colorado and Utah Territories—was declared to be the 32nd meridian west from Washington. This line was derived from the reference used at the time, the Washington meridian.

In 1860, just prior to the outbreak of the American Civil War, a group of people in the southern portion of New Mexico Territory passed a resolution condemning the United States for creating such a vast territory with only a single, small government in place at Santa Fe. They claimed that by doing so, the U.S. had ignored the needs of the southern portion, left it without a functional system of law and order, and allowed the situation to deteriorate into a state of chaos and near-anarchy. The group declared secession from the United States and announced their intent to join the Confederate States of America under the name of the Arizona Territory. The U.S. Congress responded in 1863 by creating another Arizona Territory with different but partially overlapping boundaries. The Confederate boundaries split New Mexico along an east–west line, the 34th parallel north, allowing for a single state connection from Texas to the Colorado River. This would give the Confederacy access to California and the Pacific coast. The Union definition split New Mexico along a north-south line, the 32nd meridian west from Washington, which simply extended the boundary between Colorado and Utah southward. The Union plan eventually became reality, and this created the quadripoint at the modern Four Corners. After the split, New Mexico resembled its modern form, with only slight differences.

Surveying the boundaries
After the Civil War, efforts began to survey and mark the actual borders. In 1868, the United States General Land Office (GLO) had Ehud N. Darling survey and set markers along the border between the Colorado and New Mexico Territories (the 37th parallel north); this border over time has become known as the "Darling Line". In 1875, another GLO surveyor, Chandler Robbins, surveyed and marked the border between the Arizona and New Mexico Territories (the 32nd meridian west of Washington). Robbins began near the Mexico–United States border and worked his way north, marking the border every so often. Near the 37th parallel north, he intersected the Darling Line, and here he erected a sandstone shaft. This sandstone shaft marked today's location of the Four Corners Monument.

In 1878, Rollin J. Reeves surveyed and marked the border between the newly created State of Colorado and the Utah Territory. Reeves located the sandstone shaft marker placed by Robbins at today's Four Corners Monument. He then began to survey and mark the border between Colorado and Utah from this point northward. In 1901, Howard B. Carpenter surveyed and marked the border between Arizona and Utah, completing the survey of borders making up the Four Corners Monument.

The results of these surveys and the markers placed were later accepted as the legal boundaries between the various states.

Development into a monument
By 1899, the sandstone shaft marker placed by Chandler Robbins in 1875 had been disturbed and broken, so it was replaced with a new stone by two U.S. surveyors, Hubert D. Page and James M. Lentz. In 1912, a simple concrete pad was poured around the marker. The first modern Navajo government convened in 1923 in an effort to organize and regulate an increasing amount of oil exploration activities on Navajo lands, and they played a significant role in the monument's further development. In 1931, Everett H. Kimmell, another U.S. surveyor, found this newer stone had broken too, and he replaced it with a brass disc marker set in concrete. In 1962, the Bureau of Land Management and the Bureau of Indian Affairs poured an elevated concrete pad around the 1931 brass marker; this pad included the state border lines and names in tile. The monument was rebuilt in 1992, and the 1931 brass marker was replaced with a disc-shaped aluminum-bronze plate set in granite. The monument was again rebuilt in 2010, although the disc-shaped plate from 1992 remained in place.

Misplacement controversy
Since the early 20th century, controversies have arisen regarding the accuracy of the monument's placement. After the initial surveys, it was found that the borders did not always follow the lines of meridian and parallel (as had been intended) due to the primitive surveying technology available at the time. This discrepancy left the four states asking if the correct borders were the exact lines of meridian and parallel (and if new, more accurate, surveys needed to be done), or if the markers placed during the initial surveys were now the actual border.

New Mexico sued Colorado in 1919, and when the Supreme Court in 1925 ruled that the markers placed during the initial surveys were the actual borders, even if the markers were off in some locations (this includes the Four Corners Monument), the issue was resolved. Today's legal description of these border lines is based on the original markers, and not the written description of the borders created when the territories were formed. Because of this, the borders between these states are not perfectly straight and often zigzag.

One example is the border between Colorado and Utah, where in one area the border jogs west about 1.5 mi from where it was intended to be placed by the written description (i.e. the 32nd meridian west from Washington – 38.27619°N, -109.06065°W). Because of the Supreme Court decision, the border set out by the markers remains the border between the two states.

This issue resurfaced briefly in 2009 with U.S. media reports that the monument was placed 2.5 mi west of its intended location. This was soon found to be the result of a mistaken assumption: that the Prime Meridian, used in the United States since 1912, was used. In actuality, the 19th century surveys used the previous Washington meridian. A spokesperson for the U.S. National Geodetic Survey (USNGS) has stated that the USNGS has determined that the modern monument is located roughly 1800 ft east of where the Four Corners marker had originally been intended to be located by the US Congress in 1863. The spokesperson, however, reiterated that the 1875 survey was accepted by all states and therefore its markers, including the Four Corners Monument, are legally binding. Similar statements were issued by the Navajo Nation, defending their work in maintaining and promoting the monument.

COVID-19 closures
From 2020 to 2021, the Four Corners Monument was closed to the public as part of Navajo Nation coronavirus safety regulations. The monument was reopened in 2021, with a requirement for visitors to wear masks.

Similar places

 * Canadian four corners
 * No Man's Heath
 * Tres Fronteras
 * Triple Frontier
 * Three-Country Cairn
 * Vaalserberg

title: Four Corners Monument