An asteroid family is a population of asteroids that share similar proper orbital elements, such as semimajor axis and orbital inclination. The members of the families are thought to be fragments of past asteroid collisions. An asteroid family is a more specific term than asteroid group whose members, while sharing some broad orbital characteristics, may be otherwise unrelated to each other. Large prominent families contain several hundred recognized asteroids. Small, compact families may have only about ten identified members. About 33% to 35% of asteroids in the main belt are family members. There are about 20 to 30 reliably recognized families, with several tens of less certain groupings. Most asteroid families are found in the main asteroid belt, although several family-like groups such as the Pallas family, Hungaria family, the Phocaea family lie at smaller semi-major axis or larger inclination than the main belt. One family has been identified associated with the dwarf planet Haumea; some studies have tried to find evidence of collisional families among the trojan asteroids, but at present the evidence is inconclusive.
The families are thought to form as a result of collisions between asteroids. In many or most cases the parent body was shattered, but there are several families which resulted from a large cratering event which did not disrupt the parent body; such cratering families consist of a single large body and a swarm of asteroids that are much smaller. Some families have complex internal structures which are not satisfactorily explained at the moment, but may be due to several collisions in the same region at different times. Due to the method of origin, all the members have matching compositions for most families. Notable exceptions are those families. Asteroid families are thought to have lifetimes of the order of a billion years, depending on various factors; this is shorter than the Solar System's age, so few if any are relics of the early Solar System. Decay of families occurs both because of slow dissipation of the orbits due to perturbations from Jupiter or other large bodies, because of collisions between asteroids which grind them down to small bodies.
Such small asteroids become subject to perturbations such as the Yarkovsky effect that can push them towards orbital resonances with Jupiter over time. Once there, they are rapidly ejected from the asteroid belt. Tentative age estimates have been obtained for some families, ranging from hundreds of millions of years to less than several million years as for the compact Karin family. Old families are thought to contain few small members, this is the basis of the age determinations, it is supposed that many old families have lost all the smaller and medium-sized members, leaving only a few of the largest intact. A suggested example of such old family remains are 113 Amalthea pair. Further evidence for a large number of past families comes from analysis of chemical ratios in iron meteorites; these show that there must have once been at least 50 to 100 parent bodies large enough to be differentiated, that have since been shattered to expose their cores and produce the actual meteorites. When the orbital elements of main belt asteroids are plotted, a number of distinct concentrations are seen against the rather uniform distribution of non-family background asteroids.
These concentrations are the asteroid families. Interlopers are asteroids classified as family members based on their so-called proper orbital elements but having spectroscopic properties distinct from the bulk of the family, suggesting that they, contrary to the true family members, did not originate from the same parent body that once fragmented upon a collisional impact. Speaking and their membership are identified by analysing the proper orbital elements rather than the current osculating orbital elements, which fluctuate on timescales of tens of thousands of years; the proper elements are related constants of motion that remain constant for times of at least tens of millions of years, longer. The Japanese astronomer Kiyotsugu Hirayama pioneered the estimation of proper elements for asteroids, first identified several of the most prominent families in 1918. In his honor, asteroid families are sometimes called Hirayama families; this applies to the five prominent groupings discovered by him.
Present day computer-assisted searches have identified more than a hundred asteroid families. The most prominent algorithms have been the hierarchical clustering method, which looks for groupings with small nearest-neighbour distances in orbital element space, wavelet analysis, which builds a density-of-asteroids map in orbital element space, looks for density peaks; the boundaries of the families are somewhat vague because at the edges they blend into the background density of asteroids in the main belt. For this reason the number of members among discovered asteroids is only known and membership is uncertain for asteroids near the edges. Additionally, some interlopers from the heterogeneous background asteroid population are expected in the central regions of a family. Since the true family members caused by the collision are expected to have similar compositions, most such interlopers can in principle be recognised by spectral properties which do not matc
In celestial mechanics, an orbital resonance occurs when orbiting bodies exert a regular, periodic gravitational influence on each other because their orbital periods are related by a ratio of small integers. Most this relationship is found for a pair of objects; the physical principle behind orbital resonance is similar in concept to pushing a child on a swing, where the orbit and the swing both have a natural frequency, the other body doing the "pushing" will act in periodic repetition to have a cumulative effect on the motion. Orbital resonances enhance the mutual gravitational influence of the bodies, i.e. their ability to alter or constrain each other's orbits. 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 stable and self-correcting, so that the bodies remain in resonance. Examples are the 1:2:4 resonance of Jupiter's moons Ganymede, Europa and Io, the 2:3 resonance between Pluto and Neptune.
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 Solar System bodies to eject most other bodies sharing their orbits. A binary resonance ratio in this article should be interpreted as the ratio of number of orbits completed in the same time interval, rather than as the ratio of orbital periods, which would be the inverse ratio, thus the 2:3 ratio above means Pluto completes two orbits in the time it takes Neptune to complete three. In the case of resonance relationships among three or more bodies, either type of ratio may be used and the type of ratio will be specified. Since the discovery of Newton's law of universal gravitation in the 17th century, the stability of the Solar System has preoccupied many mathematicians, starting with Pierre-Simon Laplace; the stable orbits that arise in a two-body approximation ignore the influence of other bodies. The effect of these added interactions on the stability of the Solar System is small, but at first it was not known whether they might add up over longer periods to change the orbital parameters and lead to a different configuration, or whether some other stabilising effects might maintain the configuration of the orbits of the planets.
It was Laplace. Before Newton, there was consideration of ratios and proportions in orbital motions, in what was called "the music of the spheres", or Musica universalis. In general, an orbital resonance may involve any combination of the orbit parameters. Act on any time scale from short term, commensurable with the orbit periods, to secular, measured in 104 to 106 years. Lead to either long-term stabilization of the orbits or be the cause of their destabilization. A mean-motion orbital resonance occurs when two bodies have periods of revolution that are a simple integer ratio of each other. Depending on the details, this can either destabilize the orbit. Stabilization may occur when the two bodies move in such a synchronised fashion that they never approach. For instance: The orbits of Pluto and the plutinos are stable, despite crossing that of the much larger Neptune, because they are in a 2:3 resonance with it; the resonance ensures that, when they approach perihelion and Neptune's orbit, Neptune is distant.
Other Neptune-crossing bodies that were not in resonance were ejected from that region by strong perturbations due to Neptune. There are smaller but significant groups of resonant trans-Neptunian objects occupying the 1:1, 3:5, 4:7, 1:2 and 2:5 resonances, among others, with respect to Neptune. In the asteroid belt beyond 3.5 AU from the Sun, the 3:2, 4:3 and 1:1 resonances with Jupiter are populated by clumps of asteroids. Orbital resonances can destabilize one of the orbits; this process can be exploited to find energy-efficient ways of deorbiting spacecraft. For small bodies, destabilization is far more likely. For instance: In the asteroid belt within 3.5 AU from the Sun, the major mean-motion resonances with Jupiter are locations of gaps in the asteroid distribution, the Kirkwood gaps. Asteroids have been ejected from these empty lanes by repeated perturbations. However, there are still populations of asteroids temporarily present near these resonances. For example, asteroids of the Alinda family are in or close to the 3:1 resonance, with their orbital eccentricity increased by interactions with Jupiter until they have a close encounter with an inner planet that ejects them from the resonance.
In the rings of Saturn, the Cassini Division is a gap between the inner B Ring and the outer A Ring, cleared by a 2:1 resonance with the moon Mimas. In the rings of Saturn, the Encke and Keeler gaps within the A Ring are cleared by 1:1 resonances with the embedded moonlets Pan and Daphnis, respectively; the A Ring's outer edge is maintained by a destabilizing 7:6 resonance with the moon Janus. Most bodies that
The astronomical unit is a unit of length the distance from Earth to the Sun. However, that distance varies as Earth orbits the Sun, from a maximum to a minimum and back again once a year. Conceived as the average of Earth's aphelion and perihelion, since 2012 it has been defined as 149597870700 metres or about 150 million kilometres; the astronomical unit is used for measuring distances within the Solar System or around other stars. It is a fundamental component in the definition of another unit of astronomical length, the parsec. A variety of unit symbols and abbreviations have been in use for the astronomical unit. In a 1976 resolution, the International Astronomical Union used the symbol A to denote a length equal to the astronomical unit. In the astronomical literature, the symbol AU was common. In 2006, the International Bureau of Weights and Measures recommended ua as the symbol for the unit. In the non-normative Annex C to ISO 80000-3, the symbol of the astronomical unit is "ua". In 2012, the IAU, noting "that various symbols are presently in use for the astronomical unit", recommended the use of the symbol "au".
In the 2014 revision of the SI Brochure, the BIPM used the unit symbol "au". Earth's orbit around the Sun is an ellipse; the semi-major axis of this elliptic orbit is defined to be half of the straight line segment that joins the perihelion and aphelion. The centre of the Sun lies on this straight line segment, but not at its midpoint; because ellipses are well-understood shapes, measuring the points of its extremes defined the exact shape mathematically, made possible calculations for the entire orbit as well as predictions based on observation. In addition, it mapped out the largest straight-line distance that Earth traverses over the course of a year, defining times and places for observing the largest parallax in nearby stars. Knowing Earth's shift and a star's shift enabled the star's distance to be calculated, but all measurements are subject to some degree of error or uncertainty, the uncertainties in the length of the astronomical unit only increased uncertainties in the stellar distances.
Improvements in precision have always been a key to improving astronomical understanding. Throughout the twentieth century, measurements became precise and sophisticated, more dependent on accurate observation of the effects described by Einstein's theory of relativity and upon the mathematical tools it used. Improving measurements were continually checked and cross-checked by means of improved understanding of the laws of celestial mechanics, which govern the motions of objects in space; the expected positions and distances of objects at an established time are calculated from these laws, assembled into a collection of data called an ephemeris. NASA's Jet Propulsion Laboratory HORIZONS System provides one of several ephemeris computation services. In 1976, in order to establish a yet more precise measure for the astronomical unit, the IAU formally adopted a new definition. Although directly based on the then-best available observational measurements, the definition was recast in terms of the then-best mathematical derivations from celestial mechanics and planetary ephemerides.
It stated that "the astronomical unit of length is that length for which the Gaussian gravitational constant takes the value 0.01720209895 when the units of measurement are the astronomical units of length and time". Equivalently, by this definition, one AU is "the radius of an unperturbed circular Newtonian orbit about the sun of a particle having infinitesimal mass, moving with an angular frequency of 0.01720209895 radians per day". Subsequent explorations of the Solar System by space probes made it possible to obtain precise measurements of the relative positions of the inner planets and other objects by means of radar and telemetry; as with all radar measurements, these rely on measuring the time taken for photons to be reflected from an object. Because all photons move at the speed of light in vacuum, a fundamental constant of the universe, the distance of an object from the probe is calculated as the product of the speed of light and the measured time. However, for precision the calculations require adjustment for things such as the motions of the probe and object while the photons are transiting.
In addition, the measurement of the time itself must be translated to a standard scale that accounts for relativistic time dilation. Comparison of the ephemeris positions with time measurements expressed in the TDB scale leads to a value for the speed of light in astronomical units per day. By 2009, the IAU had updated its standard measures to reflect improvements, calculated the speed of light at 173.1446326847 AU/d. In 1983, the International Committee for Weights and Measures modified the International System of Units to make the metre defined as the distance travelled in a vacuum by light in 1/299792458 second; this replaced the previous definition, valid between 1960 and 1983, that the metre equalled a certain number of wavelengths of a certain emission line of krypton-86. The speed of light could be expressed as c0 = 299792458 m/s, a standard adopted by the IERS numerical standards. From this definition and the 2009 IAU standard, the time for light to traverse an AU is found to be
In celestial mechanics, the Lagrangian points are the points near two large bodies in orbit where a smaller object will maintain its position relative to the large orbiting bodies. At other locations, a small object would go into its own orbit around one of the large bodies, but at the Lagrangian points the gravitational forces of the two large bodies, the centripetal force of orbital motion, the Coriolis acceleration all match up in a way that cause the small object to maintain a stable or nearly stable position relative to the large bodies. There are five such points, labeled L1 to L5, all in the orbital plane of the two large bodies, for each given combination of two orbital bodies. For instance, there are five Lagrangian points L1 to L5 for the Sun-Earth system, in a similar way there are five different Lagrangian points for the Earth-Moon system. L1, L2, L3 are on the line through the centers of the two large bodies. L4 and L5 each form an equilateral triangle with the centers of the large bodies.
L4 and L5 are stable, which implies that objects can orbit around them in a rotating coordinate system tied to the two large bodies. Several planets have trojan satellites near their L5 points with respect to the Sun. Jupiter has more than a million of these trojans. Artificial satellites have been placed at L1 and L2 with respect to the Sun and Earth, with respect to the Earth and the Moon; the Lagrangian points have been proposed for uses in space exploration. The three collinear Lagrange points were discovered by Leonhard Euler a few years before Joseph-Louis Lagrange discovered the remaining two. In 1772, Lagrange published an "Essay on the three-body problem". In the first chapter he considered the general three-body problem. From that, in the second chapter, he demonstrated two special constant-pattern solutions, the collinear and the equilateral, for any three masses, with circular orbits; the five Lagrangian points are labeled and defined as follows: The L1 point lies on the line defined by the two large masses M1 and M2, between them.
It is the most intuitively understood of the Lagrangian points: the one where the gravitational attraction of M2 cancels M1's gravitational attraction. Explanation An object that orbits the Sun more than Earth would have a shorter orbital period than Earth, but that ignores the effect of Earth's own gravitational pull. If the object is directly between Earth and the Sun Earth's gravity counteracts some of the Sun's pull on the object, therefore increases the orbital period of the object; the closer to Earth the object is, the greater this effect is. At the L1 point, the orbital period of the object becomes equal to Earth's orbital period. L1 is 0.01 au, 1/100th the distance to the Sun. The L2 point lies on the line beyond the smaller of the two. Here, the gravitational forces of the two large masses balance the centrifugal effect on a body at L2. Explanation On the opposite side of Earth from the Sun, the orbital period of an object would be greater than that of Earth; the extra pull of Earth's gravity decreases the orbital period of the object, at the L2 point that orbital period becomes equal to Earth's.
Like L1, L2 is 0.01 au from Earth. The L3 point lies on the line defined beyond the larger of the two. Explanation Within the Sun-Earth system, the L3 point exists on the opposite side of the Sun, a little outside Earth's orbit and further from the Sun than Earth is; this placement occurs because the Sun is affected by Earth's gravity and so orbits around the two bodies' barycenter, well inside the body of the Sun. At the L3 point, the combined pull of Earth and Sun cause the object to orbit with the same period as Earth; the L4 and L5 points lie at the third corners of the two equilateral triangles in the plane of orbit whose common base is the line between the centers of the two masses, such that the point lies behind or ahead of the smaller mass with regard to its orbit around the larger mass. The triangular points are stable equilibria, provided that the ratio of M1/M2 is greater than 24.96. This is the case for the Sun–Earth system, the Sun–Jupiter system, and, by a smaller margin, the Earth–Moon system.
When a body at these points is perturbed, it moves away from the point, but the factor opposite of that, increased or decreased by the perturbation will increase or decrease, bending the object's path into a stable, kidney bean-shaped orbit around the point. In contrast to L4 and L5, where stable equilibrium exists, the points L1, L2, L3 are positions of unstable equilibrium. Any object orbiting at L1, L2, or L3 will tend to fall out of orbit, it is common to orbiting the L4 and L5 points of natural orbital systems. These are called "trojans". In the 20th century, asteroids discovered orbiting at the Sun–Jupiter L4 and L5 points were named after characters from Homer's Iliad. Asteroids at the L4 point, which leads Jupiter, are referred to as the "Greek camp", whereas those at the L5 point are referred to as the "Trojan camp". Other examples of natural objects orbiting at Lagrange points: The Sun–Earth L4 and L5 points contain interplanetary dust and at least one asteroid, 2010 TK7, detected in October 2010 by Wide-field Infrared Survey Explorer and announced during July 2011.
The Earth–Moon L4 and
The Jupiter trojans called Trojan asteroids or 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 two stable Lagrange points: L4, lying 60° ahead of the planet in its orbit, 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 first Jupiter trojan discovered, 588 Achilles, was spotted in 1906 by German astronomer Max Wolf. A total of 7,040 Jupiter trojans have been found as of October 2018. By convention, they are each named from Greek mythology after a figure of the Trojan War, hence the name "Trojan"; the total number of Jupiter trojans larger than 1 km in diameter is believed to be about 1 million equal to the number of asteroids larger than 1 km in the asteroid belt. Like main-belt asteroids, Jupiter trojans form families. Jupiter trojans are dark bodies with featureless spectra.
No firm evidence of the presence of water, or any other specific compound on their surface has been obtained, but it is thought that they are coated in tholins, organic polymers formed by the Sun's radiation. The Jupiter trojans' densities vary from 0.8 to 2.5 g·cm−3. Jupiter trojans are thought to have been captured into their orbits during the early stages of the Solar System's formation or later, during the migration of giant planets; the term "Trojan Asteroid" refers to the asteroids co-orbital with Jupiter, but the general term "trojan" is sometimes more applied to other small Solar System bodies with similar relationships to larger bodies: for example, there are both Mars trojans and Neptune trojans, as well as a recently-discovered Earth trojan. The term "Trojan asteroid" is understood to mean the Jupiter trojans because the first Trojans were discovered near Jupiter's orbit and Jupiter has by far the most known Trojans. In 1772, Italian-born mathematician Joseph-Louis Lagrange, in studying the restricted three-body problem, predicted that a small body sharing an orbit with a planet but lying 60° ahead or behind it will be trapped near these points.
The trapped body will librate around the point of equilibrium in a tadpole or horseshoe orbit. These leading and trailing points are called the L5 Lagrange points; the first asteroids trapped in Lagrange points were observed more than a century after Lagrange's hypothesis. Those associated with Jupiter were the first to be discovered. E. E. Barnard made the first recorded observation of a trojan, 1999 RM11, in 1904, but neither he nor others appreciated its significance at the time. Barnard believed he had seen the discovered Saturnian satellite Phoebe, only two arc-minutes away in the sky at the time, or an asteroid; the object's identity was not understood until its orbit was calculated in 1999. The first accepted discovery of a trojan occurred in February 1906, when astronomer Max Wolf of Heidelberg-Königstuhl State Observatory discovered an asteroid at the L4 Lagrangian point of the Sun–Jupiter system named 588 Achilles. In 1906–1907 two more Jupiter trojans were found by fellow German astronomer August Kopff.
Hektor, like Achilles, belonged to the L4 swarm, whereas Patroclus was the first asteroid known to reside at the L5 Lagrangian point. By 1938, 11 Jupiter trojans had been detected; this number increased to 14 only in 1961. As instruments improved, the rate of discovery grew rapidly: by January 2000, a total of 257 had been discovered; as of October 2018 there are 4,601 known Jupiter trojans at L4 and 2,439 at L5. The custom of naming all asteroids in Jupiter's L4 and L5 points after famous heroes of the Trojan War was suggested by Johann Palisa of Vienna, the first to calculate their orbits. Asteroids in the leading orbit are named after Greek heroes, those at the trailing orbit are named after the heroes of Troy; the asteroids 617 Patroclus and 624 Hektor were named before the Greece/Troy rule was devised, resulting in a Greek spy in the Trojan node and a Trojan spy in the Greek node. Estimates of the total number of Jupiter trojans are based on deep surveys of limited areas of the sky; the L4 swarm is believed to hold between 160–240,000 asteroids with diameters larger than 2 km and about 600,000 with diameters larger than 1 km.
If the L5 swarm contains a comparable number of objects, there are more than 1 million Jupiter trojans 1 km in size or larger. For the objects brighter than absolute magnitude 9.0 the population is complete. These numbers are similar to that of comparable asteroids in the asteroid belt; the total mass of the Jupiter trojans is estimated at 0.0001 of the mass of Earth or one-fifth of the mass of the asteroid belt. Two more recent studies indicate that the above numbers may overestimate the number of Jupiter trojans by several-fold; this overestimate is caused by the assumption that all Jupiter trojans have a low albedo of about 0.04, whereas small bodies may have an average albedo as high as 0.12. According to the new estimates, the total number of Jupiter trojans with a diameter larger than 2 km is 6,300 ± 1,000 and 3,400 ± 500 in the L4 and L5 swarms, respectively; these numbers would be reduced by a factor of 2 if small Jupiter trojans are more reflective than large ones. The number of Jupiter trojans observed in the L4
The ecliptic is the mean plane of the apparent path in the Earth's sky that the Sun follows over the course of one year. This plane of reference is coplanar with Earth's orbit around the Sun; the ecliptic is not noticeable from Earth's surface because the planet's rotation carries the observer through the daily cycles of sunrise and sunset, which obscure the Sun's apparent motion against the background of stars during the year. The motions as described above are simplifications. Due to the movement of Earth around the Earth–Moon center of mass, the apparent path of the Sun wobbles with a period of about one month. Due to further perturbations by the other planets of the Solar System, the Earth–Moon barycenter wobbles around a mean position in a complex fashion; the ecliptic is the apparent path of the Sun throughout the course of a year. Because Earth takes one year to orbit the Sun, the apparent position of the Sun takes one year to make a complete circuit of the ecliptic. With more than 365 days in one year, the Sun moves a little less than 1° eastward every day.
This small difference in the Sun's position against the stars causes any particular spot on Earth's surface to catch up with the Sun about four minutes each day than it would if Earth would not orbit. Again, this is a simplification, based on a hypothetical Earth that orbits at uniform speed around the Sun; the actual speed with which Earth orbits the Sun varies during the year, so the speed with which the Sun seems to move along the ecliptic varies. For example, the Sun is north of the celestial equator for about 185 days of each year, south of it for about 180 days; the variation of orbital speed accounts for part of the equation of time. Because Earth's rotational axis is not perpendicular to its orbital plane, Earth's equatorial plane is not coplanar with the ecliptic plane, but is inclined to it by an angle of about 23.4°, known as the obliquity of the ecliptic. If the equator is projected outward to the celestial sphere, forming the celestial equator, it crosses the ecliptic at two points known as the equinoxes.
The Sun, in its apparent motion along the ecliptic, crosses the celestial equator at these points, one from south to north, the other from north to south. The crossing from south to north is known as the vernal equinox known as the first point of Aries and the ascending node of the ecliptic on the celestial equator; the crossing from north to south is descending node. The orientation of Earth's axis and equator are not fixed in space, but rotate about the poles of the ecliptic with a period of about 26,000 years, a process known as lunisolar precession, as it is due to the gravitational effect of the Moon and Sun on Earth's equatorial bulge; the ecliptic itself is not fixed. The gravitational perturbations of the other bodies of the Solar System cause a much smaller motion of the plane of Earth's orbit, hence of the ecliptic, known as planetary precession; the combined action of these two motions is called general precession, changes the position of the equinoxes by about 50 arc seconds per year.
Once again, this is a simplification. Periodic motions of the Moon and apparent periodic motions of the Sun cause short-term small-amplitude periodic oscillations of Earth's axis, hence the celestial equator, known as nutation; this adds a periodic component to the position of the equinoxes. Obliquity of the ecliptic is the term used by astronomers for the inclination of Earth's equator with respect to the ecliptic, or of Earth's rotation axis to a perpendicular to the ecliptic, it is about 23.4° and is decreasing 0.013 degrees per hundred years due to planetary perturbations. The angular value of the obliquity is found by observation of the motions of Earth and other planets over many years. Astronomers produce new fundamental ephemerides as the accuracy of observation improves and as the understanding of the dynamics increases, from these ephemerides various astronomical values, including the obliquity, are derived; until 1983 the obliquity for any date was calculated from work of Newcomb, who analyzed positions of the planets until about 1895: ε = 23° 27′ 08″.26 − 46″.845 T − 0″.0059 T2 + 0″.00181 T3 where ε is the obliquity and T is tropical centuries from B1900.0 to the date in question.
From 1984, the Jet Propulsion Laboratory's DE series of computer-generated ephemerides took over as the fundamental ephemeris of the Astronomical Almanac. Obliquity based on DE200, which analyzed observations from 1911 to 1979, was calculated: ε = 23° 26′ 21″.45 − 46″.815 T − 0″.0006 T2 + 0″.00181 T3 where hereafter T is Julian centuries from J2000.0. JPL's fundamental ephemerides have been continually updated; the Astronomical Almanac for 2010 specifies:ε = 23° 26′ 21″.406 − 46″.836769 T − 0″.0001831 T2 + 0″.00200340 T3 − 0″.576×10−6 T4 − 4″.34×10−8 T5 These expressions for the obliquity are intended for high precision over a short time span ± several centuries. J. Laskar computed an expression to order T10 good to 0″.04/1000 years over 10,000 years. All of these expressions are for the mean obliquity, that is, without the nutation of the equator included; the true or instantaneous obliquity includes the nutation. Most of the major bodies of the Solar System o
The Panoramic Survey Telescope and Rapid Response System located at Haleakala Observatory, Hawaii, USA, consists of astronomical cameras, telescopes and a computing facility, surveying the sky for moving or variable objects on a continual basis, producing accurate astrometry and photometry of already-detected objects. In January 2019 the second Pan-STARRS data release was announced. At 1.6 petabytes, it is the largest volume of astronomical data released. The Pan-STARRS Project is a collaboration between the University of Hawaii Institute for Astronomy, MIT Lincoln Laboratory, Maui High Performance Computing Center and Science Applications International Corporation. Telescope construction was funded by the U. S. Air Force. By detecting differences from previous observations of the same areas of the sky, Pan-STARRS is discovering a large number of new asteroids, variable stars and other celestial objects, its primary mission is now to detect Near-Earth Objects that threaten impact events and it is expected to create a database of all objects visible from Hawaii down to apparent magnitude 24.
Construction of Pan-STARRS was funded in large part by the United States Air Force through their Research Labs. Additional funding to complete Pan-STARRS2 came from the NASA Near Earth Object Observation Program. Most of the funding presently used to operate the Pan-STARRS telescopes comes from the NASA Near Earth Object Observation Program; the Pan-STARRS NEO survey searches all the sky north of declination −47.5. The first Pan-STARRS telescope is located at the summit of Haleakalā on Maui and went online on December 6, 2008, under the administration of the University of Hawaii. PS1 began full-time science observations on May 13, 2010, the PS1 Science Mission ran until March 2014. Operations were funded by the PS1 Science Consortium, PS1SC, a consortium including the Max Planck Society in Germany, National Central University in Taiwan, Edinburgh and Queen's Belfast Universities in the UK, Johns Hopkins and Harvard Universities in the United States and the Las Cumbres Observatory Global Telescope Network.
Consortium observations for the all sky survey were completed in April 2014. Having completed PS1, the Pan-STARRS Project focused on building Pan-STARRS 2, for which first light was achieved in 2013, with full science operations scheduled for 2014 and the full array of four telescopes, sometimes called PS4. Completing the array of four telescopes is estimated at a total cost of US$100 million for the entire array; as of mid-2014, Pan-STARRS 2 was in the process of being commissioned. In the wake of substantial funding problems, no clear timeline existed for additional telescopes beyond the second. In March 2018, Pan-STARRS 2 was credited by the Minor Planet Center for the discovery of the hazardous Apollo asteroid 2015 JA2, its first minor-planet discovery made at Haleakala on 13 May 2015. Pan-STARRS consists of two 1.8 m Ritchey–Chrétien telescopes located at Haleakala in Hawaii. The initial telescope, PS1, saw first light using a low-resolution camera in June 2006; the telescope has a 3° field of view, large for telescopes of this size, is equipped with the largest digital camera built, recording 1.4 billion pixels per image.
The focal plane has 60 separately mounted close packed CCDs arranged in an 8 × 8 array. The corner positions are not populated; each CCD device, called an Orthogonal Transfer Array, has 4800 × 4800 pixels, separated into 64 cells, each of 600 × 600 pixels. This gigapixel camera or ` GPC' saw first light on August 2007, imaging the Andromeda Galaxy. After initial technical difficulties that were mostly solved, PS1 began full operation on May 13, 2010. Nick Kaiser, principal investigator of the Pan-STARRS project, summed it up saying “PS1 has been taking science-quality data for six months, but now we are doing it dusk-to-dawn every night.”. The PS1 images however remain less sharp than planned, which affects some scientific uses of the data; each image requires about 2 gigabytes of storage and exposure times will be 30 to 60 seconds, with an additional minute or so used for computer processing. Since images will be taken on a continuous basis, it is expected that 10 Terabytes of data will be acquired by PS4 every night.
Comparing against a database of known unvarying objects compiled from earlier observations will yield objects of interest: anything that has changed brightness and/or position for any reason. As of June 30/10 University of Hawaii in Honolulu received an $8.4 million contract modification under the PanSTARRS multi-year program to develop and deploy a telescope data management system for the project. At this time, all funds have been committed The large field of view of the telescopes and the short exposure times enable 6000 square degrees of sky to be imaged every night; the entire sky is 4π steradians, or 4π × ² ≈ 41,253.0 square degrees, of which about 30,000 square degrees are visible from Hawaii, which means that the entire sky can be imaged in a period of 40 hours. Given the need to avoid times when the Moon is bright, this means that an area equivalent to the entire sky will be surveyed four times a month, unprecedented. By the end of its initial three-year mission in April 2014, PS1 had imaged the sky 12 times in each of 5 filters.
Pan-STARRS is mostly funded by a grant