Semi-major and semi-minor axes
In geometry, the major axis of an ellipse is its longest diameter, a line segment that runs through the center and both foci, with ends at the widest points of the perimeter. The semi-major axis is one half of the axis, and thus runs from the centre, through a focus. Essentially, it is the radius of an orbit at the two most distant points. For the special case of a circle, the axis is the radius. One can think of the axis as an ellipses long radius. The semi-major axis of a hyperbola is, depending on the convention, thus it is the distance from the center to either vertex of the hyperbola. A parabola can be obtained as the limit of a sequence of ellipses where one focus is fixed as the other is allowed to move arbitrarily far away in one direction. Thus a and b tend to infinity, a faster than b, the semi-minor axis is a line segment associated with most conic sections that is at right angles with the semi-major axis and has one end at the center of the conic section. It is one of the axes of symmetry for the curve, in an ellipse, the one, in a hyperbola.
The semi-major axis is the value of the maximum and minimum distances r max and r min of the ellipse from a focus — that is. In astronomy these extreme points are called apsis, the semi-minor axis of an ellipse is the geometric mean of these distances, b = r max r min. The eccentricity of an ellipse is defined as e =1 − b 2 a 2 so r min = a, r max = a. Now consider the equation in polar coordinates, with one focus at the origin, the mean value of r = ℓ / and r = ℓ /, for θ = π and θ =0 is a = ℓ1 − e 2. In an ellipse, the axis is the geometric mean of the distance from the center to either focus. The semi-minor axis of an ellipse runs from the center of the ellipse to the edge of the ellipse, the semi-minor axis is half of the minor axis. The minor axis is the longest line segment perpendicular to the axis that connects two points on the ellipses edge. The semi-minor axis b is related to the axis a through the eccentricity e. A parabola can be obtained as the limit of a sequence of ellipses where one focus is fixed as the other is allowed to move arbitrarily far away in one direction
Orders of magnitude (length)
The following are examples of orders of magnitude for different lengths. To help compare different orders of magnitude, the following list describes various lengths between 1. 6×10−35 meters and 101010122 meters,100 pm –1 Ångström 120 pm – radius of a gold atom 150 pm – Length of a typical covalent bond. 280 pm – Average size of the water molecule 298 pm – radius of a caesium atom, light travels 1 metre in 1⁄299,792,458, or 3. 3356409519815E-9 of a second. 25 metres – wavelength of the broadcast radio shortwave band at 12 MHz 29 metres – height of the lighthouse at Savudrija, Slovenia. 31 metres – wavelength of the broadcast radio shortwave band at 9.7 MHz 34 metres – height of the Split Point Lighthouse in Aireys Inlet, Australia. 1 kilometre is equal to,1,000 metres 0.621371 miles 1,093.61 yards 3,280.84 feet 39,370.1 inches 100,000 centimetres 1,000,000 millimetres Side of a square of area 1 km2. Radius of a circle of area π km2,1.637 km – deepest dive of Lake Baikal in Russia, the worlds largest fresh water lake.
2.228 km – height of Mount Kosciuszko, highest point in Australia Most of Manhattan is from 3 to 4 km wide, farsang, a modern unit of measure commonly used in Iran and Turkey. Usage of farsang before 1926 may be for a precise unit derived from parasang. It is the altitude at which the FAI defines spaceflight to begin, to help compare orders of magnitude, this page lists lengths between 100 and 1,000 kilometres. 7.9 Gm – Diameter of Gamma Orionis 9, the newly improved measurement was 30% lower than the previous 2007 estimate. The size was revised in 2012 through improved measurement techniques and its faintness gives us an idea how our Sun would appear when viewed from even so close a distance as this. 350 Pm –37 light years – Distance to Arcturus 373.1 Pm –39.44 light years - Distance to TRAPPIST-1, a star recently discovered to have 7 planets around it. 400 Pm –42 light years – Distance to Capella 620 Pm –65 light years – Distance to Aldebaran This list includes distances between 1 and 10 exametres.
13 Em –1,300 light years – Distance to the Orion Nebula 14 Em –1,500 light years – Approximate thickness of the plane of the Milky Way galaxy at the Suns location 30.8568 Em –3,261. At this scale, expansion of the universe becomes significant, Distance of these objects are derived from their measured redshifts, which depends on the cosmological models used. At this scale, expansion of the universe becomes significant, Distance of these objects are derived from their measured redshifts, which depends on the cosmological models used. 590 Ym –62 billion light years – Cosmological event horizon, displays orders of magnitude in successively larger rooms Powers of Ten Travel across the Universe
A minor-planet moon is an astronomical object that orbits a minor planet as its natural satellite. It is thought that many asteroids and Kuiper belt objects may possess moons, the first modern era mention of the possibility of an asteroid satellite was in connection with an occultation of the bright star Gamma Ceti by the minor planet Hebe in 1977. The observer, amateur astronomer Paul D. Maley, detected an unmistakable 0.5 second disappearance of this naked eye star from a site near Victoria, many hours later, several observations were reported in Mexico attributed to the occultation by Hebe itself. Although not confirmed this documents the first formally documented case of a companion of an asteroid. As of October 2016, there are over 300 minor planets known to have moons, in addition to the terms satellite and moon, the term binary is sometimes used for minor planets with moons, and triple for minor planets with two moons. If one object is much bigger it can be referred to as the primary, when binary minor planets are similar in size, the Minor Planet Center refers to them as binary companions instead of referring to the smaller body as a satellite.
A good example of a true binary is the 90 Antiope system, small satellites are often referred to as moonlets. As of February 2017, over 330 moons of planets have been discovered. For example, in 1978, stellar occultation observations were claimed as evidence of a satellite for the asteroid 532 Herculina, more-detailed imaging by the Hubble Telescope did not reveal a satellite, and the current consensus is that Herculina does not have a significant satellite. There were other reports of asteroids having companions in the following years. In 1993, the first asteroid moon was confirmed when the Galileo probe discovered the small Dactyl orbiting 243 Ida in the asteroid belt, the second was discovered around 45 Eugenia in 1998. In 2001,617 Patroclus and its same-sized companion Menoetius became the first known asteroids in the Jupiter trojans. The first trans-Neptunian binary after Pluto–Charon,1998 WW31, was resolved in 2002. Triple asteroids, or trinary asteroids, are known since 2005 and this was followed by the discovery of a second moon orbiting 45 Eugenia.
Also in 2005, the Kuiper belt object Haumea was discovered to have two moons, making it the second KBO after Pluto known to have more than one moon, additionally,216 Kleopatra and 93 Minerva were discovered to be trinary asteroids in 2008 and 2009 respectively. Since the first few trinary asteroids were discovered, more continue to be discovered at a rate of one a year. Most recently discovered was a moon orbiting the belt asteroid 130 Elektra. List of multiple planets, The data about the populations of binary objects are still patchy
Jet Propulsion Laboratory
The Jet Propulsion Laboratory is a federally funded research and development center and NASA field center in La Cañada Flintridge and Pasadena, United States. The JPL is managed by the nearby California Institute of Technology for NASA, the laboratorys primary function is the construction and operation of planetary robotic spacecraft, though it conducts Earth-orbit and astronomy missions. It is responsible for operating NASAs Deep Space Network and they are responsible for managing the JPL Small-Body Database, and provides physical data and lists of publications for all known small Solar System bodies. The JPLs Space Flight Operations Facility and Twenty-Five-Foot Space Simulator are designated National Historic Landmarks, JPL traces its beginnings to 1936 in the Guggenheim Aeronautical Laboratory at the California Institute of Technology when the first set of rocket experiments were carried out in the Arroyo Seco. Malinas thesis advisor was engineer/aerodynamicist Theodore von Kármán, who arranged for U. S.
Army financial support for this GALCIT Rocket Project in 1939. In 1941, Parsons, Martin Summerfield, in 1943, von Kármán, Malina and Forman established the Aerojet Corporation to manufacture JATO motors. The project took on the name Jet Propulsion Laboratory in November 1943, during JPLs Army years, the laboratory developed two deployed weapon systems, the MGM-5 Corporal and MGM-29 Sergeant intermediate range ballistic missiles. These missiles were the first US ballistic missiles developed at JPL and it developed a number of other weapons system prototypes, such as the Loki anti-aircraft missile system, and the forerunner of the Aerobee sounding rocket. At various times, it carried out testing at the White Sands Proving Ground, Edwards Air Force Base. A lunar lander was developed in 1938-39 which influenced design of the Apollo Lunar Module in the 1960s. The team lost that proposal to Project Vanguard, and instead embarked on a project to demonstrate ablative re-entry technology using a Jupiter-C rocket.
They carried out three successful flights in 1956 and 1957. Using a spare Juno I, the two organizations launched the United States first satellite, Explorer 1, on February 1,1958, JPL was transferred to NASA in December 1958, becoming the agencys primary planetary spacecraft center. JPL engineers designed and operated Ranger and Surveyor missions to the Moon that prepared the way for Apollo, JPL led the way in interplanetary exploration with the Mariner missions to Venus and Mercury. In 1998, JPL opened the Near-Earth Object Program Office for NASA, as of 2013, it has found 95% of asteroids that are a kilometer or more in diameter that cross Earths orbit. JPL was early to employ women mathematicians, in the 1940s and 1950s, using mechanical calculators, women in an all-female computations group performed trajectory calculations. In 1961, JPL hired Dana Ulery as their first woman engineer to work alongside male engineers as part of the Ranger and Mariner mission tracking teams, when founded, JPLs site was a rocky flood-plain just outside the city limits of Pasadena.
Almost all of the 177 acres of the U. S, the city of La Cañada Flintridge, California was incorporated in 1976, well after JPL attained international recognition with a Pasadena address
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, compact families can have only about ten identified members. About 33% to 35% of asteroids in the belt are family members. There are about 20 to 30 reliably recognized families, with tens of less certain groupings. 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 typically consist of a large body and a swarm of asteroids that are much smaller. Some families have complex structures which are not satisfactorily explained at the moment. Due to the method of origin, all the members have closely matching compositions for most families, notable exceptions are those families which formed from a large differentiated parent body. Asteroid families are thought to have lifetimes of the order of a billion years and this is significantly shorter than the Solar Systems age, so few if any are relics of the early Solar System. Such small asteroids become subject to such as the Yarkovsky effect that can push them towards orbital resonances with Jupiter over time. Once there, they are relatively 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, and this is the basis of the age determinations and it is supposed that many very old families have lost all the smaller and medium-sized members, leaving only a few of the largest intact.
A suggested example of old family remains are the 9 Metis and 113 Amalthea pair. Further evidence for a 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, when the orbital elements of main belt asteroids are plotted, a number of distinct concentrations are seen against the rather uniform background distribution of generic asteroids. These concentrations are the asteroid families, the proper elements are related constants of motion that remain almost constant for times of at least tens of millions of years, and perhaps longer
Jupiter is the fifth planet from the Sun and the largest in the Solar System. It is a giant planet with a mass one-thousandth that of the Sun and Saturn are gas giants, the other two giant planets and Neptune are ice giants. Jupiter has been known to astronomers since antiquity, the Romans named it after their god Jupiter. Jupiter is primarily composed of hydrogen with a quarter of its mass being helium and it may have a rocky core of heavier elements, but like the other giant planets, Jupiter lacks a well-defined solid surface. Because of its rotation, the planets shape is that of an oblate spheroid. The outer atmosphere is visibly segregated into several bands at different latitudes, resulting in turbulence, a prominent result is the Great Red Spot, a giant storm that is known to have existed since at least the 17th century when it was first seen by telescope. Surrounding Jupiter is a faint planetary ring system and a powerful magnetosphere, Jupiter has at least 67 moons, including the four large Galilean moons discovered by Galileo Galilei in 1610.
Ganymede, the largest of these, has a greater than that of the planet Mercury. Jupiter has been explored on several occasions by robotic spacecraft, most notably during the early Pioneer and Voyager flyby missions and by the Galileo orbiter. In late February 2007, Jupiter was visited by the New Horizons probe, the latest probe to visit the planet is Juno, which entered into orbit around Jupiter on July 4,2016. Future targets for exploration in the Jupiter system include the probable ice-covered liquid ocean of its moon Europa and its neighbor planets may have formed from fragments of planets after collisions with Jupiter destroyed those super-Earths near the Sun. Astronomers have discovered nearly 500 planetary systems with multiple planets, Jupiter moving out of the inner Solar System would have allowed the formation of inner planets, including Earth. Jupiter is composed primarily of gaseous and liquid matter and it is the largest of the four giant planets in the Solar System and hence its largest planet.
It has a diameter of 142,984 km at its equator, the average density of Jupiter,1.326 g/cm3, is the second highest of the giant planets, but lower than those of the four terrestrial planets. Jupiters upper atmosphere is about 88–92% hydrogen and 8–12% helium by percent volume of gas molecules, a helium atom has about four times as much mass as a hydrogen atom, so the composition changes when described as the proportion of mass contributed by different atoms. Thus, Jupiters atmosphere is approximately 75% hydrogen and 24% helium by mass, the atmosphere contains trace amounts of methane, water vapor and silicon-based compounds. There are traces of carbon, hydrogen sulfide, oxygen, the outermost layer of the atmosphere contains crystals of frozen ammonia. The interior contains denser materials - by mass it is roughly 71% hydrogen, 24% helium, through infrared and ultraviolet measurements, trace amounts of benzene and other hydrocarbons have been found
University of Pisa
The University of Pisa is an Italian public research university located in Pisa, Italy. It was founded in 1343 by an edict of Pope Clement VI and it is the 19th oldest extant university in the world and the 10th oldest in Italy. The prestigious university is ranked within the top 10 nationally and the top 400 in the according to the ARWU. It houses the Orto botanico di Pisa, Europes oldest academic botanical garden, the University of Pisa is part of the Pisa University System, which includes the Scuola Normale Superiore and the SantAnna School of Advanced Studies. The university has about 50,000 students and its the only university in Italy which has become a member of the prestigious Universities Research Association. In 2013, the University of Pisa finished with La Sapienza University of Rome in first place among the Italian universities, the University of Pisa was officially established on September 3,1343. However, a number of scholars claim its origin back to the 11th century. The following century formed the first documents to prove the presence of doctors of medicine, the earliest evidence of a Pisan Studium dates to 1338, when jurist Ranieri Arsendi transferred to Pisa from Bologna.
He, along with Bartolo da Sassoferrato, a lecturer in law, were paid by the municipality to teach public lessons. Pisa was one of the first European universities to boast this papal attestation, the first taught subjects were theology, civil law, canon law and medicine. In 1355, Francesco da Buti, the commentator of Dantes Divine Comedy. Pisa and its Studium underwent a period of crisis around the turn of the 15th century, in 1473, thanks to Lorenzo de Medici, the Pisan Studium resumed its systematic development, and the construction of a building for holding lessons was provided for in 1486. The building — known as Palazzo della Sapienza — was located in the 14th-century Piazza del Grano, the image of a cherub was placed above the gate DellAbbondanza, leading to the piazza, and today is still the symbol of the university. Following the rebellion and the war against Florence in 1494, the Pisan Studium suffered a period of decline and was transferred to Pistoia and Florence. The ceremonial reopening of the university on November 1,1543, the quality of the university was furthered by the statute of 1545 and the Pisan Athenaeum became one of the most significant in Europe for teaching and research.
The chair of Semplici was held by Luca Ghini, founder of the worlds first botanical gardens and he was succeeded by Andrea Cesalpino, who pioneered the first scientific methodology for the classification of plants, and is considered a forerunner in the discovery of blood circulation. Gabriele Falloppio and Marcello Malpighi lectured in anatomy and medicine, galileo Galilei, who was born and studied in Pisa, became professor of mathematics at the Pisan Studium in 1589. The universitys role as an institution became more accentuated during the Medici Grand Duchy period
The astronomical unit is a unit of length, roughly the distance from Earth to the Sun. However, that varies as Earth orbits the Sun, from a maximum to a minimum. Originally conceived as the average of Earths aphelion and perihelion, it is now defined as exactly 149597870700 metres, the astronomical unit is used primarily as a convenient yardstick for measuring distances within the Solar System or around other stars. However, it is a component in the definition of another unit of astronomical length. A variety of symbols and abbreviations have been in use for the astronomical unit. In a 1976 resolution, the International Astronomical Union used the symbol A for the astronomical unit, in 2006, the International Bureau of Weights and Measures recommended ua as the symbol for the unit. In 2012, the IAU, noting that various symbols are presently in use for the astronomical unit, in the 2014 revision of the SI Brochure, the BIPM used the unit symbol au. In ISO 80000-3, the symbol of the unit is ua.
Earths orbit around the Sun is an ellipse, the semi-major axis of this ellipse is defined to be half of the straight line segment that joins the aphelion and perihelion. The centre of the sun lies on this line segment. In addition, it mapped out exactly the largest straight-line distance that Earth traverses over the course of a year, knowing Earths shift and a stars shift enabled the stars distance to be calculated. But all measurements are subject to some degree of error or uncertainty, improvements in precision have always been a key to improving astronomical understanding. Improving measurements were continually checked and cross-checked by means of our understanding of the laws of celestial mechanics, the expected positions and distances of objects at an established time are calculated from these laws, and assembled into a collection of data called an ephemeris. NASAs Jet Propulsion Laboratory 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.
Equivalently, by definition, one AU is the radius of an unperturbed circular Newtonian orbit about the sun of a particle having infinitesimal mass. As with all measurements, these rely on measuring the time taken for photons to be reflected from an object. However, for precision the calculations require adjustment for such as the motions of the probe. In addition, the measurement of the time itself must be translated to a scale that accounts for relativistic time dilation
A near-Earth object is any small Solar System body whose orbit brings it into proximity with Earth. By definition, a solar system body is a NEO if its closest approach to the Sun is less than 1.3 astronomical unit and it is now widely accepted that collisions in the past have had a significant role in shaping the geological and biological history of the Earth. NEOs have become of increased interest since the 1980s because of increased awareness of the potential danger some of the asteroids or comets pose, and mitigations are being researched. In January 2016, NASA announced the Planetary Defense Coordination Office to track NEOs larger than 30 to 50 meters in diameter and coordinate an effective threat response, NEAs have orbits that lie partly between 0.983 and 1.3 AU away from the Sun. When a NEA is detected it is submitted to the IAUs Minor Planet Center for cataloging, some NEAs orbits intersect that of Earths so they pose a collision danger. The United States, European Union, and other nations are currently scanning for NEOs in an effort called Spaceguard.
In the United States and since 1998, NASA has a mandate to catalogue all NEOs that are at least 1 kilometer wide. In 2006, it was estimated that 20% of the objects had not yet been found. In 2011, largely as a result of NEOWISE, it was estimated that 93% of the NEAs larger than 1 km had been found, as of 5 February 2017, there have been 875 NEAs larger than 1 km discovered, of which 157 are potentially hazardous. The inventory is much less complete for smaller objects, which still have potential for scale, though not global. Potentially hazardous objects are defined based on parameters that measure the objects potential to make threatening close approaches to the Earth. Mostly objects with an Earth minimum orbit intersection distance of 0.05 AU or less, objects that cannot approach closer to the Earth than 0.05 AU, or are smaller than about 150 m in diameter, are not considered PHOs. This makes them a target for exploration. As of 2016, three near-Earth objects have been visited by spacecraft, more recently, a typical frame of reference for looking at NEOs has been through the scientific concept of risk.
In this frame, the risk that any near-Earth object poses is typically seen through a lens that is a function of both the culture and the technology of human society, NEOs have been understood differently throughout history. Each time an NEO is observed, a different risk was posed and it is not just a matter of scientific knowledge. Such perception of risk is thus a product of religious belief, philosophic principles, scientific understanding, technological capabilities, and even economical resourcefulness.03 E −0.4 megatonnes. For instance, it gives the rate for bolides of 10 megatonnes or more as 1 per thousand years, the authors give a rather large uncertainty, due in part to uncertainties in determining the energies of the atmospheric impacts that they used in their determination