C-type asteroids are the most common variety, forming around 75% of known asteroids. They are distinguished by a low albedo because their composition includes a large amount of carbon, in addition to rocks and minerals, they occur most at the outer edge of the asteroid belt, 3.5 astronomical units from the Sun, where 80% of the asteroids are of this type, whereas only 40% of asteroids at 2 AU from the Sun are C-type. The proportion of C-types may be greater than this, because C-types are much darker than most other asteroid types except for D-types and others that are at the extreme outer edge of the asteroid belt. Asteroids of this class have spectra similar to those of carbonaceous chondrite meteorites; the latter are close in chemical composition to the Sun and the primitive solar nebula, except for the absence of hydrogen and other volatiles. Hydrated minerals are present. C-type asteroids are dark, with albedos in the 0.03 to 0.10 range. Whereas a number of S-type asteroids can be viewed with binoculars at opposition the largest C-type asteroids require a small telescope.
The brightest C-type asteroid is 324 Bamberga, but that object's high eccentricity means it reaches its maximum magnitude. Their spectra contain moderately strong ultraviolet absorption at wavelengths below about 0.4 μm to 0.5 μm, while at longer wavelengths they are featureless but reddish. The so-called "water" absorption feature of around 3 μm, which can be an indication of water content in minerals, is present; the largest unequivocally C-type asteroid is 10 Hygiea, although the SMASS classification places the largest asteroid, 1 Ceres, here as well, because that scheme lacks a G-type. In the Tholen classification, the C-type is grouped along with three less numerous types into a wider C-group of carbonaceous asteroids which contains: B-type C-type F-type G-type In the SMASS classification, the wider C-group contains the types: B-type corresponding to the Tholen B and F-types a core C-type for asteroids having the most "typical" spectra in the group Cg and Cgh types corresponding to the Tholen G-type Ch type with an absorption feature around 0.7μm Cb type corresponding to transition objects between the SMASS C and B types Asteroid spectral types
The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit, greater than 1 is a hyperbola; the term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is used for the isolated two-body problem, but extensions exist for objects following a Klemperer rosette orbit through the galaxy. In a two-body problem with inverse-square-law force, every orbit is a Kepler orbit; the eccentricity of this Kepler orbit is a non-negative number. The eccentricity may take the following values: circular orbit: e = 0 elliptic orbit: 0 < e < 1 parabolic trajectory: e = 1 hyperbolic trajectory: e > 1 The eccentricity e is given by e = 1 + 2 E L 2 m red α 2 where E is the total orbital energy, L is the angular momentum, mred is the reduced mass, α the coefficient of the inverse-square law central force such as gravity or electrostatics in classical physics: F = α r 2 or in the case of a gravitational force: e = 1 + 2 ε h 2 μ 2 where ε is the specific orbital energy, μ the standard gravitational parameter based on the total mass, h the specific relative angular momentum.
For values of e from 0 to 1 the orbit's shape is an elongated ellipse. The limit case between an ellipse and a hyperbola, when e equals 1, is parabola. Radial trajectories are classified as elliptic, parabolic, or hyperbolic based on the energy of the orbit, not the eccentricity. Radial orbits hence eccentricity equal to one. Keeping the energy constant and reducing the angular momentum, elliptic and hyperbolic orbits each tend to the corresponding type of radial trajectory while e tends to 1. For a repulsive force only the hyperbolic trajectory, including the radial version, is applicable. For elliptical orbits, a simple proof shows that arcsin yields the projection angle of a perfect circle to an ellipse of eccentricity e. For example, to view the eccentricity of the planet Mercury, one must calculate the inverse sine to find the projection angle of 11.86 degrees. Next, tilt any circular object by that angle and the apparent ellipse projected to your eye will be of that same eccentricity; the word "eccentricity" comes from Medieval Latin eccentricus, derived from Greek ἔκκεντρος ekkentros "out of the center", from ἐκ- ek-, "out of" + κέντρον kentron "center".
"Eccentric" first appeared in English in 1551, with the definition "a circle in which the earth, sun. Etc. deviates from its center". By five years in 1556, an adjectival form of the word had developed; the eccentricity of an orbit can be calculated from the orbital state vectors as the magnitude of the eccentricity vector: e = | e | where: e is the eccentricity vector. For elliptical orbits it can be calculated from the periapsis and apoapsis since rp = a and ra = a, where a is the semimajor axis. E = r a − r p r a + r p = 1 − 2 r a r p + 1 where: ra is the radius at apoapsis. Rp is the radius at periapsis; the eccentricity of an elliptical orbit can be used to obtain the ratio of the periapsis to the apoapsis: r p r a = 1 − e 1 + e For Earth, orbital eccentricity ≈ 0.0167, apoapsis= aphelion and periapsis= perihelion relative to sun. For Earth's annual orbit path, ra/rp ratio = longest_radius / shortest_radius ≈ 1.034 relative to center point of path. The eccentricity of the Earth's orbit is about 0.0167.
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
Johann Wolfgang von Goethe
Johann Wolfgang Goethe was a German writer and statesman. His works include four novels. In addition, there are numerous literary and scientific fragments, more than 10,000 letters, nearly 3,000 drawings by him extant. A literary celebrity by the age of 25, Goethe was ennobled by the Duke of Saxe-Weimar, Karl August, in 1782 after taking up residence there in November 1775 following the success of his first novel, The Sorrows of Young Werther, he was an early participant in the Sturm und Drang literary movement. During his first ten years in Weimar, Goethe was a member of the Duke's privy council, sat on the war and highway commissions, oversaw the reopening of silver mines in nearby Ilmenau, implemented a series of administrative reforms at the University of Jena, he contributed to the planning of Weimar's botanical park and the rebuilding of its Ducal Palace. In 1998 both these sites together with nine others were designated a UNESCO World Heritage site under the name Classical Weimar. Goethe's first major scientific work, the Metamorphosis of Plants, was published after he returned from a 1788 tour of Italy.
In 1791, he was made managing director of the theatre at Weimar, in 1794 he began a friendship with the dramatist and philosopher Friedrich Schiller, whose plays he premiered until Schiller's death in 1805. During this period, Goethe published Wilhelm Meister's Apprenticeship, his conversations and various common undertakings throughout the 1790s with Schiller, Johann Gottlieb Fichte, Johann Gottfried Herder, Alexander von Humboldt, Wilhelm von Humboldt, August and Friedrich Schlegel have come to be collectively termed Weimar Classicism. The German philosopher Arthur Schopenhauer named Wilhelm Meister's Apprenticeship one of the four greatest novels written, while the American philosopher and essayist Ralph Waldo Emerson selected Goethe as one of six "representative men" in his work of the same name. Goethe's comments and observations form the basis of several biographical works, notably Johann Peter Eckermann's Conversations with Goethe. Goethe's father, Johann Caspar Goethe, lived with his family in a large house in Frankfurt an Imperial Free City of the Holy Roman Empire.
Though he had studied law in Leipzig and had been appointed Imperial Councillor, he was not involved in the city's official affairs. Johann Caspar married Goethe's mother, Catharina Elizabeth Textor at Frankfurt on 20 August 1748, when he was 38 and she was 17. All their children, with the exception of Johann Wolfgang and his sister, Cornelia Friederica Christiana, born in 1750, died at early ages, his father and private tutors gave Goethe lessons in all the common subjects of their time languages. Goethe received lessons in dancing and fencing. Johann Caspar, feeling frustrated in his own ambitions, was determined that his children should have all those advantages that he had not. Although Goethe's great passion was drawing, he became interested in literature, he had a lively devotion to theater as well and was fascinated by puppet shows that were annually arranged in his home. He took great pleasure in reading works on history and religion, he writes about this period: I had from childhood the singular habit of always learning by heart the beginnings of books, the divisions of a work, first of the five books of Moses, of the'Aeneid' and Ovid's'Metamorphoses'....
If an busy imagination, of which that tale may bear witness, led me hither and thither, if the medley of fable and history and religion, threatened to bewilder me, I fled to those oriental regions, plunged into the first books of Moses, there, amid the scattered shepherd tribes, found myself at once in the greatest solitude and the greatest society. Goethe became acquainted with Frankfurt actors. Among early literary attempts, he was infatuated with Gretchen, who would reappear in his Faust and the adventures with whom he would concisely describe in Dichtung und Wahrheit, he adored Caritas Meixner, a wealthy Worms trader's daughter and friend of his sister, who would marry the merchant G. F. Schuler. Goethe studied law at Leipzig University from 1765 to 1768, he detested learning age-old judicial rules by heart, preferring instead to attend the poetry lessons of Christian Fürchtegott Gellert. In Leipzig, Goethe fell in love with Anna Katharina Schönkopf and wrote cheerful verses about her in the Rococo genre.
In 1770, he anonymously released his first collection of poems. His uncritical admiration for many contemporary poets vanished as he became interested in Gotthold Ephraim Lessing and Christoph Martin Wieland. At this time, Goethe wrote a good deal, but he threw away nearly all of these works, except for the comedy Die Mitschuldigen; the restaurant Auerbachs Keller and its legend of Faust's 1525 barrel ride impressed him so much that Auerbachs Keller became the only real place in his closet drama Faust Part One. As his studies did not progress, Goethe was forced to return to Frankfurt at the close of August 1768. Goethe became ill in Frankfurt. Durin
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
Ulrike von Levetzow
Theodore Ulrike Sophie von Levetzow, known as Baroness Ulrike von Levetzow was a friend and the last love of Johann Wolfgang von Goethe. She was born at Löbnitz in Saxony, the daughter of the ducal Mecklenburg-Schwerin chamberlain and Hofmarschall Joachim Otto Ulrich von Levetzow and his wife Amalie; the seventeen-year-old girl first met Goethe in 1821 at Marienbad and again at Carlsbad in 1822 and 1823. The poet 72, was so carried away with her wit and beauty that he thought for a time of marrying her and urged Grand Duke Karl August of Saxe-Weimar-Eisenach to ask for her hand in his name. Rejected, he left for Thuringia and addressed to her the poems which he afterward called Trilogie der Leidenschaft; these poems include the famous Marienbad Elegy. Ulrike confessed she was not prepared to marry and angrily denied a liaison with Goethe, she died at the age of 95 at Trziblitz Castle in Bohemia. Suphan, Goethe Jahrbuch, volume xxi Kirschoer, Erinnerungen an Goethes Ulrike und an die Familie von Levetzow-Rauch This article incorporates text from a publication now in the public domain: Gilman, D. C..
"article name needed". New International Encyclopedia. New York: Dodd, Mead
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