An apsis is an extreme point in an objects orbit. The word comes via Latin from Greek and is cognate with apse, for elliptic orbits about a larger body, there are two apsides, named with the prefixes peri- and ap-, or apo- added to a reference to the thing being orbited. For a body orbiting the Sun, the point of least distance is the perihelion, the terms become periastron and apastron when discussing orbits around other stars. For any satellite of Earth including the Moon the point of least distance is the perigee, for objects in Lunar orbit, the point of least distance is the pericynthion and the greatest distance the apocynthion. For any orbits around a center of mass, there are the terms pericenter and apocenter and apoapsis are equivalent alternatives. A straight line connecting the pericenter and apocenter is the line of apsides and this is the major axis of the ellipse, its greatest diameter. For a two-body system the center of mass of the lies on this line at one of the two foci of the ellipse.
When one body is larger than the other it may be taken to be at this focus. Historically, in systems, apsides were measured from the center of the Earth. In orbital mechanics, the apsis technically refers to the distance measured between the centers of mass of the central and orbiting body. However, in the case of spacecraft, the family of terms are used to refer to the orbital altitude of the spacecraft from the surface of the central body. The arithmetic mean of the two limiting distances is the length of the axis a. The geometric mean of the two distances is the length of the semi-minor axis b, the geometric mean of the two limiting speeds is −2 ε = μ a which is the speed of a body in a circular orbit whose radius is a. The words pericenter and apocenter are often seen, although periapsis/apoapsis are preferred in technical usage, various related terms are used for other celestial objects. The -gee, -helion and -astron and -galacticon forms are used in the astronomical literature when referring to the Earth, stars.
The suffix -jove is occasionally used for Jupiter, while -saturnium has very rarely used in the last 50 years for Saturn. The -gee form is used as a generic closest approach to planet term instead of specifically applying to the Earth. During the Apollo program, the terms pericynthion and apocynthion were used when referring to the Moon, regarding black holes, the term peri/apomelasma was used by physicist Geoffrey A. Landis in 1998 before peri/aponigricon appeared in the scientific literature in 2002
In astronomy, declination is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. Declinations angle is measured north or south of the celestial equator, the root of the word declination means a bending away or a bending down. It comes from the root as the words incline and recline. Declination in astronomy is comparable to geographic latitude, projected onto the celestial sphere, points north of the celestial equator have positive declinations, while those south have negative declinations. Any units of measure can be used for declination, but it is customarily measured in the degrees, minutes. Declinations with magnitudes greater than 90° do not occur, because the poles are the northernmost and southernmost points of the celestial sphere, the Earths axis rotates slowly westward about the poles of the ecliptic, completing one circuit in about 26,000 years. This effect, known as precession, causes the coordinates of stationary celestial objects to change continuously, equatorial coordinates are inherently relative to the year of their observation, and astronomers specify them with reference to a particular year, known as an epoch.
Coordinates from different epochs must be rotated to match each other. The currently used standard epoch is J2000.0, which is January 1,2000 at 12,00 TT, the prefix J indicates that it is a Julian epoch. Prior to J2000.0, astronomers used the successive Besselian Epochs B1875.0, B1900.0, the declinations of Solar System objects change very rapidly compared to those of stars, due to orbital motion and close proximity. This similarly occurs in the Southern Hemisphere for objects with less than −90° − φ. An extreme example is the star which has a declination near to +90°. Circumpolar stars never dip below the horizon, there are other stars that never rise above the horizon, as seen from any given point on the Earths surface. Generally, if a star whose declination is δ is circumpolar for some observer, a star whose declination is −δ never rises above the horizon, as seen by the same observer. Likewise, if a star is circumpolar for an observer at latitude φ, neglecting atmospheric refraction, declination is always 0° at east and west points of the horizon.
At the north point, it is 90° − |φ|, and at the south point, from the poles, declination is uniform around the entire horizon, approximately 0°. Non-circumpolar stars are visible only during certain days or seasons of the year, the Suns declination varies with the seasons. As seen from arctic or antarctic latitudes, the Sun is circumpolar near the summer solstice, leading to the phenomenon of it being above the horizon at midnight
Earth, otherwise known as the World, or the Globe, is the third planet from the Sun and the only object in the Universe known to harbor life. It is the densest planet in the Solar System and the largest of the four terrestrial planets, according to radiometric dating and other sources of evidence, Earth formed about 4.54 billion years ago. Earths gravity interacts with objects in space, especially the Sun. During one orbit around the Sun, Earth rotates about its axis over 365 times, Earths axis of rotation is tilted, producing seasonal variations on the planets surface. The gravitational interaction between the Earth and Moon causes ocean tides, stabilizes the Earths orientation on its axis, Earths lithosphere is divided into several rigid tectonic plates that migrate across the surface over periods of many millions of years. About 71% of Earths surface is covered with water, mostly by its oceans, the remaining 29% is land consisting of continents and islands that together have many lakes and other sources of water that contribute to the hydrosphere.
The majority of Earths polar regions are covered in ice, including the Antarctic ice sheet, Earths interior remains active with a solid iron inner core, a liquid outer core that generates the Earths magnetic field, and a convecting mantle that drives plate tectonics. Within the first billion years of Earths history, life appeared in the oceans and began to affect the Earths atmosphere and surface, some geological evidence indicates that life may have arisen as much as 4.1 billion years ago. Since then, the combination of Earths distance from the Sun, physical properties, in the history of the Earth, biodiversity has gone through long periods of expansion, occasionally punctuated by mass extinction events. Over 99% of all species that lived on Earth are extinct. Estimates of the number of species on Earth today vary widely, over 7.4 billion humans live on Earth and depend on its biosphere and minerals for their survival. Humans have developed diverse societies and cultures, the world has about 200 sovereign states, the modern English word Earth developed from a wide variety of Middle English forms, which derived from an Old English noun most often spelled eorðe.
It has cognates in every Germanic language, and their proto-Germanic root has been reconstructed as *erþō, earth was written in lowercase, and from early Middle English, its definite sense as the globe was expressed as the earth. By early Modern English, many nouns were capitalized, and the became the Earth. More recently, the name is simply given as Earth. House styles now vary, Oxford spelling recognizes the lowercase form as the most common, another convention capitalizes Earth when appearing as a name but writes it in lowercase when preceded by the. It almost always appears in lowercase in colloquial expressions such as what on earth are you doing, the oldest material found in the Solar System is dated to 4. 5672±0.0006 billion years ago. By 4. 54±0.04 Gya the primordial Earth had formed, the formation and evolution of Solar System bodies occurred along with the Sun
In many fields of mathematics and physics, almost all scientific papers are self-archived on the arXiv repository. Begun on August 14,1991, arXiv. org passed the half-million article milestone on October 3,2008, by 2014 the submission rate had grown to more than 8,000 per month. The arXiv was made possible by the low-bandwidth TeX file format, around 1990, Joanne Cohn began emailing physics preprints to colleagues as TeX files, but the number of papers being sent soon filled mailboxes to capacity. Additional modes of access were added, FTP in 1991, Gopher in 1992. The term e-print was quickly adopted to describe the articles and its original domain name was xxx. lanl. gov. Due to LANLs lack of interest in the rapidly expanding technology, in 1999 Ginsparg changed institutions to Cornell University and it is now hosted principally by Cornell, with 8 mirrors around the world. Its existence was one of the factors that led to the current movement in scientific publishing known as open access. Mathematicians and scientists regularly upload their papers to arXiv.
org for worldwide access, Ginsparg was awarded a MacArthur Fellowship in 2002 for his establishment of arXiv. The annual budget for arXiv is approximately $826,000 for 2013 to 2017, funded jointly by Cornell University Library, annual donations were envisaged to vary in size between $2,300 to $4,000, based on each institution’s usage. As of 14 January 2014,174 institutions have pledged support for the period 2013–2017 on this basis, in September 2011, Cornell University Library took overall administrative and financial responsibility for arXivs operation and development. Ginsparg was quoted in the Chronicle of Higher Education as saying it was supposed to be a three-hour tour, Ginsparg remains on the arXiv Scientific Advisory Board and on the arXiv Physics Advisory Committee. The lists of moderators for many sections of the arXiv are publicly available, additionally, an endorsement system was introduced in 2004 as part of an effort to ensure content that is relevant and of interest to current research in the specified disciplines.
Under the system, for categories that use it, an author must be endorsed by an established arXiv author before being allowed to submit papers to those categories. Endorsers are not asked to review the paper for errors, new authors from recognized academic institutions generally receive automatic endorsement, which in practice means that they do not need to deal with the endorsement system at all. However, the endorsement system has attracted criticism for allegedly restricting scientific inquiry, perelman appears content to forgo the traditional peer-reviewed journal process, stating, If anybody is interested in my way of solving the problem, its all there – let them go and read about it. The arXiv generally re-classifies these works, e. g. in General mathematics, papers can be submitted in any of several formats, including LaTeX, and PDF printed from a word processor other than TeX or LaTeX. The submission is rejected by the software if generating the final PDF file fails, if any image file is too large.
ArXiv now allows one to store and modify an incomplete submission, the time stamp on the article is set when the submission is finalized
Taurus is one of the constellations of the zodiac, which means it is crossed by the plane of the ecliptic. Taurus is a large and prominent constellation in the northern hemispheres winter sky and it is one of the oldest constellations, dating back to at least the Early Bronze Age when it marked the location of the Sun during the spring equinox. Its importance to the agricultural calendar influenced various bull figures in the mythologies of Ancient Sumer, Assyria, Egypt, Greece, a number of features exist that are of interest to astronomers. Taurus hosts two of the nearest open clusters to Earth, the Pleiades and the Hyades, both of which are visible to the naked eye, at first magnitude, the red giant Aldebaran is the brightest star in the constellation. In the northwest part of Taurus is the supernova remnant Messier 1, one of the closest regions of active star formation, the Taurus-Auriga complex, crosses into the northern part of the constellation. The variable star T Tauri is the prototype of a class of pre-main-sequence stars, in September and October, Taurus is visible in the evening along the eastern horizon.
The most favorable time to observe Taurus in the sky is during the months of December. By March and April, the constellation will appear to the west during the evening twilight and this constellation forms part of the zodiac, and hence is intersected by the ecliptic. This circle across the sphere forms the apparent path of the Sun as the Earth completes its annual orbit. As the orbital plane of the Moon and the planets lie near the ecliptic, the galactic plane of the Milky Way intersects the northeast corner of the constellation and the galactic anticenter is located near the border between Taurus and Auriga. Taurus is the only constellation crossed by all three of the equator, celestial equator, and ecliptic. A ring-like galactic structure known as the Goulds Belt passes through the Taurus constellation, the recommended three-letter abbreviation for the constellation, as adopted by the International Astronomical Union in 1922, is Tau. The official constellation boundaries, as set by Eugène Delporte in 1930, are defined by a polygon of 26 segments.
In the equatorial coordinate system, the right ascension coordinates of these borders lie between 03h 23. 4m and 05h 53. 3m, while the coordinates are between 31. 10° and −1. 35°. Because a small part of the lies to the south of the celestial equator. During November, the Taurid meteor shower appears to radiate from the direction of this constellation. The Beta Taurid meteor shower occurs during the months of June and July in the daytime, between 18 and 29 October, both the Northern Taurids and the Southern Taurids are active, though the latter stream is stronger. However, between November 1 and 10, the two streams equalize, the brightest member of this constellation is Aldebaran, an orange-hued, spectral class K5 III giant star
In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet about a star or a natural satellite around a planet. Normally, orbit refers to a regularly repeating path around a body, to a close approximation and satellites follow elliptical orbits, with the central mass being orbited at a focal point of the ellipse, as described by Keplers laws of planetary motion. For ease of calculation, in most situations orbital motion is adequately approximated by Newtonian Mechanics, the apparent motions of the planets were described by European and Arabic philosophers using the idea of celestial spheres. This model posited the existence of perfect moving spheres or rings to which the stars and it assumed the heavens were fixed apart from the motion of the spheres, and was developed without any understanding of gravity. After the planets motions were accurately measured, theoretical mechanisms such as deferent. Originally geocentric it was modified by Copernicus to place the sun at the centre to help simplify the model, the model was further challenged during the 16th century, as comets were observed traversing the spheres.
The basis for the understanding of orbits was first formulated by Johannes Kepler whose results are summarised in his three laws of planetary motion. Second, he found that the speed of each planet is not constant, as had previously been thought. Third, Kepler found a relationship between the orbital properties of all the planets orbiting the Sun. For the planets, the cubes of their distances from the Sun are proportional to the squares of their orbital periods. Jupiter and Venus, for example, are respectively about 5.2 and 0.723 AU distant from the Sun, their orbital periods respectively about 11.86 and 0.615 years. The proportionality is seen by the fact that the ratio for Jupiter,5. 23/11.862, is equal to that for Venus,0. 7233/0.6152. Idealised orbits meeting these rules are known as Kepler orbits, isaac Newton demonstrated that Keplers laws were derivable from his theory of gravitation and that, in general, the orbits of bodies subject to gravity were conic sections. Newton showed that, for a pair of bodies, the sizes are in inverse proportion to their masses.
Where one body is more massive than the other, it is a convenient approximation to take the center of mass as coinciding with the center of the more massive body. Lagrange developed a new approach to Newtonian mechanics emphasizing energy more than force, in a dramatic vindication of classical mechanics, in 1846 le Verrier was able to predict the position of Neptune based on unexplained perturbations in the orbit of Uranus. This led astronomers to recognize that Newtonian mechanics did not provide the highest accuracy in understanding orbits, in relativity theory, orbits follow geodesic trajectories which are usually approximated very well by the Newtonian predictions but the differences are measurable. Essentially all the evidence that can distinguish between the theories agrees with relativity theory to within experimental measurement accuracy
In scientific analysis, in general, the term resolution is used to describe the precision with which any instrument measures and records any variable in the specimen or sample under study. The imaging systems resolution can be limited either by aberration or by diffraction causing blurring of the image and these two phenomena have different origins and are unrelated. Aberrations can be explained by geometrical optics and can in principle be solved by increasing the optical quality —, on the other hand, diffraction comes from the wave nature of light and is determined by the finite aperture of the optical elements. The lens circular aperture is analogous to a version of the single-slit experiment. The interplay between diffraction and aberration can be characterised by the point spread function, the narrower the aperture of a lens the more likely the PSF is dominated by diffraction. If the distance is greater, the two points are well resolved and if it is smaller, they are regarded as not resolved, Rayleigh defended this criteria on sources of equal strength.
Considering diffraction through an aperture, this translates into, θ =1.220 λ D where θ is the angular resolution, λ is the wavelength of light. The factor 1.220 is derived from a calculation of the position of the first dark circular ring surrounding the central Airy disc of the diffraction pattern and this number is more precisely 1.21966989. The first zero of the order-one Bessel function of the first kind J1 divided by π, the formal Rayleigh criterion is close to the empirical resolution limit found earlier by the English astronomer W. R. Dawes who tested human observers on close binary stars of equal brightness. The result, θ =4. 3% dip, modern image processing techniques including deconvolution of the point spread function allow resolution of binaries with even less angular separation. The angular resolution may be converted into a resolution, Δℓ. For a microscope, that distance is close to the length f of the objective. For this case, the Rayleigh criterion reads, Δ ℓ =1.220 f λ D. This is the size, in the plane, of smallest object that the lens can resolve.
The size is proportional to wavelength, λ, and thus, for example and this result is related to the Fourier properties of a lens.220 f λ D =1.22 λ ⋅. Since this is the radius of the Airy disk, the resolution is better estimated by the diameter,2.44 λ ⋅ Point-like sources separated by a smaller than the angular resolution cannot be resolved. A single optical telescope may have a resolution less than one arcsecond. The angular resolution R of a telescope can usually be approximated by R = λ D where λ is the wavelength of the observed radiation, the Resulting R is in radians
In astronomy, stellar classification is the classification of stars based on their spectral characteristics. Electromagnetic radiation from the star is analyzed by splitting it with a prism or diffraction grating into a spectrum exhibiting the rainbow of colors interspersed with absorption lines, each line indicates an ion of a certain chemical element, with the line strength indicating the abundance of that ion. The relative abundance of the different ions varies with the temperature of the photosphere, the spectral class of a star is a short code summarizing the ionization state, giving an objective measure of the photospheres temperature and density. Most stars are classified under the Morgan–Keenan system using the letters O, B, A, F, G, K, and M. Each letter class is subdivided using a numeric digit with 0 being hottest and 9 being coolest. The sequence has been expanded with classes for other stars and star-like objects that do not fit in the system, such as class D for white dwarfs. In the MK system, a luminosity class is added to the class using Roman numerals.
This is based on the width of absorption lines in the stars spectrum. The full spectral class for the Sun is G2V, indicating a main-sequence star with a temperature around 5,800 K, the conventional color description takes into account only the peak of the stellar spectrum. This means that the assignment of colors of the spectrum can be misleading. There are no green, indigo, or violet stars, the brown dwarfs do not literally appear brown. The modern classification system is known as the Morgan–Keenan classification, each star is assigned a spectral class from the older Harvard spectral classification and a luminosity class using Roman numerals as explained below, forming the stars spectral type. The spectral classes O through M, as well as more specialized classes discussed later, are subdivided by Arabic numerals. For example, A0 denotes the hottest stars in the A class, fractional numbers are allowed, for example, the star Mu Normae is classified as O9.7. The Sun is classified as G2, the conventional color descriptions are traditional in astronomy, and represent colors relative to the mean color of an A-class star, which is considered to be white.
The apparent color descriptions are what the observer would see if trying to describe the stars under a dark sky without aid to the eye, or with binoculars. However, most stars in the sky, except the brightest ones, red supergiants are cooler and redder than dwarfs of the same spectral type, and stars with particular spectral features such as carbon stars may be far redder than any black body. O-, B-, and A-type stars are called early type
A binary star is a star system consisting of two stars orbiting around their common barycenter. Systems of two or more stars are called multiple star systems and these systems, especially when more distant, often appear to the unaided eye as a single point of light, and are revealed as multiple by other means. Research over the last two centuries suggests that half or more of visible stars are part of star systems. The term double star is used synonymously with binary star, however. Optical doubles are so called because the two stars close together in the sky as seen from the Earth, they are almost on the same line of sight. Nevertheless, their doubleness depends only on this effect, the stars themselves are distant from one another. A double star can be revealed as optical by means of differences in their measurements, proper motions. Most known double stars have not been studied closely to determine whether they are optical doubles or they are doubles physically bound through gravitation into a multiple star system.
This determines an empirical mass-luminosity relationship from which the masses of stars can be estimated. Binary stars are often detected optically, in case they are called visual binaries. Many visual binaries have long periods of several centuries or millennia. They may be detected by indirect techniques, such as spectroscopy or astrometry, if components in binary star systems are close enough they can gravitationally distort their mutual outer stellar atmospheres. In some cases, these close binary systems can exchange mass, examples of binaries are Sirius, and Cygnus X-1. Binary stars are common as the nuclei of many planetary nebulae. This should be called a double star, and any two stars that are thus mutually connected, form the binary sidereal system which we are now to consider. By the modern definition, the binary star is generally restricted to pairs of stars which revolve around a common center of mass. Binary stars which can be resolved with a telescope or interferometric methods are known as visual binaries, for most of the known visual binary stars one whole revolution has not been observed yet, they are observed to have travelled along a curved path or a partial arc.
The more general term double star is used for pairs of stars which are seen to be together in the sky
The Doppler effect is the change in frequency or wavelength of a wave for an observer moving relative to its source. It is named after the Austrian physicist Christian Doppler, who proposed it in 1842 in Prague, a common example of Doppler shift is the change of pitch heard when a vehicle sounding a siren or horn approaches and recedes from an observer. Compared to the frequency, the received frequency is higher during the approach, identical at the instant of passing by. When the source of the waves is moving towards the observer, each wave takes slightly less time to reach the observer than the previous wave. Hence, the time between the arrival of successive wave crests at the observer is reduced, causing an increase in the frequency, while they are travelling, the distance between successive wave fronts is reduced, so the waves bunch together. The distance between wave fronts is increased, so the waves spread out. For waves that propagate in a medium, such as sound waves, the total Doppler effect may therefore result from motion of the source, motion of the observer, or motion of the medium.
Each of these effects is analyzed separately, for waves which do not require a medium, such as light or gravity in general relativity, only the relative difference in velocity between the observer and the source needs to be considered. Doppler first proposed this effect in 1842 in his treatise Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels, the hypothesis was tested for sound waves by Buys Ballot in 1845. He confirmed that the pitch was higher than the emitted frequency when the sound source approached him. Hippolyte Fizeau discovered independently the same phenomenon on electromagnetic waves in 1848, in Britain, John Scott Russell made an experimental study of the Doppler effect. The frequency is decreased if either is moving away from the other, the above formula assumes that the source is either directly approaching or receding from the observer. If the source approaches the observer at an angle, the frequency that is first heard is higher than the objects emitted frequency.
When the observer is close to the path of the object. When the observer is far from the path of the object, to understand what happens, consider the following analogy. Someone throws one ball every second at a man, assume that balls travel with constant velocity. If the thrower is stationary, the man will receive one every second. However, if the thrower is moving towards the man, he will receive balls more frequently because the balls will be spaced out