Ancient Greek includes the forms of Greek used in ancient Greece and the ancient world from around the 9th century BC to the 6th century AD. It is often divided into the Archaic period, Classical period. It is antedated in the second millennium BC by Mycenaean Greek, the language of the Hellenistic phase is known as Koine. Koine is regarded as a historical stage of its own, although in its earliest form it closely resembled Attic Greek. Prior to the Koine period, Greek of the classic and earlier periods included several regional dialects, Ancient Greek was the language of Homer and of fifth-century Athenian historians and philosophers. It has contributed many words to English vocabulary and has been a subject of study in educational institutions of the Western world since the Renaissance. This article primarily contains information about the Epic and Classical phases of the language, Ancient Greek was a pluricentric language, divided into many dialects. The main dialect groups are Attic and Ionic, Arcadocypriot, some dialects are found in standardized literary forms used in literature, while others are attested only in inscriptions.
There are several historical forms, homeric Greek is a literary form of Archaic Greek used in the epic poems, the Iliad and Odyssey, and in poems by other authors. Homeric Greek had significant differences in grammar and pronunciation from Classical Attic, the origins, early form and development of the Hellenic language family are not well understood because of a lack of contemporaneous evidence. Several theories exist about what Hellenic dialect groups may have existed between the divergence of early Greek-like speech from the common Proto-Indo-European language and the Classical period and they have the same general outline, but differ in some of the detail. The invasion would not be Dorian unless the invaders had some relationship to the historical Dorians. The invasion is known to have displaced population to the Attic-Ionic regions, the Greeks of this period believed there were three major divisions of all Greek people—Dorians and Ionians, each with their own defining and distinctive dialects.
Often non-west is called East Greek, Arcadocypriot apparently descended more closely from the Mycenaean Greek of the Bronze Age. Boeotian had come under a strong Northwest Greek influence, and can in some respects be considered a transitional dialect, thessalian likewise had come under Northwest Greek influence, though to a lesser degree. Most of the dialect sub-groups listed above had further subdivisions, generally equivalent to a city-state and its surrounding territory, Doric notably had several intermediate divisions as well, into Island Doric, Southern Peloponnesus Doric, and Northern Peloponnesus Doric. The Lesbian dialect was Aeolic Greek and this dialect slowly replaced most of the older dialects, although Doric dialect has survived in the Tsakonian language, which is spoken in the region of modern Sparta. Doric has passed down its aorist terminations into most verbs of Demotic Greek, by about the 6th century AD, the Koine had slowly metamorphosized into Medieval Greek
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
Classical physics refers to theories of physics that predate modern, more complete, or more widely applicable theories. As such, the definition of a classical theory depends on context, classical physical concepts are often used when modern theories are unnecessarily complex for a particular situation. Classical theory has at least two meanings in physics. In the context of mechanics, classical theory refers to theories of physics that do not use the quantisation paradigm. Likewise, classical field theories, such as general relativity and classical electromagnetism, are those that do not use quantum mechanics, in the context of general and special relativity, classical theories are those that obey Galilean relativity. Modern physics includes quantum theory and relativity, when applicable, a physical system can be described by classical physics when it satisfies conditions such that the laws of classical physics are approximately valid. In practice, physical objects ranging from larger than atoms and molecules, to objects in the macroscopic and astronomical realm.
Beginning at the level and lower, the laws of classical physics break down. Electromagnetic fields and forces can be described well by classical electrodynamics at length scales, unlike quantum physics, classical physics is generally characterized by the principle of complete determinism, although deterministic interpretations of quantum mechanics do exist. Mathematically, classical physics equations are those in which Plancks constant does not appear, according to the correspondence principle and Ehrenfests theorem, as a system becomes larger or more massive the classical dynamics tends to emerge, with some exceptions, such as superfluidity. This is why we can usually ignore quantum mechanics when dealing with everyday objects, one of the most vigorous on-going fields of research in physics is classical-quantum correspondence. This field of research is concerned with the discovery of how the laws of physics give rise to classical physics found at the limit of the large scales of the classical level.
Computer modeling is essential for quantum and relativistic physics, classic physics is considered the limit of quantum mechanics for large number of particles. On the other hand, classic mechanics is derived from relativistic mechanics, for example, in many formulations from special relativity, a correction factor 2 appears, where v is the velocity of the object and c is the speed of light. For velocities much smaller than that of light, one can neglect the terms with c2 and these formulas reduce to the standard definitions of Newtonian kinetic energy and momentum. This is as it should be, for special relativity must agree with Newtonian mechanics at low velocities, computer modeling has to be as real as possible. Classical physics would introduce an error as in the superfluidity case, in order to produce reliable models of the world, we can not use classic physics. It is true that quantum theories consume time and computer resources, and the equations of physics could be resorted to provide a quick solution
Despite the clerical origin of many of its authors, medieval Latin should not be confused with Ecclesiastical Latin. There is no consensus on the exact boundary where Late Latin ends. Medieval Latin had a vocabulary, which freely borrowed from other sources. Greek provided much of the vocabulary of Christianity. The various Germanic languages spoken by the Germanic tribes, who invaded southern Europe, were major sources of new words. Germanic leaders became the rulers of parts of the Roman Empire that they conquered, other more ordinary words were replaced by coinages from Vulgar Latin or Germanic sources because the classical words had fallen into disuse. Latin was spread to such as Ireland and Germany. Works written in the lands, where Latin was a language with no relation to the local vernacular, influenced the vocabulary. English words like abstract, communicate, probable, the high point of the development of medieval Latin as a literary language came with the Carolingian renaissance, a rebirth of learning kindled under the patronage of Charlemagne, king of the Franks.
On the other hand, strictly speaking there was no form of medieval Latin. Every Latin author in the period spoke Latin as a second language, with varying degrees of fluency, and syntax, grammar. For instance, rather than following the classical Latin practice of placing the verb at the end. Unlike classical Latin, where esse was the auxiliary verb, medieval Latin writers might use habere as an auxiliary, similar to constructions in Germanic. The accusative and infinitive construction in classical Latin was often replaced by a clause introduced by quod or quia. This is almost identical, for example, to the use of que in similar constructions in French. In every age from the late 8th century onwards, there were learned writers who were familiar enough with classical syntax to be aware that these forms and usages were wrong, however the use of quod to introduce subordinate clauses was especially pervasive and is found at all levels. That resulted in two features of Medieval Latin compared with Classical Latin.
First, many attempted to show off their knowledge of Classical Latin by using rare or archaic constructions
A parabola is a two-dimensional, mirror-symmetrical curve, which is approximately U-shaped when oriented as shown in the diagram below, but which can be in any orientation in its plane. It fits any of several different mathematical descriptions which can all be proved to define curves of exactly the same shape. One description of a parabola involves a point and a line, the focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from both the directrix and the focus, a parabola is a graph of a quadratic function, y = x2, for example. The line perpendicular to the directrix and passing through the focus is called the axis of symmetry, the point on the parabola that intersects the axis of symmetry is called the vertex, and is the point where the parabola is most sharply curved. The distance between the vertex and the focus, measured along the axis of symmetry, is the focal length, the latus rectum is the chord of the parabola which is parallel to the directrix and passes through the focus.
Parabolas can open up, left, right, or in some arbitrary direction. Any parabola can be repositioned and rescaled to fit exactly on any other parabola — that is, light that originates from a point source at the focus is reflected into a parallel beam, leaving the parabola parallel to the axis of symmetry. The same effects occur with sound and other forms of energy and this reflective property is the basis of many practical uses of parabolas. The parabola has many important applications, from an antenna or parabolic microphone to automobile headlight reflectors to the design of ballistic missiles. They are frequently used in physics and many other areas, the earliest known work on conic sections was by Menaechmus in the fourth century BC. He discovered a way to solve the problem of doubling the cube using parabolas, the name parabola is due to Apollonius who discovered many properties of conic sections. It means application, referring to application of concept, that has a connection with this curve.
The focus–directrix property of the parabola and other conics is due to Pappus, Galileo showed that the path of a projectile follows a parabola, a consequence of uniform acceleration due to gravity. The idea that a reflector could produce an image was already well known before the invention of the reflecting telescope. Designs were proposed in the early to mid seventeenth century by many mathematicians including René Descartes, Marin Mersenne, when Isaac Newton built the first reflecting telescope in 1668, he skipped using a parabolic mirror because of the difficulty of fabrication, opting for a spherical mirror. Parabolic mirrors are used in most modern reflecting telescopes and in satellite dishes, solving for y yields y =14 f x 2. The length of the chord through the focus is called latus rectum, one half of it semi latus rectum
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
Electrostatics is a branch of physics that deals with the phenomena and properties of stationary or slow-moving electric charges. Since classical physics, it has known that some materials such as amber attract lightweight particles after rubbing. The Greek word for amber, ήλεκτρον, or electron, was the source of the word electricity, Electrostatic phenomena arise from the forces that electric charges exert on each other. Such forces are described by Coulombs law, Electrostatics involves the buildup of charge on the surface of objects due to contact with other surfaces. This is because the charges that transfer are trapped there for a long enough for their effects to be observed. We begin with the magnitude of the force between two point charges q and Q. It is convenient to one of these charges, q, as a test charge. As we develop the theory, more source charges will be added.854187817 ×10 −12 C2 N −1 m −2, the SI units of ε0 are equivalently A2s4 kg−1m−3 or C2N−1m−2 or F m−1. Coulombs constant is, k e ≈14 π ε0 ≈8.987551787 ×109 N m 2 C −2. A single proton has a charge of e, and the electron has a charge of −e and these physical constants are currently defined so that ε0 and k0 are exactly defined, and e is a measured quantity.
Electric field lines are useful for visualizing the electric field, field lines begin on positive charge and terminate on negative charge. Electric field lines are parallel to the direction of the field. The electric field, E →, is a field that can be defined everywhere. It is convenient to place a hypothetical test charge at a point, by Coulombs Law, this test charge will experience a force that can be used to define the electric field as follow F → = q E →. For a single point charge at the origin, the magnitude of electric field is E = k e Q / R2. The fact that the force can be calculated by summing all the contributions due to individual source particles is an example of the superposition principle. If the charge is distributed over a surface or along a line, the Divergence Theorem allows Gausss Law to be written in differential form, ∇ → ⋅ E → = ρ ε0. Where ∇ → ⋅ is the divergence operator, the definition of electrostatic potential, combined with the differential form of Gausss law, provides a relationship between the potential Φ and the charge density ρ, ∇2 ϕ = − ρ ε0
An astronomical object or celestial object is a naturally occurring physical entity, association, or structure that current astronomy has demonstrated to exist in the observable universe. In astronomy, the object and body are often used interchangeably. Examples for astronomical objects include planetary systems, star clusters and galaxies, while asteroids, moons and stars are astronomical bodies. A comet may be identified as both body and object, It is a body when referring to the nucleus of ice and dust. The universe can be viewed as having a hierarchical structure, at the largest scales, the fundamental component of assembly is the galaxy. Galaxies are organized groups and clusters, often within larger superclusters. Disc galaxies encompass lenticular and spiral galaxies with features, such as spiral arms, at the core, most galaxies have a supermassive black hole, which may result in an active galactic nucleus. Galaxies can have satellites in the form of dwarf galaxies, the constituents of a galaxy are formed out of gaseous matter that assembles through gravitational self-attraction in a hierarchical manner.
At this level, the fundamental components are the stars. The great variety of forms are determined almost entirely by the mass, composition. Stars may be found in systems that orbit about each other in a hierarchical organization. A planetary system and various objects such as asteroids and debris. The various distinctive types of stars are shown by the Hertzsprung–Russell diagram —a plot of stellar luminosity versus surface temperature. Each star follows a track across this diagram. If this track takes the star through a region containing a variable type. An example of this is the instability strip, a region of the H-R diagram that includes Delta Scuti, RR Lyrae, the table below lists the general categories of bodies and objects by their location or structure. International Astronomical Naming Commission List of light sources List of Solar System objects Lists of astronomical objects SkyChart, Sky & Telescope Monthly skymaps for every location on Earth
Orbital state vectors
State vectors are defined with respect to some frame of reference, usually but not always an inertial reference frame. The position vector r describes the position of the body in the frame of reference. Together, these two vectors and the time at which they are valid uniquely describe the bodys trajectory. The body does not actually have to be in orbit for its state vector to determine its trajectory, it only has to move ballistically, i. e. solely under the effects of its own inertia and gravity. For example, it could be a spacecraft or missile in a suborbital trajectory, if other forces such as drag or thrust are significant, they must be added vectorially to those of gravity when performing the integration to determine future position and velocity. For any object moving through space, the velocity vector is tangent to the trajectory, the state vectors can be easily used to compute the angular momentum vector as h = r × v. Because even satellites in low Earth orbit experience significant perturbations, the Keplerian elements computed from the vector at any moment are only valid at that time.
Such element sets are known as osculating elements because they coincide with the actual orbit only at that moment
Venus is the second planet from the Sun, orbiting it every 224.7 Earth days. It has the longest rotation period of any planet in the Solar System and it is named after the Roman goddess of love and beauty. It is the second-brightest natural object in the sky after the Moon, reaching an apparent magnitude of −4.6. Because Venus orbits within Earths orbit it is a planet and never appears to venture far from the Sun. Venus is a planet and is sometimes called Earths sister planet because of their similar size, proximity to the Sun. It is radically different from Earth in other respects and it has the densest atmosphere of the four terrestrial planets, consisting of more than 96% carbon dioxide. The atmospheric pressure at the surface is 92 times that of Earth. Venus is by far the hottest planet in the Solar System, with a surface temperature of 735 K. Venus is shrouded by an layer of highly reflective clouds of sulfuric acid. It may have had water oceans in the past, but these would have vaporized as the temperature rose due to a greenhouse effect.
The water has probably photodissociated, and the hydrogen has been swept into interplanetary space by the solar wind because of the lack of a planetary magnetic field. Venuss surface is a dry desertscape interspersed with rocks and is periodically resurfaced by volcanism. As one of the brightest objects in the sky, Venus has been a fixture in human culture for as long as records have existed. It has been sacred to gods of many cultures, and has been a prime inspiration for writers and poets as the morning star. Venus was the first planet to have its motions plotted across the sky, as the closest planet to Earth, Venus has been a prime target for early interplanetary exploration. It was the first planet beyond Earth visited by a spacecraft, Venuss thick clouds render observation of its surface impossible in visible light, and the first detailed maps did not emerge until the arrival of the Magellan orbiter in 1991. Plans have been proposed for rovers or more missions. Venus is one of the four planets in the Solar System
In mathematics, a conic section is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse, the circle is a special case of the ellipse, and is of sufficient interest in its own right that it was sometimes called a fourth type of conic section. The conic sections have been studied by the ancient Greek mathematicians with this work culminating around 200 BC, the conic sections of the Euclidean plane have various distinguishing properties. Many of these have used as the basis for a definition of the conic sections. The type of conic is determined by the value of the eccentricity, in analytic geometry, a conic may be defined as a plane algebraic curve of degree 2, that is, as the set of points whose coordinates satisfy a quadratic equation in two variables. This equation may be written in form, and some geometric properties can be studied as algebraic conditions. In the Euclidean plane, the conic sections appear to be different from one another.
By extending the geometry to a projective plane this apparent difference vanishes, further extension, by expanding the real coordinates to admit complex coordinates, provides the means to see this unification algebraically. The conic sections have been studied for thousands of years and have provided a source of interesting. A conic is the curve obtained as the intersection of a plane, called the cutting plane and we shall assume that the cone is a right circular cone for the purpose of easy description, but this is not required, any double cone with some circular cross-section will suffice. Planes that pass through the vertex of the cone will intersect the cone in a point and these are called degenerate conics and some authors do not consider them to be conics at all. Unless otherwise stated, we assume that conic refers to a non-degenerate conic. There are three types of conics, the ellipse and hyperbola, the circle is a special kind of ellipse, although historically it had been considered as a fourth type.
The circle and the ellipse arise when the intersection of the cone and plane is a closed curve, if the cutting plane is parallel to exactly one generating line of the cone, the conic is unbounded and is called a parabola. In the remaining case, the figure is a hyperbola, in this case, the plane will intersect both halves of the cone, producing two separate unbounded curves. A property that the conic sections share is often presented as the following definition, a conic section is the locus of all points P whose distance to a fixed point F is a constant multiple of the distance from P to a fixed line L. For 0 < e <1 we obtain an ellipse, for e =1 a parabola, a circle is a limiting case and is not defined by a focus and directrix, in the plane. The eccentricity of a circle is defined to be zero and its focus is the center of the circle, an ellipse and a hyperbola each have two foci and distinct directrices for each of them
In astrodynamics or celestial mechanics an elliptic orbit is a Kepler orbit with the eccentricity less than 1, this includes the special case of a circular orbit, with eccentricity equal to zero. In a stricter sense, it is a Kepler orbit with the eccentricity greater than 0, in a wider sense it is a Kepler orbit with negative energy. This includes the radial elliptic orbit, with eccentricity equal to 1, in a gravitational two-body problem with negative energy both bodies follow similar elliptic orbits with the same orbital period around their common barycenter. Also the relative position of one body with respect to the other follows an elliptic orbit, examples of elliptic orbits include, Hohmann transfer orbit, Molniya orbit and tundra orbit. A is the length of the semi-major axis, the velocity equation for a hyperbolic trajectory has either +1 a, or it is the same with the convention that in that case a is negative. Conclusions, For a given semi-major axis the orbital energy is independent of the eccentricity. ν is the true anomaly.
The angular momentum is related to the cross product of position and velocity. Here ϕ is defined as the angle which differs by 90 degrees from this and this set of six variables, together with time, are called the orbital state vectors. Given the masses of the two bodies they determine the full orbit, the two most general cases with these 6 degrees of freedom are the elliptic and the hyperbolic orbit. Special cases with fewer degrees of freedom are the circular and parabolic orbit, another set of six parameters that are commonly used are the orbital elements. In the Solar System, asteroids, most comets, the following chart of the perihelion and aphelion of the planets, dwarf planets and Halleys Comet demonstrates the variation of the eccentricity of their elliptical orbits. For similar distances from the sun, wider bars denote greater eccentricity, note the almost-zero eccentricity of Earth and Venus compared to the enormous eccentricity of Halleys Comet and Eris. A radial trajectory can be a line segment, which is a degenerate ellipse with semi-minor axis =0.
Although the eccentricity is 1, this is not a parabolic orbit, most properties and formulas of elliptic orbits apply. However, the orbit cannot be closed and it is an open orbit corresponding to the part of the degenerate ellipse from the moment the bodies touch each other and move away from each other until they touch each other again. In the case of point masses one full orbit is possible, the velocities at the start and end are infinite in opposite directions and the potential energy is equal to minus infinity. The radial elliptic trajectory is the solution of a problem with at some instant zero speed