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Retrograde

Retrograde

:This article is about the movement of the planets. For the musical term retrograde see Counterpoint, Musical set theory, Operation, Permutation, and Transformation. Prograde motion is the rotational or orbital motion of a body in a direction similar to that of other bodies within a given system, and is sometimes called direct motion. Retrograde motion is in the contrary direction. The word 'retrograde' derives from the Latin words retro, backwards, and gradus, step.

Two notations

The north orbital pole of a celestial body is defined by the right-hand rule: If you curve the fingers of your right hand along the direction of orbital motion, with your thumb extended parallel to the orbital axis, the direction your thumb points is defined to be north. Similarly, the north rotational pole of a body is defined by the direction of your thumb if you were to wrap your fingers around its equator in the direction it spins. There are two notations for retrograde motion that are mathematically equivalent: The body can be considered to orbit backwards, or it can be considered to orbit forwards, but with its orbit upside-down. For example, a moon in a retrograde orbit that is inclined from the pole of its planet by 10°, and with a 6-hour orbital period, could be said to have the orbital parameters of:
- 10° (rightside-up) and −6 h (backwards), in which case no inclination would ever exceed 90° (anything more than 90° would be upside-down), or of:
- 170° (upside-down) and +6 h (forwards), in which case no period would ever be negative. Similarly, a moon spinning backwards on an axis inclined by 10° from the axis of its orbit can instead be described as being flipped upside-down and spinning forwards. It is more common to keep the orbital or rotational period positive and let the inclination vary between 90° and 180° for retrograde motion, and between 0° and 90° for prograde motion, but when this inclination isn't listed, a negative orbital period is the only indication that an object is retrograde. (See natural satellite.)

Retrograde orbits

In the Solar system, most bodies orbit in a similar (prograde) direction to the rotation of the Sun. All planets and most smaller bodies orbit the Sun counterclockwise as seen from the [http://www.astro.uiuc.edu/~kaler/celsph.html north ecliptic pole] (which is in Draco, about 23° from the pole star, Polaris). The exceptions are mostly comets, which generally have highly disturbed orbits. Similarly, the larger and closer moons orbit their planet in the same direction as the planet's rotation, and so are also considered prograde. However, the gas giant planets have large numbers of small "irregular" moons in highly inclined or elliptical orbits, thought to be captured asteroids or Kuiper belt objects, or fragments thereof, and the majority of these are retrograde: 48 retrograde to 7 prograde for Jupiter, 18 to 8 for Saturn, and 8 to 1 for Uranus. One of the largest is the Saturnian moon Phoebe. Neptune is somewhat different: It seems to have captured its only surviving large moon, the retrograde but otherwise regular Triton, from the Kuiper Belt Object. The six irregular moons beyond Triton's orbit are evenly divided between prograde and retrograde; some of these may be original Neptunian moons whose orbits were distubed by Triton's capture, rather than being captured bodies themselves.

Retrograde rotation

Most planets, including Earth, spin in the prograde sense: That is, the north rotational pole and north orbital pole point in similar directions, more or less in the direction of the Solar north pole. The exceptions among the planets are Venus, Uranus and Pluto. Uranus rotates nearly on its side relative to its orbit. It has been described as having an axial tilt of 82° and a negative rotation of −17 hours, or, equivalently, of having an axis tilted at 98° and a positive rotation. Since current speculation is that Uranus started off with a typical prograde orientation and was knocked on its side by a large impact early in its history, it is most commonly described as having the higher axial tilt and positive rotation. (Since Uranus' moons are considered relative to Uranus itself, their description is unaffected by the choice made for the planet.) Retrograde Venus, on the other hand, has an axial tilt of less than 3°, and a very slow rotation of 243 days. Perhaps because it is easier to conceive of Venus as rotating slowly backwards than being 'upside down' relative to its near-twin Earth, but also because it is thought that an early massive impact may have resulted in Venus' current rotation while leaving its axis more or less unaffected, Venus is nearly always described as having its axis at 3° and a rotation of −243 days, rather than 187° and +243 days. When we observe the sky, we expect most objects to appear to move in a particular direction with the passing of time (diurnal motion). The apparent motion of most bodies in the sky is from east to west. However it is possible to observe a body moving west to east, such as an artificial satellite or Space Shuttle that is orbiting eastward (the preferred direction, because the rotation of the Earth assists in acquiring the required orbital speed). This orbit might be considered retrograde motion in this sense. However, as the Space Shuttle and such satellites you see going eastward would be seen orbiting the Earth counterclockwise if seen from the Pole Star, they are considered direct satellites. There are also artificial satellites which go clockwise as seen from the pole star; they are called retrograde satellites and you can see them in the sky going westward.

Retrogradation, or apparent retrograde motion

Retrograde motion should not be confused with retrogradation. The latter term is used in reference to the motion of the outer planets (Mars, Jupiter, Saturn, Neptune, Uranus, and Pluto). Though these planets appear to move from east to west on a nightly basis in response to the spin of Earth, they are most of the time drifting slowly eastward with respect to the background of stars, which can be observed by noting the position of these planets for several nights in a row. This motion is normal for these planets, so it is called direct motion (not retrograde). However, since Earth completes its orbit in a shorter period of time than these outer planets, we occasionally overtake an outer planet, like a faster car on a multiple-lane highway. When this occurs, the planet we are passing will first appear to stop its eastward drift, and it will then appear to drift back toward the west. This is retrogradation, since the planet seems to be moving in a direction opposite to that which is typical for planets. Finally as Earth swings past the planet in its orbit, it appears to resume its normal west-to-east drift on successive nights. Mars goes through retrogradation about every 25.7 months. The more distant outer planets retrograde more frequently. The period between such retrogradations is the synodic period of the planet. This retrogradation puzzled ancient astronomers, and was one reason why they named these bodies 'planets' which in Greek means 'wanderers'. In the geocentric model of the solar system, this motion was accounted for by having the planets travel in deferents and epicycles. In modern astronomy, the term retrograde motion refers to objects which are actually moving in a direction opposite that which is normal to spatial bodies within a given system, as opposed to merely observed phenomena (retrogradation) such as that described above.

Examples

Some significant examples of retrograde motion in the solar system:
- Venus rotates slowly in the retrograde direction.
- The moons Ananke, Carme, Pasiphaë and Sinope all orbit Jupiter in a retrograde direction. Many other minor moons of Jupiter orbit retrograde.
- The moon Phoebe orbits Saturn in a retrograde direction, and is thought to be a captured Kuiper belt object.
- The moon Triton orbits Neptune in a retrograde direction, and is also thought to be a captured Kuiper belt object.
- The planet Uranus has an axial tilt of 98°, which is near to 90°, and can be considered to be rotating in a retrograde direction depending on one's interpretation.

Reference

This article originated from Jason Harris' Astroinfo which comes along with KStars, a Desktop Planetarium for Linux/KDE. See http://edu.kde.org/kstars/index.phtml See also: Hipparchus, positional astronomy, Ptolemy Category:Astrodynamics Category:Celestial mechanics

Counterpoint

:This article is about the concept of counterpoint in music. For the Star Trek: Voyager episode of the same title, see Counterpoint (Voyager episode). Counterpoint is a musical technique involving the simultaneous sounding of separate musical lines. It is especially prominent in Western music. In all eras, writing of counterpoint has been subject to rules, sometimes strict. Counterpoint written before approximately 1600 is usually known as polyphony. The term comes from the Latin punctus contra punctum ("note against note"). The adjectival form contrapuntal shows this Latin source more transparently. By definition, chords occur when multiple notes sound simultaneously; however, chordal, harmonic, "vertical" features are considered secondary and almost incidental when counterpoint is the predominant textural element. Counterpoint focuses on melodic interaction rather than harmonic effects generated when melodic strands sound together. It was elaborated extensively in the Renaissance period, but composers of the Baroque period brought counterpoint to a kind of culmination, and it may be said that, broadly speaking, harmony then took over as the predominant organising principle in musical composition. The late Baroque composer Johann Sebastian Bach wrote most of his music incorporating counterpoint, and explicitly and systematically explored the full range of contrapuntal possibilities in such works as The Art of the Fugue. Given the way terminology in music history has evolved, such music created from the Baroque period on is described as contrapuntal, while music from before Baroque times is called polyphonic. Hence, the earlier composer Josquin Des Prez is said to have written polyphonic music. Homophony, by contrast with polyphony, features music in which chords or vertical intervals work with a single melody without much consideration of the melodic character of the added accompanying elements, or of their melodic interactions with the melody they accompany. As suggested above, most popular music written today is predominantly homophonic — governed by considerations of chord and harmony. But these are only strong general tendencies, and there are many qualifications one could add. The form or compositional genre known as fugue is perhaps the most complex contrapuntal convention. Other examples include the round (familiar in folk traditions) and the canon. In musical composition, counterpoint is an essential means for the generation of musical ironies; a melodic fragment, heard alone, may make a particular impression, but when it is heard simultaneously with other melodic ideas, or combined in unexpected ways with itself, as in a canon or fugue, surprising new facets of meaning are revealed. This is a means for bringing about development of a musical idea, revealing it to the listener as conceptually more profound than a merely pleasing melody.

Species counterpoint

Species counterpoint is a type of strict counterpoint, developed as a pedagagical tool, in which a student progresses through several "species" of increasing complexity, gradually attaining the ability to write free counterpoint according to the rules at the given time. The idea is at least as old as 1532, when Giovanni Maria Lanfraco described a similar concept in his Scintille de musica. The late 16th century Venetian theorist Zarlino elaborated on the idea in his influential Le institutioni harmoniche, and it was first presented in a codified form in 1619 by Lodovico Zacconi in his Prattica di musica. Zacconi, unlike later theorists, included a few extra contrapuntal techniques as species, for example invertible counterpoint. By far the most famous pedagogue to use the term, and the one who made it famous, was Johann Fux. In 1725 he published Gradus ad Parnassum (Step by Step Up Mount Parnassus) a work intended to help teach students how to compose, using counterpoint — specifically, the contrapuntal style as practiced by Palestrina in the late 16th century — as the principal technique. Fux described five species: #Note against note; #Two notes against one; #Four notes against one; #Notes offset against each other (as suspensions); #All the first four species together, as "florid" counterpoint.

Considerations for all species

Students of species counterpoint usually practice writing counterpoint in all the modes (Ionian, Dorian, Phrygian, Lydian, Mixolydian and Aeolian). The following rules apply to melodic writing in all species: #The counterpoint must begin and end on a perfect consonance. #The final must be approached by step. If approached from below, the leading tone must be raised, except in the case of the Phrygian mode. Thus, in the Dorian mode on D, a C# is necessary at the cadence. #Permitted melodic intervals are the perfect fourth, fifth, and octave, as well as the major and minor second, major and minor third, and ascending minor sixth. When the ascending minor sixth is used it must be immediately followed by motion downwards. #If writing two skips in the same direction--something which must be done only rarely--the second must be smaller than the first, and the interval between the first and the third note may not be dissonant. #If writing a skip in one direction, it is best to proceed after the skip with motion in the other direction. #Contrary motion should predominate. #The interval of a tenth should not be exceeded between the two parts, unless necessary. #The interval of a tritone in three notes is to be avoided (for example, a melodic motion F - A - B natural), as is the interval of a seventh in three notes.

First species

In first species counterpoint, each note in an added part
- (or parts) sounds against one note in the cantus firmus. Notes in all parts are sounded simultaneously, and move against each other simultaneously. The species is said to be expanded if any of the added notes is broken up (simply repeated). A few further rules given by Fux, by study of the Palestrina style, and usually given in the works of later counterpoint pedagogues, are as follows. Some are vague, and since good judgement and taste have been regarded by contrapuntists as more important than strict observance of mechanical rules, there are many more cautions than prohibitions. #Begin and end on either the unison, octave, or fifth, unless the added part is underneath, in which case begin and end only on unison or octave. #Use no unisons except at the beginning or end. #Avoid hidden or parallel fifths or octaves. #Attempt to keep the two parts within a tenth of each other, unless an exceptionally pleasing line can be written outside of that range. #Avoid moving in parallel thirds or sixths for too long. #Avoid having both parts move in the same direction by skip. #Attempt to have as much contrary motion as possible. In the following examples, all in two voices, the cantus firmus — the given part — is in the lower voice. The same cantus firmus is used for each, and each is in the Dorian mode. Dorian mode

Second species

In second species counterpoint, two notes in the added part (or parts) work against each longer note in the given part. The species is said to be expanded if one of the two shorter notes differs in length from the other. Additional considerations in second species counterpoint are as follows, and are in addition to the considerations for first species: #It is permissible to begin on an upbeat, leaving a half-rest in the added voice. #The accented beat must have only consonance (perfect or imperfect). The unaccented beat may have dissonance, but only as a passing tone, i.e. it must be approached and left by step in the same direction. #Avoid the interval of the unison except at the beginning or end of the example, except that it may occur on the unaccented portion of the bar. #Use caution with successive accented perfect fifths or octaves. They must not be used as part of a sequential pattern. Dorian mode

Third species

In third species counterpoint, four (or three) notes move against each longer note in the given part. As with second species, it is expanded if the shorter notes vary in length among themselves. Dorian mode

Fourth species

In fourth species counterpoint, a note is sustained or suspended in an added part while notes move against it in the given part, creating a dissonance, followed by the suspended note then changing (and "catching up") to create a subsequent consonance with the note in the given part as it continues to sound. Fourth species counterpoint is said to be expanded when the added-part notes vary in length from each other. The technique requires chains of notes sustained across the boundaries determined by beat, and so creates syncopation. syncopation

Florid counterpoint

In fifth species counterpoint, sometimes called florid counterpoint, the other four species of counterpoint are combined within the added part (or added parts). In the example, the first and second bars are second species, the third bar is third species, and the fourth and fifth bars are third and embellished fourth species. syncopation

General notes

It is a common and pedantic misconception that counterpoint is defined by these five species, and therefore anything that does not follow the strict rules of the five species is not counterpoint. This is not true; although much contrapuntal music of the common practice period indeed adheres to the rules, there are exceptions. Fux's book and its concept of "species" was purely a method of teaching counterpoint, not a definitive or rigidly prescriptive set of rules for it. He arrived at his method of teaching (or so he believed, at least) by examining the works of Giovanni Pierluigi da Palestrina, an important late 16th century composer and one who in Fux's time was held in the highest esteem as a contrapuntist. Works in the contrapuntal style of the 16th century—the "prima pratica" or "stile antico," it was called by modernist composers then—were often said by Fux's contemporaries to be in "Palestrina style." Indeed, Fux's treatise is a rather accurate compendeum of Palestrina's techniques.
- (Note: in counterpoint, the parts or individual melodic strands are often called voices, even if the music is thought of as instrumental.)

Contrapuntal derivations

Since the Renaissance period in European music, much music which is considered contrapuntal has been written in imitative counterpoint. In imitative counterpoint, two or more voices enter at different times, and (especially when entering) each voice repeats some version of the same melodic element. The fantasia, the ricercar, and later, the fugue (the contrapuntal form par excellence) all feature imitative counterpoint, which also frequently appears in choral works such as motets and madrigals. Imitative counterpoint has spawned a number of devices that composers have turned to in order to give their works both mathematical rigor and expressive range. Some of these devices include:
- Inversion: The inverse of a given fragment of melody is the fragment turned upside down – so if the original fragment has a rising major third (see interval), the inverted fragment has a falling major (or perhaps minor) third. (Compare, in twelve tone technique, the inversion of the tone row, which is the so-called prime series turned upside down.) In a completely separate sense, a contrapuntal inversion of melodies being simultaneously sounded by voices is the subsequent switching of the melodies between voices, so that for example an upper-voice melody is now sounded in some lower voice, and vice versa.
- Retrograde refers to the contrapuntal device whereby notes in an imitative voice sound backwards in relation to their order in the original.
- Retrograde inversion is where the imitative voice sounds notes both backwards and upside down.
- Augmentation is when in one of the parts in imitative counterpoint the notes are extended in duration compared to the rate at which they were sounded when introduced.
- Diminution is when in one of the parts in imitative counterpoint the notes are reduced in duration compared to the rate at which they were sounded when introduced.

Dissonant counterpoint

Dissonant counterpoint was first theorized by Charles Seeger as "at first purely a school-room discipline," consisting of species counterpoint but with all the traditional rules reversed. First species counterpoint is required to be all dissonances, establishing "dissonance, rather than consonance, as the rule," and consonances are "resolved" through a skip, not step. He wrote that "the effect of this discipline" was "one of purification." Other aspects of composition, such as rhythm, could be "dissonated" by applying the same principle (Charles Seeger, "On Dissonant Counterpoint," Modern Music 7, no. 4 (June-July 1930): 25-26). Seeger was not the first to employ dissonant counterpoint, but was the first to theorize and promote it. Other composers who have used dissonant counterpoint, if not in the exact manner prescribed by Charles Seeger, include Ruth Crawford-Seeger, Carl Ruggles, Dane Rudhyar, and Arnold Schoenberg.

External links

- [http://www.ntoll.org/interests/music/species/ A guide to species counterpoint]
- [http://www.musique.umontreal.ca/personnel/Belkin/bk.C/index.html Principles of Counterpoint]
- [http://www.o-art.org/history/early/Seeger.html On Dissonant Counterpoint by David Nicholls]
- [http://www.findarticles.com/cf_dls/m2298/2_17/61551810/p6/article.jhtml?term= Dane Rudhyar's Vision of American Dissonance by Carol J. Oja]
- [http://www.music.vt.edu/musicdictionary/textd/Dissonantcounterpoint.html Dissonant counterpoint examples and definition]
- [http://www.music.columbia.edu/~chris/ctrpnt.html De-Mystifying Tonal Counterpoint or How to Overcome Your Fear of Composing Counterpoint Exercises] by Christopher Dylan Bailey, composer at Columbia
- [http://www.greenwych.ca/musicmid.htm New Tonal Music composed with emphasis on counterpoint]
- [http://www.greenwych.ca/drone.htm Role of the drone in the evolution of counterpoint and harmony] Category:Counterpoint ko:대위법 ja:対位法

Operation

The word operation can mean any of several things:
- The method, act, process, or effect of using a device or system. See military operation, manufacturing operations, anomalous operation.
- In medicine, a surgical procedure to diagnose, cure or palliate a certain disease.
- In mathematics, an operation is an action applied to (one or more, but usually finitely many) numbers or other mathematical entities (e.g., vectors) to produce a well-defined result. Examples include addition, multiplication, root extraction, and comparison. See unary operation, binary operation, arity.
- In computer programming, a program step, usually specified by a part of an instruction word, that is undertaken or executed by a computer. Logical operations such as And, Or and Not are also operations typically performed by devices known as logic gates.
- In music a basic operation is one which may be performed on a set of pitches or pitch classes, including transposition, inversion, and multiplication. These may be combined to form compound operations, and inversion may be more accurately thought of as the compound operation transpositional inversion. See: transformation, permutation, counterpoint.
- If something happens by operation of law, then it occurs automatically based on circumstances not intended by the affected parties.
- The tactical shooting PC game Operation Flashpoint.
- The game of physical skill, Operation.
- In business, an organizational unit or set of procedures and processes that lead to business outcomes. See Business Operations
- In law enforcement a sting operation can be used to catch a law breaker in the act. ja:手術

Transformation

Transformation may refer to:
- Metamorphosis and shapeshifting - the change of an entity into another in myth and in fiction.
- In molecular biology:
- In genetics , transformation involves the genetic alteration of a cell resulting from the introduction, uptake and expression of foreign DNA.
- In cell division, the transformation process converts normal cells into cells that will continue to divide without limit. Normal cells can divide only a certain number of times before they stop dividing. Transformed cells no longer have such a limit (for example, cancer cells) and can grow and divide potentially forever.
- In mathematics, transformation as a general term applies to mathematical functions, usually but not always meaning that they are considered in terms of their geometry and are invertible.
- In chemistry, a chemical transformation shows the conversion of a substrate to a product omitting the reagents or catalysts.
- In music, a transformation consists of any operation or process that a composer or performer may apply to a musical variable (usually a set or tone row in twelve tone music) - such as transposition, inversion, multiplication, retrograde, or rotation and combinations thereof. See: operation, permutation.
- In military operations, transformation may refer to the process of transitioning to a lightweight, fast-moving force that heavily utilizes network-centric warfare. [http://www.oft.osd.mil/]
- In post-apartheid South Africa, transformation has come to mean the processes by which the previously disenfranchised (predominantly black) majority population enter the mainstream of public life and commercial activity. Legislation and public policy make black economic empowerment a key aspect of most equity-related business deals or government contracts.
- In anime, magical girls may use a naked transformation to change from their "normal" to "magical" forms, although typically they will appear partially obscured for purposes of censorship in order to maintain an equivalent to PG rating. This functions simply as an act of pure fanservice. The video cut that features this process has become known as a transformation sequence. In the anime Transformers they transform from a vehicle-mode into a more powerful warrior mode.
- In literature:
- Transformation, a 2000 novel by Carol Berg
- The Transformation Stories Archive.
- In New Age-like contexts, transformation can refer to a nebulous but often sudden spurt of personal psychic growth, personal enlightenment or self-realisation, which may also imply transforming the Universe into a "better" place.
- In computing, program transformation can convert special source code into other detailed structures.

Orbit

.]] :For other meanings of the term "orbit", see orbit (disambiguation) In physics, an orbit is the path that an object makes around another object while under the influence of a source of centripetal force, such as gravity.

History

Orbits were first analysed mathematically by Johannes Kepler who formulated his results in his laws of planetary motion. He found that the orbits of the planets in our solar system are elliptical, not circular (or epicyclic), as had previously been believed. Isaac Newton demonstrated that Kepler's laws were derivable from his theory of gravitation and that, in general, the orbits of bodies responding to the force of gravity were conic sections. Newton showed that a pair of bodies follow orbits of dimensions that are in inverse proportion to their masses about their common center of mass. Where one body is much 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.

Planetary orbits

Within a planetary system, planets, asteroids, comets and space debris orbit the central star in elliptical orbits. Any comet in a parabolic or hyperbolic orbit about the central star is not gravitationally bound to the star and therefore is not considered part of the star's planetary system. To date, no comet has been observed in our solar system with a distinctly hyperbolic orbit. Bodies which are gravitationally bound to one of the planets in a planetary system, either natural or artificial satellites, follow orbits about that planet. Due to mutual gravitational perturbations, the eccentricities of the orbits of the planets in our solar system vary over time. Pluto and Mercury have the most eccentric orbits. At the present epoch, Mars has the next largest eccentricity while the smallest eccentricities are those of the orbits of Venus and Neptune. As an object orbits another, the periapsis is that point at which the two objects are closest to each other and the apoapsis is that point at which they are the farthest from each other. In the elliptical orbit, the centre of mass of the orbiting-orbited system will sit at one focus of both orbits, with nothing present at the other focus. As a planet approaches periapsis, the planet will increase in velocity. As a planet approaches apoapsis, the planet will decrease in velocity. See also: Kepler's laws of planetary motion

Understanding orbits

There are a few common ways of understanding orbits.
- As the object moves sideways, it falls toward the orbited object. However it moves so quickly that the curvature of the orbited object will fall away beneath it.
- A force, such as gravity, pulls the object into a curved path as it attempts to fly off in a straight line.
- As the object falls, it moves sideways fast enough (has enough tangential velocity) to miss the orbited object. This understanding is particularly useful for mathematical analysis, because the object's motion can be described as the sum of the three one-dimensional coordinates oscillating around a gravitational center. As an illustration of the orbit around a planet (eg Earth), the much-used cannon model may prove useful (see image below). Imagine a cannon sitting on top of a (very) tall mountain, which fires a cannonball horizontally. The mountain needs to be very tall, so that the cannon will be above the Earth's atmosphere and we can ignore the effects of air friction on the cannon ball. 300px If the cannon fires its ball with a low initial velocity, the trajectory of the ball will curve downwards and hit the ground (A). As the firing velocity is increased, the cannonball will hit the ground further (B) and further (C) away from the cannon, because while the ball is still falling towards the ground, the ground is curving away from it (see first point, above). If the cannonball is fired with sufficient velocity, the ground will curve away from the ball at the same rate as the ball falls - it is now in orbit (D). The orbit may be circular like (D) or if the firing velocity is increased even more, the orbit may become more (E) and more (F) elliptical. At a certain even faster velocity (called the escape velocity) the motion changes from an elliptical orbit to a parabola.

Newton's laws of motion

For a system of only two bodies that are only influenced by their mutual gravity, their orbits can be exactly calculated by Newton's laws of motion and gravity. Briefly, the sum of the forces will equal the mass times its acceleration. Gravity is proportional to mass, and falls off proportionally to the square of distance. To calculate, it is convenient to describe the motion in a coordinate system that is centered on the heavier body, and we can say that the lighter body is in orbit around the heavier body. An unmoving body that's far from a large object has more energy than one that's close. This is because it can fall farther. This is called "potential energy" because it is not yet actual. With two bodies, an orbit is a flat curve. The orbit can be open (so the object never returns) or closed (returning), depending on the total kinetic + potential energy of the system. In the case of an open orbit, the speed at any position of the orbit is at least the escape velocity for that position, in the case of a closed orbit, always less. The path of a free-falling (orbiting) body is always a conic section. An open orbit has the shape of a hyperbola (or in the limiting case, a parabola); the bodies approach each other for a while, curve around each other around the time of their closest approach, and then separate again forever. This is often the case with comets that occasionally approach the Sun. A closed orbit has the shape of an ellipse (or in the limiting case, a circle). The point where the orbiting body is closest to Earth is the perigee, called periapsis (less properly, "perifocus" or "pericentron") when the orbit is around a body other than Earth. The point where the satellite is farthest from Earth is called apogee, apoapsis, or sometimes apifocus or apocentron. A line drawn from periapsis to apoapsis is the line-of-apsides. This is the major axis of the ellipse, the line through its longest part. Orbiting bodies in closed orbits repeat their path after a constant period of time. This motion is described by the empirical laws of Kepler, which can be mathematically derived from Newton's laws. These can be formulated as follows: # The orbit of a planet around the Sun is an ellipse, with the Sun in one of the focal points of the ellipse. Therefore the orbit lies in a plane, called the orbital plane. The point on the orbit closest to the attracting body is the periapsis. The point farthest from the attracting body is called the apoapsis. There are also specific terms for orbits around particular bodies; things orbiting the Sun have a perihelion and aphelion, things orbiting the Earth have a perigee and apogee, and things orbiting the Moon have a perilune and apolune (or, synonymously, periselene and aposelene). An orbit around any star, not just the Sun, has a periastron and an apastron # As the planet moves around its orbit during a fixed amount of time, the line from Sun to planet sweeps a constant area of the orbital plane, regardless of which part of its orbit the planet traces during that period of time. This means that the planet moves faster near its perihelion than near its aphelion, because at the smaller distance it needs to trace a greater arc to cover the same area. This law is usually stated as "equal areas in equal time." # For each planet, the ratio of the 3rd power of its semi-major axis to the 2nd power of its period is the same constant value for all planets. Except for special cases like Lagrangian points, no method is known to solve the equations of motion for a system with four or more bodies. The 2-body solutions were published by Newton in Principia in 1687. In 1912, K. F. Sundman developed a converging infinite series that solves the 3-body problem, however it converges too slowly to be of much use. Instead, orbits can be approximated with arbitrarily high accuracy. These approximations take two forms. One form takes the pure elliptic motion as a basis, and adds perturbation terms to account for the gravitational influence of multiple bodies. This is convenient for calculating the positions of astronomical bodies. The equations of motion of the moon, planets and other bodies are known with great accuracy, and are used to generate tables for celestial navigation. The differential equation form is used for scientific or mission-planning purposes. According to Newton's laws, the sum of all the forces will equal the mass times its acceleration (F = ma). Therefore accelerations can be expressed in terms of positions. The perturbation terms are much easier to describe in this form. Predicting subsequent positions and velocities from initial ones corresponds to solving an initial value problem. Numerical methods calculate the positions and velocities of the objects a tiny time in the future, then repeat this. However, tiny arithmetic errors from the limited accuracy of a computer's math accumulate, limiting the accuracy of this approach. Differential simulations with large numbers of objects perform the calculations in a hierarchical pairwise fashion between centers of mass. Using this scheme, galaxies, star clusters and other large objects have been simulated.

Analysis of orbital motion

(see also orbit equation and Kepler's first law) To analyse the motion of a body moving under the influence of a force which is always directed towards a fixed point, it is convenient to use polar coordinates with the origin coinciding with the centre of force. In such coordinates the radial and transverse components of the acceleration are, respectively: :

\frac - r\left( \frac \right)^2

and :

\frac\frac\left( r^2\frac \right)

. Since the force is always radial, the transverse acceleration is zero, and it follows that: :

\frac = hu^2

, where h is a constant of integration and we have introduced the auxiliary variable u defined as 1/r. If magnitude of the radial force is f(r) per unit mass of the orbiting body, then the elimination of the time variable from the radial component of the equation of motion yields: :

\frac + u = \frac

. In the case of an inverse square force law the right hand side of the equation becomes a constant and the equation is seen to be the harmonic equation (up to a shift of origin of the dependent variable). The equation of the orbit described by the particle is thus: :

r = \frac = \frac

, where φ and e are constants of integration and L is the Semi-latus rectum. This can be recognised as the equation of a conic section in polar coordinates.

Orbital parameters

See: Orbital elements For a general elliptic orbit, the relations between the axis, eccentricity, and least and largest distance are: :Semimajor axis = (periapsis + apoapsis)/2 = mean of the extreme radii :Periapsis = semimajor axis × (1 - eccentricity) = least distance :Apoapsis = semimajor axis × (1 + eccentricity) = largest distance Note that there are alternative definitions for a "mean radius" or "average distance": if you average the radius over time for one orbit (mean anomaly), or over the orbital angle as observed by the primary (true anomaly), then you get a different result. See here for details.

Orbital period

See: orbital period

Orbital decay

If some part of a body's orbit enters an atmosphere, its orbit can decay because of drag. At each periapsis, the object scrapes the air, losing energy. Each time, the orbit grows less eccentric (more circular) because the object loses kinetic energy precisely when that energy is at its maximum. Eventually, the orbit circularises and then the object spirals into the atmosphere. The bounds of an atmosphere vary wildly. During solar maxima, the Earth's atmosphere causes drag up to a hundred kilometres higher than during solar minimums. Some satellites with long conductive tethers can also decay because of electromagnetic drag from the Earth's magnetic field. Basically, the wire cuts the magnetic field, and acts as a generator. The wire moves electrons from the near vacuum on one end to the near-vacuum on the other end. The orbital energy is converted to heat in the wire. Another method of artificially influencing an orbit is through the use of solar sails or magnetic sails. These forms of propulsion require no propellant or energy input, and so can be used indefinitely. See statite for one such proposed use. Orbital decay can also occur due to tidal forces for objects below the synchronous orbit for the body they're orbiting. The gravity of the orbiting object raises tidal bulges in the primary, and since below the synchronous orbit the orbiting object is moving faster than the body's surface the bulges lag a short angle behind it. The gravity of the bulges is slightly off of the primary-satellite axis and thus has a component along the satellite's motion. The near bulge slows the object more than the far bulge speeds it up, and as a result the orbit decays. Conversely, the gravity of the satellite on the bulges applies torque on the primary and speeds up its rotation. Artificial satellites are too small to have an appreciable tidal effect on the planets they orbit, but several moons in the solar system are undergoing orbital decay by this mechanism. Mars' innermost moon Phobos is a prime example, and is expected to either impact Mars' surface or break up into a ring within 50 million years. Finally, orbits can decay via the emission of gravitational waves. This mechanism is extremely weak for most stellar objects, only becoming significant in cases where there is a combination of extreme mass and extreme acceleration, such as with black holes or neutron stars that are orbiting each other closely.

Earth orbits

See Earth orbit for more details.
- Low Earth orbit
- High Earth Orbit
- Intermediate circular orbit
- Geostationary orbit
- Geosynchronous orbit
- Geostationary transfer orbit
- Molniya orbit
- Polar orbit
- Polar Sun Synchronous Orbit (this is not a complete list).

Scaling in gravity

The gravitational constant G is defined to be:
- 6.6742 × 10⁻¹¹ N·m²/kg²
- 6.6742 × 10⁻¹¹ m³/(kg·s²)
- 6.6742 × 10⁻¹¹(kg/m³)^-1s^-2. Thus the constant has dimension density^-1 time^-2. This corresponds to the following properties. Scaling of distances (including sizes of bodies, while keeping the densities the same) gives similar orbits without scaling the time: if for example distances are halved, masses are divided by 8, gravitational forces by 16 and gravitational accelerations by 2. Hence orbital periods remain the same. Similarly, when an object is dropped from a tower, the time it takes to fall to the ground remains the same with a scale model of the tower on a scale model of the earth. When all densities are multiplied by four, orbits are the same, but with orbital velocities doubled. When all densities are multiplied by four, and all sizes are halved, orbits are similar, with the same orbital velocities. These properties are illustrated in the formula :

GT^2 \sigma = 3\pi \left( \frac \right)^3,

for an elliptical orbit with semi-major axis a, of a small body around a spherical body with radius r and average density σ, where T is the orbital period.

Role in the evolution of atomic theory

When atomic structure was first probed experimentally early in the twentieth century, an early picture of the atom portrayed it as a miniature solar system bound by the coulomb force rather than by gravity. This was inconsistent with electrodynamics and the model was progressively refined as quantum theory evolved, but there is a legacy of the picture in the term orbital for the wave function of an energetically bound electron state.

External links

- An on-line orbit plotter: http://www.bridgewater.edu/departments/physics/ISAW/PlanetOrbit.html
- [http://www.braeunig.us/space/orbmech.htm Orbital Mechanics] (Rocket and Space Technology) Category:Celestial mechanics Category:Solar System als:Umlaufbahn ja:軌道 (力学) simple:Orbit th:วงโคจร

Latin

Latin is an ancient Indo-European language originally spoken in the region around Rome called Latium. It gained great importance as the formal language of the Roman Empire. All Romance languages, those being most notably Spanish, French, Portuguese, Italian, and Romanian, are descended from Latin, and many words based on Latin are found in other modern languages such as English. The Latin alphabet, derived from the Greek, remains the most widely-used alphabet in the world. It is said that 80 percent of scholarly English words are derived from Latin (in a large number of cases by way of French). Moreover, in the Western world, Latin was a lingua franca, the learned language for scientific and political affairs, for more than a thousand years, being eventually replaced by French in the 18th century and English in the late 19th. Ecclesiastical Latin remains the formal language of the Roman Catholic Church to this day, and thus the official national language of the Vatican. The Church used Latin as its primary liturgical language until the Second Vatican Council in the 1960s. Latin is also still used (drawing heavily on Greek roots) to furnish the names used in the scientific classification of living things. The modern study of Latin, along with Greek, is known as Classics.

Main features

Latin is a synthetic inflectional language: affixes (which usually encode more than one grammatical category) are attached to fixed stems to express gender, number, and case in adjectives, nouns, and pronouns, which is called declension; and person, number, tense, voice, mood, and aspect in verbs, which is called conjugation. There are five declensions (declinationes) of nouns and four conjugations of verbs. There are six noun cases: #nominative (used as the subject of the verb or the predicate nominative), #genitive (used to indicate relation or possession, often represented by the English of or the addition of s to a noun), #dative (used of the indirect object of the verb, often represented by the English to or for), #accusative (used of the direct object of the verb, or object of the preposition in some cases), #ablative (separation, source, cause, or instrument, often represented by the English by, with, from), #vocative (used of the person or thing being addressed). In addition, some nouns have a locative case used to express location (otherwise expressed by the ablative with a preposition such as in), but this survival from Proto-Indo-European is found only in the names of lakes, cities, towns, small islands, and a few other words related to locations, such as "house", "ground", and "countryside". Latin itself, being a very old language, is far closer to Proto-Indo-European than are most modern Western European languages; it has, in fact, about the same relationship with PIE as modern Italian or French has to Latin. There are six general tenses in Latin (technically they are tense/aspect/mood complexes). The indicative mood can be used with all of them. The subjunctive mood, however, has only present, imperfect, perfect, and pluperfect tenses. These tenses in the subjunctive mood do not completely correlate in meaning to the tenses in the indicative. The following examples are of the first conjugation verb "laudare" ("to praise") in the indicative mood and the active voice:
Primary sequence tenses
# present (laudo, "I praise") # imperfect (laudabam, "I was praising") # future (laudabo, "I shall praise," "I will praise")
Secondary sequence tenses
# perfect (laudavi, "I praised", "I have praised") # pluperfect (laudaveram, "I had praised") # future perfect (laudavero, "I shall have praised," "I will have praised") The future perfect tense can also imply a normal future idea (like in "When I will have run...") and so may also sometimes be included in the primary sequence.
Latin and Romance
After the collapse of the Roman Empire, Latin evolved into the various Romance languages. These were for many centuries only spoken languages, Latin still being used for writing. For example, Latin was the official language of Portugal until 1296 when it was replaced by Portuguese. The Romance languages evolved from Vulgar Latin, the spoken language of common usage, which in turn evolved from an older speech which also produced the formal classical standard. Latin and Romance differ (for example) in that Romance had distinctive stress, whereas Latin had distinctive length of vowels. In Italian and Sardo logudorese, there is distinctive length of consonants and stress, in Spanish only distinctive stress, and in French even stress is no longer distinctive. Another major distinction between Romance and Latin is that all Romance languages, excluding Romanian, have lost their case endings in most words except for some pronouns. Romanian retains a direct case (nominative/accusative), an indirect case (dative/genitive), and vocative. In Italy, Latin is still compulsory in secondary schools as Liceo Classico and Liceo Scientifico which are usually attended by people who aim to the highest level of education. In Liceo Classico Ancient Greek is a compulsory subject.
Latin and English
See Latin influence in English for a more complete exposition. English grammar is independent of Latin grammar, though prescriptive grammarians in English have been heavily influenced by Latin. Attempts to make English grammar follow Latin rules — such as the prohibition against the split infinitive — have not worked successfully in regular usage. However, as many as half the words in English were derived from Latin, including many words of Greek origin first adopted by the Romans, not to mention the thousands of French, hundreds of Spanish, Portuguese and Italian words of Latin origin that have also enriched English. During the 16th and on through the 18th century English writers created huge numbers of new words from Latin and Greek roots. These words were dubbed "inkhorn" or "inkpot" words (as if they had spilled from a pot of ink). Many of these words were used once by the author and then forgotten, but some remain. Imbibe, extrapolate, dormant and inebriation are all inkhorn terms carved from Latin words. In fact, the word etymology is derived from the Greek word etymologia, meaning "true sense of the word." Latin was once taught in many of the schools in Britain with academic leanings - perhaps 25% of the total [http://www.channel4.com/history/microsites/T/teachem2/thennow/]. However, the requirement for it was gradually abandoned in the professions such as the law and medicine, and then, from around the late 1960s, for admission to university. After the introduction of the Modern Language GCSE in the 1980s, it was gradually replaced by other languages, although it is now being taught by more schools along with other classical languages.
Latin education
The linguistic element of Latin courses offered in high schools or secondary schools, and in universities, is primarily geared toward an ability to translate Latin texts into modern languages, rather than using it in oral communication. As such, the skill of reading is heavily emphasized, whereas speaking and listening skills are barely touched upon. However, there is a growing movement, sometimes known as the Living Latin movement, whose supporters believe that Latin can, or should, be taught in the same way that modern "living" languages are taught, that is, as a means of both spoken and written communication. One of the most interesting aspects of such an approach is that it assists speculative insight into how many of the ancient authors spoke and incorporated sounds of the language stylistically; without understanding how the language is meant to be heard it is very difficult to identify patterns in Latin poetry. Institutions offering Living Latin instruction include the Vatican and the University of Kentucky. In Britain the Classical Association encourages this approach, and there has been something of a vogue for books describing the adventures of a mouse called Minimus. In the United States there is a thriving competitive organization for high school Latin students, the National Junior Classical League (the second-largest youth organization in the world after the Boy Scouts), backed up by the Senior Classical League for college students. Many would-be international auxiliary languages have been heavily influenced by Latin, and the moderately successful Interlingua considers itself to be the modernized and simplified version of the language (le latino moderne international e simplificate). Latin translations of modern literature such as Paddington Bear, Winnie the Pooh, Harry Potter and the Philosopher's Stone, Le Petit Prince, Max und Moritz, and The Cat in the Hat have also helped boost interest in the language.
See also

About the Latin language

- Latin grammar
- Latin spelling and pronunciation
- Latin declension
- Latin conjugation
- Latin alphabet
- List of Latin words with English derivatives
- Latin verbs with English derivatives
- Latin nouns with English derivatives
- ablative absolute
- Word order in Latin
About the Latin literary heritage

- Latin literature
- Romance languages
- Loeb Classical Library
- List of Latin phrases
- List of Latin proverbs
- Brocard
- List of Latin and Greek words commonly used in systematic names
- List of Latin place names in Europe
- Carmen Possum
Other related topics

- Roman Empire
- Internationalism
References

- Bennett, Charles E. Latin Grammar (Allyn and Bacon, Chicago, 1908)
- N. Vincent: "Latin", in The Romance Languages, M. Harris and N. Vincent, eds., (Oxford Univ. Press. 1990), ISBN 0195208293
- Waquet, Françoise, Latin, or the Empire of a Sign: From the Sixteenth to the Twentieth Centuries (Verso, 2003) ISBN 1859844022; translated from the French by John Howe.
- Wheelock, Frederic. Latin: An Introduction (Collins, 6th ed., 2005) ISBN 0060784237
External links

- [http://www.jambell.com/latin.html Latin Phrases for after dinner conversation (Thanks to Elaine Poole)]
- [http://www.ethnologue.com/show_language.asp?code=lat Ethnologue report for Latin]
- [http://forumromanum.org/literature/index.html Corpus Scriptorum Latinorum] is a comprehensive webography of Latin texts and their translations.
- [http://www.perseus.tufts.edu/ The Perseus Project] has many useful pages for the study of classical languages and literatures, including [http://www.perseus.tufts.edu/cgi-bin/resolveform?lang=Latin an interactive Latin dictionary].
- [http://lysy2.archives.nd.edu/cgi-bin/words.exe words by William whitaker] is a dictionary program online capable of looking up various word forms.
- [http://retiarius.org/ Retiarius.Org] includes a Latin text search engine.
- [http://www.nd.edu/~archives/latgramm.htm Latin-English dictionary and Latin grammar from U of Notre Dame]
- [http://latin-language.co.uk/ Latin language] History of Latin language, Latin texts with English translation and a collection of dictionaries.
- [http://augustinus.eresmas.net/scl/ Societas Circulorum Latinorum] gathers together Latin Circles all over the world.
- [http://www.learnlatin.tk LearnLatin.tk] - Free online course in Latin
- [http://www.latintests.net/ LatinTests.net] - Lets Latin learners test their grammar and vocabulary with self-checking quizzes.
- [http://thelatinlibrary.com/ The Latin Library] contains many Latin etexts
- [http://www.textkit.com/ Textkit] has Latin textbooks and etexts.
- [http://www.websters-online-dictionary.org/definition/Latin-english/ Latin–English Dictionary]: from Webster's Rosetta Edition.
- [http://www.language-reference.com/ Language reference] Cross-foreign-language lexicon powered by its own search engine. All cross combinations between Latin and French, German, Italian, Spanish.
- [http://comp.uark.edu/~mreynold/rhetor.html Rhetor by Gabriel Harvey] was originally published in 1577 and never again reprinted.
- [http://freewebs.com/omniamundamundis omniamundamundis] Latin hypertexts from fourteen ancient Roman authors.
- [http://www.saltspring.com/capewest/pron.htm Pronunciation of Biological Latin, Including Taxonomic Names of Plants and Animals]
- [http://www.yleradio1.fi/nuntii Nuntii Latini (News in Latin)], written and spoken (RealAudio) news in latin. Weekly review of world news in Classical Latin, the only international broadcast of its kind in the world, produced by YLE, the Finnish Broadcasting Company.
- [http://www.tranexp.com:2000/InterTran?url=http%3A%2F%2F&type=text&text=Replace%20Me&from=eng&to=ltt InterTran Latin], Translate from Latin to ENGLISH or vice versa.
- [http://www.latinvulgate.com Latin Vulgate] The Latin and English of the Old & New Testaments in parallel, along with the Complete Sayings of Jesus in parallel Latin and English. Category:Classical languages Category:Ancient languages Category:Fusional languages Category:Languages of Italy Category:Languages of Vatican City als:Latein zh-min-nan:Latin-gí ko:라틴어 ja:ラテン語 simple:Latin language th:ภาษาละติน

Axis

The word axis has several meanings:
- In mathematics, axis can mean:
- A straight line around which a geometric figure can be rotated.
- A coordinate axis -- a line representing a coordinate system.
- In geometry, special types of axes can include
- An axis of rotation
- An axis of symmetry
- In anatomy, the axis is the second cervical vertebra of the spine.
- In politics, it may refer to:
- A quasi-mathematical parameter which is used to describe some characteristic of someone or something. See Political spectrum.
- The Axis Powers of the Second World War
- The Axis of Evil, as coined by George W. Bush
- A similar alliance
- In Gundam (Universal Century), a fictional universe, Axis may refer to:
- The Asteroid Axis, a waypoint for the Jupiter Energy Fleet.
- The Axis Zeon, a faction in the Universal Century timeline
- In the record industry, it may refer to
- Axis Records, the name of two music labels.
- In Information Technology
- Axis is an opensource Webservices platform implementation of the Apache foundation
- Axis Communications (also known as AXIS) is a swedish manufacturer of network print servers, high-end webcameras and miscellanous IT goods.
- In music:
- Axis system simple:Axis

Equator

The equator is an imaginary circle drawn around a planet (or other astronomical object) at a distance halfway between the poles. The equator divides the planet into a Northern Hemisphere and the Southern Hemisphere. The latitude of the equator is, by definition, 0°. The length of Earth's equator is about 40,075.0 km, or 24,901.5 miles. The equator is one of the five main circles of latitude based on the relationship of the Earth's rotation and plane of orbit around the sun. Additionally, the equator is the only line of latitude which is also a great circle The Sun, in its seasonal movement through the sky, passes directly over the equator twice each year on the Vernal and Autumnal Equinoxes, which occur in March and September (respectively). At the equator, the rays of the sun are perpendicular to the surface of the earth on these dates. Places near the equator experience the quickest rates of sunrise and sunset in the world, taking minutes. Such places also have a relatively constant amount of day/night time on every day throughout the year compared with more northerly or southerly places.

Equatorial climate

In many tropical regions people identify two seasons, wet and dry, but most places very close to the equator are wet throughout the year, although seasons can vary depending on a variety of factors including elevation and proximity to an ocean. ocean The surface of the Earth at the equator is mainly ocean. The highest point on the Equator is 4,690 m, at 77° 59' 31" W on the south slopes of Volcán Cayambe (summit 5,790 m) in Ecuador. This is a short distance above the snow line, and is the only point on the Equator where snow lies on the ground (Google Earth satellite data and photos).

Equatorial countries

The equator traverses the land and/or water of 13 countries in total:
- São Tomé and Príncipe - passing through Ilhéu das Rolas, an islet in this archipelago
- Gabon
- Republic of the Congo
- Democratic Republic of Congo
- Uganda
- Kenya
- Somalia
- Maldives - misses every island, passing between Gaafu Dhaalu Atoll and Gnaviyani Atoll
- Indonesia
- Sumatra - also small islands Tanah Masa to the West and Lingga to the East
- Borneo - Kalimantan
- Sulawesi
- Halmahera - also small islands Kayoa to the West and Gebe to the East
- Kawe, a small island near Waigeo - and other islets throughout Indonesia
- Kiribati - misses every island
- Gilbert Islands - passing between Aranuka and Nonouti Atolls
- Line Islands - passing between Kiritimati Island and Malden Island, though neither is very close to the equator
- Ecuador
- Galapagos Islands - passing through Isabela Island.
- Mainland Ecuador
- Colombia
- Brazil

Natural satellite

The common noun moon (not capitalized) is used to mean any natural satellite of the other planets. There are at least 140 moons within Earth's solar system, and presumably many others orbiting the planets of other stars. The large gas giants have extensive systems of moons, including half a dozen comparable in size to Earth's moon. Mercury and Venus have no moons at all, Earth has one large moon ("The Moon"), Mars has two tiny moons, and Pluto has three, including a large companion called Charon (Pluto and Charon are sometimes considered a double planet).

Origin

Most moons are assumed to have been formed out of the same collapsing region of protoplanetary disk that gave rise to its primary. However, there are many exceptions and variations to this standard model of moon formation that are known or theorized. Several moons are thought to be captured asteroids; others may be fragments of larger moons shattered by impacts, or (in the case of Earth's Moon) a portion of the planet itself blasted into orbit by a large impact. As most moons are known only through a few observations via probes or telescopes, most theories about their origins are still uncertain.

Orbital characteristics

Most moons in the solar system are tidally locked to their primaries, meaning that one side of the moon is always turned toward the planet. Exceptions are Saturn's moon Hyperion, which rotates chaotically due to a variety of external influences, and the outermost moons of the gas giants, which are too far away to become 'locked' (an example is Saturn's moon Phoebe). It is not possible for a moon to have moons of its own: the tidal effects of their primaries would make such a system unstable. However, several moons have small companions in the Lagrangian points of their orbits (e.g., Saturn's moons Tethys and Dione). The recent discovery of 243 Ida's moon Dactyl confirms that some asteroids also have moons. Some, like 90 Antiope, are double asteroids with two equal-sized components. The asteroid 87 Sylvia has two moons. See asteroid moon for further information.

Moons of the Solar system

The largest moons in the solar system (those bigger than about 3000 km across) are Earth's Moon, Jupiter's Galilean moons Io, Europa, Ganymede, and Callisto, Saturn's moon Titan, and Neptune's captured moon Triton. For smaller moons see the articles on the appropriate planet. The following is a comparative table classifying the moons of the solar system by diameter. The column on the right includes some notable planets, asteroids and Kuiper belt objects for comparison.

Diameter(km)	Earth	Mars	Jupiter	Saturn	Uranus	Neptune	Pluto	Other objects
5000-6000			Ganymede	Titan
4000-5000			Callisto					Mercury
3000-4000	Luna		Io Europa
2000-3000						Triton		Pluto
1000-2000				Rhea Iapetus Dione Tethys	Titania Oberon Umbriel Ariel		Charon	90377 Sedna 90482 Orcus 50000 Quaoar 20000 Varuna 28978 Ixion
100-1000			Himalia Amalthea	Enceladus Mimas Hyperion Phoebe Janus Epimetheus Prometheus	Miranda Sycorax Puck Portia	Proteus Nereid Larissa Galatea Despina	S/2005 P 1² S/2005 P 2²	1 Ceres 2 Pallas 4 Vesta 10 Hygiea 511 Davida 704 Interamnia 3 Juno (and many others)
50-100			Thebe Elara Pasiphaë	Pandora	Caliban Juliet Belinda Cressida Rosalind Desdemona Bianca	Thalassa Naiad S/2002 N 4		(Too many to list)
10-50		Phobos Deimos	Carme Metis Sinope Lysithea Ananke Leda Adrastea	Siarnaq Atlas Helene Albiorix Telesto Pan Paaliaq Calypso Ymir Kiviuq Tarvos Ijiraq	Ophelia Cordelia Setebos Prospero Stephano Perdita S/2001 U 2 S/2001 U 3 Margaret Trinculo Mab Cupid	S/2002 N 1 S/2002 N 2 S/2002 N 3 Psamathe		(Too many to list)
less than 10	Cruithne¹		At least 47, see Jupiter's natural satellites for a listing.	Erriapo Narvi Skathi Mundilfari Suttungr Thrymr Pallene Polydeuces Methone S/2004 S 3 Daphnis				(Too many to list)

¹) Cruithne is not a real moon; it is mainly placed here for comparison's sake.
²) Diameters of the new Plutonian satellites are still very poorly known, but they are estimated to lie between 64 and 200 km.
In addition to the moons of the various planets there are also over 30 known asteroid moons, asteroids that orbit other asteroids.

External links

Jupiter's moons

- [http://www.ifa.hawaii.edu/~sheppard/satellites/jupsatdata.html Data on Jupiter's satellites]
- [http://www.ifa.hawaii.edu/faculty/jewitt/jmoons/jmoons.html Jupiter's new moons (discovered in 2000)]
- [http://www.ifa.hawaii.edu/~sheppard/satellites/jup.html Jupiter's new moons (discovered in 2002)]
- [http://www.ifa.hawaii.edu/~sheppard/satellites/jup2003.html Jupiter's new moons (discovered in 2003)]

Saturn's moons

- [http://www.news.cornell.edu/releases/Oct00/Saturn.moons.deb.html Saturn's new moons (discovered in 2000)]
- [http://www.ifa.hawaii.edu/~sheppard/satellites/sat2003.html Saturn's new moon (discovered in 2003)]

Neptune's moons

- [http://sse.jpl.nasa.gov/whatsnew/pr/030113A.html Neptune's new moons (discovered in 2003)]

All moons

- [http://www.planetary.org/learn/solarsystem/moons.html Moons of the Solar System (The Planetary Society)]
- [http://www.ifa.hawaii.edu/~sheppard/satellites Scott Sheppard's page]
- [http://ssd.jpl.nasa.gov JPL's Solar System Dynamics page]
- [http://www.space.com/scienceastronomy/planet_photo_040910.html Moon of an Object? First Photo of Satellite Beyond the Solar System]
- [http://planetarynames.wr.usgs.gov/append7.html USGS list of named moons] ----
- als:Satellit (Astronomie) ko:위성 ms:Satelit semulajadi ja:衛星 th:ดาวบริวาร

Sun

:: For the astrological significance of the Sun, see Solar system in astrology. ::"Solar" redirects here; for the superhero by that name, see Solar (comics). The Sun (or Sol) is the star at the center of our Solar system. Earth orbits the Sun, as do many other bodies, including other planets, asteroids, meteoroids, comets and dust. Its heat and light support almost all life on Earth. The Sun is a ball of plasma with a mass of about 2 kg, which is somewhat higher than that of an average star. About 74% of its mass is hydrogen, with 25% helium and the rest made up of trace quantities of heavier elements. It is thought that the Sun is about 5 billion years old, and is about halfway through its main sequence evolution, during which nuclear fusion reactions in its core fuse hydrogen into helium. In about 5 billion years time the Sun will become a white dwarf. Although it is the nearest star to Earth and has been intensively studied by scientists, many questions about the Sun remain unanswered, such as why its outer atmosphere has a temperature of over 10⁶ K when its visible surface (the photosphere) has a temperature of just 6,000 K. Looking directly at the Sun can damage the retina and one's eyesight. See below for details.

General information

See below The Sun is classified as a main sequence star, which means it is in a state of "hydrostatic balance", neither contracting nor expanding, and is generating its energy through nuclear fusion of hydrogen nuclei into helium. The Sun has a spectral class of G2V, with the G2 meaning that its color is yellow and its spectrum contains spectral lines of ionized and neutral metals as well as very weak hydrogen lines [http://www.astro.uiuc.edu/~kaler/sow/spectra.html#classes], and the V signifying that it, like most stars, is a "dwarf" star on the main sequence[http://www.physics.uq.edu.au/people/ross/phys2080/spec/analyz.htm]. The Sun has a predicted main sequence lifetime of about 10 billion years. Its current age is thought to be about 4.5 billion years, a figure which is determined using computer models of stellar evolution, and nucleocosmochronology . The Sun orbits the center of the Milky Way galaxy at a distance of about 25,000 to 28,000 light-years from the galactic centre, completing one revolution in about 226 million years. The orbital speed is 217 km/s, equivalent to one light year every 1400 years, and one AU every 8 days. The astronomical symbol for the Sun is a circle with a point at its centre (Image:Sol.gif).

Structure

Image:Sol.gif The Sun is a near-perfect sphere, with an oblateness estimated at about 9 millionths, which means the polar diameter differs from the equatorial by about 10 km. This is because the centrifugal effect of the Sun's slow rotation is 18 million times weaker than its surface gravity (at the equator). Tidal effects from the planets do not significantly affect the shape of the Sun, although the Sun itself orbits the center of mass of the solar system, which is offset from the Sun's center mostly because of the large mass of Jupiter. The mass of the Sun is so comparatively great that the center of mass of the solar system is generally within the bounds of the Sun itself. The Sun does not have a definite boundary as rocky planets do, as the density of its gases drops off following an approximately exponential relationship with distance from the centre of the Sun. Nevertheless, the Sun has well defined interior structure, described below. The Sun's radius is measured from centre to the edges of the photosphere. The solar interior is not directly observable and the Sun itself is opaque to electromagnetic radiation. However, just as the study of the waves generated by earthquakes (seismology) can be used to study the interior structure of the Earth, helioseismology, the study of sound waves that travel through the Sun's interior, has also contributed greatly to our understanding of the Sun's structure . Computer modeling of the Sun is also used as a theoretical tool to investigate its deep layers.

Core

At the center of the Sun, where its density reaches up to 150,000 kg/m³ (150 times the density of water on Earth), thermonuclear reactions (nuclear fusion) convert hydrogen into helium, producing the energy that keeps the Sun in a state of equilibrium. About 8.9 protons (hydrogen nuclei) are converted to helium nuclei every second, releasing energy at the matter-energy conversion rate of 4.26 million tonnes per second or 383 yottawatts (9.15 tons of TNT per second). The core extends from the center of the Sun to about 0.2 solar radii, and is the only part of the Sun where an appreciable amount of heat is produced by fusion: the rest of the star is heated by energy that is transferred outward. All of the energy of the interior fusion must travel through the successive layers to the solar photosphere, before it escapes to space. The high-energy photons (gamma and X rays) released in fusion reactions take a long time to reach the Sun's surface, slowed down by the indirect path taken, as well as constant absorption and re-emission at lower energies in the solar mantle (see below). Estimates of the "photon travel time" range from as much as 50 million years (Richard S. Lewis, The Illustrated Encyclopedia of the Universe, Harmony Books, New York, 1983, p. 65) to as little as 17,000 years [http://www.badastronomy.com/bitesize/solar_system/sun.html]. Upon reaching the surface after a final trip through the convective outer layer, the photons escape as visible light. Neutrinos are also released in the fusion reactions in the core, but unlike photons they very rarely interact with matter, and so almost all are able to escape the Sun immediately.

Radiation zone

From about 0.2 to about 0.7 solar radii, the material is hot and dense enough that thermal radiation is sufficient to transfer the intense heat of the core outward. In this zone, there is no thermal convection: while the material grows cooler with altitude, this temperature gradient is slower than the adiabatic lapse rate and hence cannot drive convection. Heat is transferred by ions of hydrogen and helium emitting photons, which travel a brief distance before being re-absorbed by other ions. Because of this, it can take a photon nearly 1,000,000 years to reach the photosphere.

Convection zone

photosphere From about 0.7 solar radii to 1.0 solar radii, the material in the Sun is not dense enough or hot enough to transfer the heat energy of the interior outward via radiation. As a result, thermal convection occurs as thermal columns carry hot material to the surface (photosphere) of the Sun. Once the material cools off at the surface, it plunges back downward to the base of the convection zone, to receive more heat from the top of the radiative zone.