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Celestial Coordinate System, Horizontal Coordinate System, Polar coordinate system, Cylindrical Coordinates system, Shperical coordinate System, Geographic Coordinates, UTM Coordinate, UTM latitude zone, Overlapping Grids, Celestial Sphere, Astronomical Horizon, Hourly circle, Meridiano Celeste, Celestial Ecuator, Horizontal Coordinates, Azimut and height, Day Parallax and Light Refraction, Lunar Parallax, Solar Parallax, Stellar Parallax, Equatorial coordinates, Hourly Coordinates, Eclipses and Moon Movements, Moon relationships with Earth, Parallax, Lunar Parallax, Solar Parallax, Stellar Parallax, Dynamic or moving-cluster Parallax, Scale of the Universe, Precession and Nutation, Torque-free precession, Torque-Induced Precession, Precession of the Equinoxes, Precession of Planetary Orbits, Nutation, Nutation of Earth, Values, Earth's Axis, Movements of the Earth, Equinox, Equinoxes and Solstices, Solstice, Observatories, Telescopes, radio Telescopes, Spectrograph, Spectrometer.

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Celestial coordinate system

In astronomy, a celestial coordinate system is a coordinate system for mapping positions in the sky. There are different celestial coordinate systems each using a coordinate grid projected on the celestial sphere, in analogy to the geographic coordinate system used on the surface of the Earth. The coordinate systems differ only in their choice of the fundamental plane, which divides the sky into two equal hemispheres along a great circle. (The fundamental plane of the geographic system is the Earth's equator). Each coordinate system is named for its choice of fundamental plane; below the name of a pole and the names of the coordinates are also shown:

Horizontal coordinate system - horizon - zenith/nadir - Altitude - azimuth

Equatorial coordinate system - celestial equator - celestial pole - declination - right ascension or hour angle. Popular choices of pole and equator are the older B1950 and the modern J2000 systems, but a pole and equator "of date" can also be used, meaning one appropriate to the date under consideration, such as that at which a measurement of the position of a planet or spacecraft is made. There are also subdivisions into "mean of date" coordinates, which average out or ignore nutation, and "true of date," which include nutation.

Ecliptic coordinate system - ecliptic - ecliptic pole - ecliptic latitude - ecliptic longitude

Galactic coordinate system

Supergalactic coordinate system

Orbital characteristics

Medium Radio 384.400 km

Eccentricity 0,0549

Inclination 5,1454 °

It is a satellite of the Earth

Angular geocentric diameter

In the perigee 33 ' 28,8 "

In the climax 29 ' 23,2 "

Average diameter 31 ' 05,2 "

Physical characteristics

Equatorial diameter 3.474,8 km

Surface 38 million km ²

Mass 7.349 × 1022 kg

Average thickness 3,34 g/cm ³

Superficial gravity 1.62 m/s ²

Period of rotation 27d 7h 43,7min

Axial inclination 1,5424 °

Albedo 0,12

Superficial Temp. average min max

- K 250 K - K

Atmospheric characteristics

Atmospheric pressure 3 × 10-10Pa

Helium 25 %

Neon 25 %

Hydrogen 23 %

Argon 20 %

Methane Ammonia

Dioxide of carbon - touches

Composition of the crust

Oxygen 43 %

Silicon 21 %

Aluminum 10 %

Calcium 9 %

Iron 9 %

Magnesium 5 %

Titanium 2 %

Nickel 0,6 %

Sodium 0,3 %

Chrome 0,2 %

Potassium 0,1 %

Manganese 0,1 %

Sulfur 0,1 %

Phosphorus 500ppm

Carbon 100ppm

Nitrogen 100ppm

Hydrogen 50ppm

Helium 20ppm

The Moon is the only natural satellite of the Earth. Is the nearest star to us and the best acquaintance. Its diameter is less than one third of the terrestrial one (3.476 km), its surface, a fourteenth part (37.700.000 km ²), and its volume about a fiftieth part (21.860.000 km).

The Moon is in synchronous rotation, meaning that it keeps (almost) the same face turned to the Earth at all times. The Moon makes a complete orbit about the Earth approximately once every 27.3 days; unlike most satellites of other planets, the Moon orbits near the ecliptic and not the Earth's equatorial plane.

The Earth and Moon have many physical effects upon one another, including the tides. Most of the tidal effects seen on the Earth are caused by the Moon's gravitational pull, with a smaller contribution from the Sun.

The Moon is Earth's only natural satellite. It has no formal name other than "The Moon", although in English it is occasionally called Luna (Latin for moon), or Selene (Greek for moon), to distinguish it from the generic "moon" (natural satellites of other planets are also called moons). Its symbol is a crescent. The terms lunar, selene/seleno-, and -cynthion (from the Lunar deities Selene and Cynthia) refer to the Moon (aposelene, selenocentric, pericynthion, etc.).

Moon Movements

Climax and Perigee of the Moon

Nodes

Lunar Phases

Lunar Eclipses

Solar Eclipses

The average distance from the Moon to the Earth is 384,403 kilometers (238,857 miles). The Moon's diameter is 3,476 kilometres (2,160 mi). Reflected sunlight from the Moon's surface reaches Earth in 1.3 seconds (at the speed of light).

The first man-made object to land on the Moon was Luna 2 in 1959, the first photographs of the otherwise occluded far side of the Moon were made by Luna 3 in the same year, and the first people to land on the Moon came aboard Apollo 11 in 1969.

The two sides of the Moon

The Moon is in synchronous rotation, meaning that it keeps nearly the same face turned toward Earth at all times (there is a small variation, called libration). The side of the Moon that faces Earth is called the near side, and the opposite side is called the far side. The far side is also sometimes called the "dark side", which means "unknown and hidden", and not "lacking light" as might seem to be implied by the name; in fact, the far side receives (on average) as much sunlight as the near side, but at opposite times. Spacecraft are cut off from direct radio communication with Earth when on the far side of the Moon due to line of sight. One distinguishing feature of the far side is its almost complete lack of maria (singular: mare), which are the dark albedo features.

The inclination of the Moon's orbit makes it implausible that the Moon formed along with the Earth or was captured later; its origin is the subject of some scientific debate.

Early speculation proposed that the Moon broke off from the Earth's crust due to centrifugal force, leaving an ocean basin (presumed to be the Pacific) behind as a scar. This concept requires too great an initial spin of the Earth and the presumption of a Pacific origin is not compatible with the geological standard model, the theory of plate tectonics. Others speculated the Moon formed elsewhere and was captured into its orbit. Two of the other theories include the coformation or condensation theory and the impact theory, which speculates that the Moon formed from the debris that resulted from a collision between the early Earth and a planetesimal.

The coformation or condensation hypothesis posits that the Earth and the Moon formed together at about the same time from the primordial accretion disk, the Moon forming from material surrounding the coalescing proto-Earth, similar to the way the planets formed around the Sun. Some suggest that this hypothesis fails to adequately explain the depletion of iron in the Moon.

Recently, the giant impact hypothesis has been considered a more viable scientific hypothesis for the moon's origin than the coformation or condensation hypothesis. The Giant Impact hypothesis holds that the Moon formed from the ejecta resulting from a collision between a very early, semi-molten Earth and a planet-like object the size of Mars, which has been referred to as Theia or Orpheus. The material ejected from this impact would have gathered in orbit around Earth and formed the Moon. This hypothesis is bolstered by two main observations: First, the composition of the Moon resembles that of Earth's crust, whereas it has relatively few heavy elements that would have been present if it formed by itself out of the same material from which Earth formed. Second, through radiometric dating, it has been determined that the Moon's crust formed between 20 and 30 million years after that of Earth, despite its smallness and associated larger loss of internal heat, although it has been suggested that this hypothesis does not adequately address the abundance of volatile elements in the moon.[3]

At that time the Moon was much closer to the Earth and strong tidal forces deformed the once molten sphere into an ellipsoid, with the major axis pointed towards Earth. When the Moon started to cool a solid crust was formed along its surface, but its molten interior remained displaced in the direction of the Earth. Said otherwise: the crust on the near side was much thinner than on the far side. Especially during the late heavy bombardment, around 3.8 to 4 billion years ago, many large meteorites were able to penetrate the thin crust of the near side but only very few could do so on the far side. Where the crust was perforated the hot lavas from the interior oozed out and spread over the surface, only to cool down later into the maria as we know them nowadays (so they were seas after all, only not of water). This explains the paucity of maria on the far side.

The geological epochs of the Moon are defined based on the dating of various significant impact events in the Moon's history. The period of the late heavy bombardment is determined by analysis of craters and Moon rocks. In 2005, a team of scientists from Germany, the United Kingdom, and Switzerland measured the Moon's age at 4527 ± 10 million years, which would imply that it was formed only 30 to 50 million years after the origin of the solar system

More than 4.5 billion years ago, the surface of the Moon was a liquid magma ocean. Scientists think that one component of lunar rocks, called KREEP (potassium, rare earth elements, and phosphorus), represents the last chemical remnant of that magma ocean. KREEP is actually a composite of what scientists term "incompatible elements": those that cannot fit into a crystal structure and thus were left behind, floating to the surface of the magma. For researchers, KREEP is a convenient tracer, useful for reporting the story of the volcanic history of the lunar crust and chronicling the frequency of impacts by comets and other celestial bodies.

The lunar crust is composed of a variety of primary elements, including uranium, thorium, potassium, oxygen, silicon, magnesium, iron, titanium, calcium, aluminium and hydrogen, as determined by spectroscopy.

A complete global mapping of the Moon for the abundance of these elements has never been performed. However, some spacecraft have done so for portions of the Moon; Galileo did so when it flew by the Moon in 1992.[5] The overall composition of the Moon is believed to be similar to that of the upper parts of the Earth other than a depletion of volatile elements and of iron.

When observed with earth based telescopes, the moon can be seen to have some 30,000 craters having a diameter of at least 1 km, but close up observation from lunar orbit reveals a multitude of ever smaller craters. Most are hundreds of millions or billions of years old; the lack of atmosphere, weather and recent geological processes ensures that most of them remain permanently preserved. In the lunar terrae, it is indeed impossible to add a crater of any size without obliterating another; this is termed saturation.

The largest crater on the Moon, and indeed the largest known crater within the solar system, forms the South Pole-Aitken basin. This crater is located on the far side, near the South Pole, and is some 2,240 kilometres in diameter, and 13 kilometres in depth.

The dark and relatively featureless lunar plains are called maria, Latin for seas, since they were believed by ancient astronomers to be water-filled seas. They are actually vast ancient basaltic lava flows that filled the basins of large impact craters. The lighter-colored highlands are called terrae. Maria are found almost exclusively on the Lunar nearside, with the Lunar farside having only a few scattered patches.

Blanketed atop the Moon's crust is a dusty outer rock layer called regolith, the result of rocks shattered by billions of years of impacts. Both the crust and regolith are unevenly distributed over the entire Moon. The crust ranges from 60 kilometres (38 mi) thick on the near side to 100 kilometres (63 mi) on the far side, and the regolith varies from 3 to 5 metres (10 to 16 ft) deep in the maria to 10 to 20 metres (33 to 66 ft) deep in the highlands.

In 2004, a team led by Dr. Ben Bussey of Johns Hopkins University using images taken by the Clementine mission determined that four mountainous regions on the rim of the 73-km-wide Peary crater at the Moon's north pole appeared to remain illuminated for the entire Lunar day. These unnamed "mountains of eternal light" are possible due to the Moon's extremely small axial tilt, which also gives rise to permanent shadow at the bottoms of many polar craters. No similar regions of eternal light exist at the less mountainous south pole, although the rim of Shackleton crater is illuminated for 80% of the lunar day. Clementine's images were taken during the northern Lunar hemisphere's summer season, and it remains unknown whether these four mountains are shaded at any point during their local winter season.

Dating of the lunar impact events through 40Ar/39Ar isotop analysis of glass spherules, created during the impacts, showed a high impact number in early lunar history and in the last 400 mio years.[6] [7]

Presence of water

Over time, comets and meteoroids continuously bombard the Moon. Many of these objects are water-rich. Energy from sunlight splits much of this water into its constituent elements hydrogen and oxygen, both of which usually fly off into space immediately. However, it has been hypothesized that significant traces of water remain on the Moon, either on the surface, or embedded within the crust. The results of the Clementine mission suggested that small, frozen pockets of water ice (remnants of water-rich comet impacts) may be embedded unmelted in the permanently shadowed regions of the lunar crust. Although the pockets are thought to be small, the overall amount of water was suggested to be quite significant — 1 km³.

Some water molecules, however, may have literally hopped along the surface and become trapped inside craters at the lunar poles. Due to the very slight "tilt" of the Moon's axis, only 1.5°, some of these deep craters never receive any light from the Sun — they are permanently shadowed. Clementine has mapped[8] craters at the lunar south pole[9] which are shadowed in this way. It is in such craters that scientists expect to find frozen water if it is there at all. If found, water ice could be mined and then split into hydrogen and oxygen by solar panel-equipped electric power stations or a nuclear generator. The presence of usable quantities of water on the Moon would be an important factor in rendering lunar habitation cost-effective, since transporting water (or hydrogen and oxygen) from Earth would be prohibitively expensive.

The equatorial Moon rock collected by Apollo astronauts contained no traces of water. Neither the Lunar Prospector nor more recent surveys, such as those of the Smithsonian Institution, have found direct evidence of lunar water, ice, or water vapor. Lunar Prospector results, however, indicate the presence of hydrogen in the permanently shadowed regions, which could be in the form of water ice.

Magnetic field

Compared to that of Earth, the Moon has a very weak magnetic field. While some of the Moon's magnetism is thought to be intrinsic (such as a strip of the lunar crust called the Rima Sirsalis), collision with other celestial bodies might have imparted some of the Moon's magnetic properties. Indeed, a long-standing question in planetary science is whether an airless solar system body, such as the Moon, can obtain magnetism from impact processes such as comets and asteroids. Magnetic measurements can also supply information about the size and electrical conductivity of the lunar core — evidence that will help scientists better understand the Moon's origins. For instance, if the core contains more magnetic elements (such as iron) than Earth, then the impact theory loses some credibility (although there are alternate explanations for why the lunar core might contain less iron).

Atmosphere

The Moon has a relatively insignificant and tenuous atmosphere. One source of this atmosphere is outgassing — the release of gases, for instance radon, which originate deep within the Moon's interior. Another important source of gases is the solar wind, which is briefly captured by the Moon's gravity.

Eclipses happen only if Sun, Earth, and Moon are lined up. Solar eclipses can only occur near a new moon; lunar eclipses can only occur near a full moon.

The angular diameters of the Moon and the Sun as seen from Earth overlap in their variation, so that both total and annular solar eclipses are possible. In a total eclipse, the Moon completely covers the disc of the Sun and the solar corona becomes visible to the naked eye.

Occultation of stars

The Moon is continuously blocking our view of the sky directly behind it. The Moon blocks about 1/2 degree wide circular area. When a bright star or planet passes behind the Moon it is occulted or hidden from view. A solar eclipse is an occultation of the Sun. Because the Moon is close to Earth, occultations of stars are not visible everywhere. Because of the moving nodes of the lunar orbit, each year different stars are occulted.

During the brightest full moons, the Moon can have an apparent magnitude of about -12.6. For comparison, the Sun has an apparent magnitude of -26.8. When the Moon is in a quarter phase, its brightness is not one half of a full Moon. It is only about 1/10 of that, because the amount of solar radiation reflected towards the Earth is highly reduced by the shadows projected by the higher parts of the Moon over the lower ones.

The Moon appears larger when close to the horizon. This is a purely psychological effect (see Moon illusion). The angular diameter of the Moon from Earth is about one half of one degree, and is actually about 1.5% smaller when the Moon is near the horizon than when it is high in the sky (because it is further away by up to 1 Earth radius).

Another quirk of the visual system causes us to see the moon as almost pure white, when in fact it reflects only about 7% of the light falling on it (about as dark as a lump of coal). It has a very low albedo. Color constancy in the visual system recalibrates the relations between colors of an object and its surroundings; however, there is nothing next to the moon to reflect the light falling on the moon, therefore it is perceived as the brightest object visible. We have no standard to compare it to. An example of this is that, if you used a torch to illuminate a lump of coal in a dark room, it would look white. If you then broadened the beam of the torch to illuminate the surroundings, it would revert to black.

Various lighter and darker colored areas (primarily maria) create the patterns seen by different cultures as the Man in the Moon, the rabbit and the buffalo, amongst others. Craters and mountain chains are also prominent lunar features.

From any location on Earth, the highest altitude of the Moon on a day varies between the same limits as the Sun, and depends on season and lunar phase. For example, in winter the Moon is highest in the sky when it is full, and the full moon is highest in winter. The orientation of the Moon's crescent side also depends on the latitude of the observing site. Close to the equator an observer can see a boat Moon.[10]

We can use the Moon to visualize Earth's trajectory: When the Moon is its third quarter, it is moving in its orbit in front of the Earth. As the distance from the Earth to the moon is about 384,404 km and the Earth's orbital speed is about 107,000 km/h, the Moon is at a point where the Earth will be about three and a half hours later. And when the Moon is in its first quarter, it is "where we were" about three and a half hours ago.

Like the Sun, the Moon can also give rise to the atmospheric effects including a 22 degree halo ring and the smaller coronal rings seen more often through thin clouds.

For more information on how the Moon appears in Earth's sky, see Lunar phase.

The first leap in lunar observation was caused by the invention of the telescope. Galileo Galilei made especially good use of this new instrument and observed mountains and craters on the Moon's surface.

The Cold War-inspired space race between the Soviet Union and the United States of America led to an acceleration. What was the next big step depends on the political viewpoint: In the U.S. (and the West in general) the landing of the first humans on the moon in 1969 is seen as the culmination of the space race. The first man to walk on the lunar surface was Neil Armstrong, commander of the American mission Apollo 11, first setting foot on the moon at 02:56 UTC on July 21, 1969. The last man (as of 2006) to stand on the Moon was Eugene Cernan, who as part of the mission Apollo 17 walked on the Moon in December 1972. On the other hand, many scientifically important steps, such as the first photographs of the until then unseen far side of the moon in 1959, were first achieved by the Soviet Union. Moon samples have been brought back to Earth by three Luna missions (Luna 16, 20, and 24) and the Apollo missions 11 through 17 (excepting Apollo 13, which aborted its planned lunar landing).

Multiple scientific instruments were installed during the Apollo missions; some of them still function today. Among those were seismic detectors and reflecting prisms for laser ranging.

From the mid-1960s to the mid-1970s, there were 65 moon landings (with 10 in 1971 alone), but after Luna 24 in 1976 they stopped. The Soviet Union started focusing on Venus and space stations and the U.S. on Mars and beyond. In 1990 Japan visited the moon with the Hiten spacecraft, becoming the third country to orbit the Moon. The spacecraft released the Hagormo probe into lunar orbit, but the transmitter failed rendering the mission scientifically useless.

In 1994, the U.S. finally returned to the Moon, robotically at least, sending Clementine, a Joint Defense Department/NASA mission which completed the first global multispectral data set for the Moon. This was followed by the Lunar Prospector mission in 1998, the third mission in the Discovery Program. The neutron spectrometer on Lunar Prospector confirmed the presence of excess hydrogen at the lunar poles, which some have speculated to be due to the presence of water.

On January 14, 2004, U.S. President George W. Bush called for a plan to return manned missions to the Moon by 2020. The European Space Agency also has plans to launch probes to explore the Moon in the near future. European spacecraft Smart 1 was launched September 27, 2003 and entered lunar orbit on November 15, 2004. The People's Republic of China has expressed ambitious plans for exploring the Moon and has started the Chang'e program for lunar exploration. Japan has two planned lunar missions, LUNAR-A and Selene, and a manned lunar base is planned by the Japanese Space Agency (JAXA). India is to launch an unmanned mission Chandrayaan-1 in 2007.

A solar eclipse occurs when the Moon passes between Earth and the Sun, thereby totally or partially obscuring Earth's view of the Sun. This configuration can only occur during a New Moon, when the Sun and Moon are in conjunction as seen from the Earth. In ancient times, and in some cultures today, solar eclipses are attributed to mythical properties. Total solar eclipses can be frightening events for people unaware of their astronomical nature, as the Sun suddenly disappears in the middle of the day and the sky darkens in a matter of minutes.

However, the spiritual attribution of solar eclipses is now largely disregarded.

Total solar eclipses are very rare events for any given place on Earth because totality is only seen where the Moon's umbra touches the Earth's surface. A total solar eclipse is a spectacular natural phenomenon and many people consider travel to remote locations in order to observe one. The 1999 total eclipse in Europe, said by some to be the most-watched eclipse in human history, helped to increase public awareness of the phenomenon. This was illustrated by the number of people willing to make the trip to witness the 2005 annular eclipse and the 2006 total eclipse. The next solar eclipse takes place on September 22, 2006, while the next total solar eclipse will occur on August 1, 2008.

Types of solar eclipses

There are four types of solar eclipses:

A total eclipse occurs when the Sun is completely obscured by the Moon. The intensely bright disk of the Sun is replaced by the dark outline of the Moon, and the much fainter corona is visible (see image above). During any one eclipse, totality is visible only from at most a narrow track on the surface of the Earth.

An annular eclipse occurs when the Sun and Moon are exactly in line, but the apparent size of the Moon is smaller than that of the Sun. Hence the Sun appears as a very bright ring, or annulus, surrounding the outline of the Moon.

A hybrid eclipse is intermediate between a total and annular eclipse. At some points on the surface of the Earth it is visible as a total eclipse, whereas at others it is annular. Hybrid eclipses are rather rare.

A partial eclipse occurs when the Sun and Moon are not exactly in line, and the Moon only partially obscures the Sun. This phenomenon can usually be seen from a large part of the Earth outside of the track of an annular or total eclipse. However, some eclipses can only be seen as a partial eclipse, because the umbra never intersects the Earth's surface.

The Earth's distance from the Sun is about 400 times the Moon's distance from the Earth. The Sun's diameter is about 400 times the diameter of the Moon. Because these ratios are approximately the same, the sizes of the Sun and the Moon as seen from Earth appear to be approximately the same: about 0.5 degree of arc in angular measure.

Because the Moon's orbit around the Earth is an ellipse, as is the Earth's orbit around the Sun, the apparent sizes of the Sun and Moon vary.[1][2] The magnitude of an eclipse is the ratio of the apparent size of the Moon to the apparent size of the Sun during an eclipse. An eclipse when the Moon is near its closest distance from the Earth (i.e., near its perigee) can be a total eclipse because the Moon will appear to be large enough to cover completely the Sun's bright disk, or photosphere; a total eclipse has a magnitude greater than 1. Conversely, an eclipse when the Moon is near its farthest distance from the Earth (i.e., near its apogee) can only be an annular eclipse because the Moon will appear to be slightly smaller than the Sun; the magnitude of an annular eclipse is less than 1. Slightly more solar eclipses are annular than total because, on average, the Moon lies too far from Earth to cover the Sun completely. A hybrid eclipse occurs when the magnitude of an eclipse is very close to 1: the eclipse will appear to be total at some locations on Earth and annular at other locations.[3]

The Earth's orbit around the Sun is also elliptical, so the Earth's distance from the Sun varies throughout the year. This also affects the apparent sizes of the Sun and Moon, but not so much as the Moon's varying distance from the Earth. When the Earth approaches its farthest distance from the Sun (the aphelion) in July, this tends to favor a total eclipse. As the Earth approaches its closest distance from the Sun (the perihelion) in January, this tends to favor an annular eclipse.

Terminology

Central eclipse is often used as a generic term for a total, annular or hybrid eclipse. This is, however, not completely correct: the definition of a central eclipse is an eclipse during which the central line of the umbra touches the Earth's surface. It is possible, though extremely rare, that part of the umbra intersects with Earth (thus creating an annular or total eclipse), but not its central line. This is then called a non-central total or annular eclipse.[4]

The term solar eclipse itself is technically a misnomer. The phenomenon of the Moon passing in front of the Sun is not an eclipse, but an occultation. Properly speaking, an eclipse occurs when one object passes into the shadow cast by another object. For example, when the Moon disappears at Full Moon by passing into Earth's shadow, the event is properly called a lunar eclipse. Therefore, the proper, but rarely used, term for what is commonly called a solar eclipse is eclipse of the Earth.

Geometry of an eclipse

The diagram to the right shows the alignment of the Sun, Moon and Earth during a solar eclipse. The dark gray region below the moon is the umbra, where the Sun is completely obscured by the Moon. The small area where the umbra touches the Earth's surface is where a total eclipse can be seen. The larger light gray area is the penumbra, in which only a partial eclipse can be seen.

The Moon's orbit around the Earth is inclined at an angle of just over 5 degrees to the plane of the Earth's orbit around the Sun (the ecliptic). Because of this, at the time of a New Moon, the Moon will usually pass above or below the Sun. A solar eclipse can occur only when the New Moon occurs close to one of the points (known as nodes) where the Moon's orbit crosses the ecliptic.

As noted above, the Moon's orbit is also elliptical. The Moon's distance from the Earth can vary by about 6% from its average value. Therefore, the Moon's apparent size varies with its distance from the Earth, and it is this effect that leads to the difference between total and annular eclipses. The distance of the Earth from the Sun also varies during the year, but this is a smaller effect. On average, the Moon appears to be slightly smaller than the Sun, so the majority (about 60%) of central eclipses are annular. It is only when the Moon is closer to the Earth than average (near its perigee) that a total eclipse occurs.[5][6]

The Moon orbits the Earth in approximately 27.3 days, relative to a fixed frame of reference. This is known as the sidereal month. However, during one sidereal month, the Earth has revolved around the Sun, making the average time between one New Moon and the next longer than the sidereal month: it is approximately 29.6 days. This is known as the synodic month, and corresponds to what is commonly called the lunar month.

The Moon crosses from south to north of the ecliptic at its ascending node. However, the nodes of the Moon's orbit are gradually moving in a retrograde motion, due to the action of the Sun's gravity on the Moon's motion, and they make a complete circuit every 18.5 years. This means that the time between each passage of the Moon through the ascending node is slightly shorter than the sidereal month. This period is called the draconitic month.

Finally, the Moon's perigee is moving forwards in its orbit, and makes a complete circuit in about 9 years. The time between one perigee and the next is known as the anomalistic month.

The Moon's orbit intersects with the ecliptic at the two nodes that are 180 degrees apart. Therefore, the New Moon occurs close to the nodes at two periods of the year approximately six months apart, and there will always be at least one solar eclipse during these periods. Sometimes the New Moon occurs close enough to a node during two consecutive months. This means that in any given year, there will always be at least two solar eclipses, and there can be as many as five. However, some are visible only as partial eclipses, because the umbra passes above Earth's north or south pole, and others are central only in remote regions of the Arctic or Antarctic.[7][8]

Path of an eclipse

During a central eclipse, the Moon's umbra (or antumbra, in the case of an annular eclipse) moves rapidly from west to east across the Earth. The Earth is also rotating from west to east, but the umbra always moves faster than any given point on the Earth's surface, so it almost always appears to move in a roughly west-east direction across a map of the Earth (there are some rare exceptions to this which can occur during an eclipse of the midnight sun in Arctic or Antarctic regions).

The width of the track of a central eclipse varies according to the relative apparent diameters of the Sun and Moon. In the most favourable circumstances, when a total eclipse occurs very close to perigee, the track can be over 250 km wide and the duration of totality may be over 7 minutes. Outside of the central track, a partial eclipse can usually be seen over a much larger area of the Earth. [9]

Occurrence and eclipse cycles

Total solar eclipses are rare events. Although they occur somewhere on Earth approximately every 18 months, it has been estimated that they recur at any given place only once every 370 years, on average. Then, after waiting so long, the total eclipse only lasts for a few minutes, as the Moon's umbra moves eastward at over 1700 km/h. Totality can never last more than 7 min 40 s, and is usually much shorter: during each millennium there are typically fewer than 10 total solar eclipses exceeding 7 minutes. The last time this happened was June 30, 1973. Observers aboard a Concorde aircraft were able to stretch totality to about 74 minutes by flying along the path of the Moon's umbra. The next eclipse of comparable duration will not occur until June 25, 2150. The longest total solar eclipse during the 8,000-year period from 3000 BC to 5000 AD will occur on July 16, 2186, when totality will last 7 min 29 s.[11]

If the date and time of any solar eclipse are known, it is possible to predict other eclipses using eclipse cycles. Two such cycles are the Saros and the Inex. The Saros cycle is probably the best known, and one of the most accurate, eclipse cycles. The Inex cycle is itself a poor cycle, but it is very convenient in the classification of eclipse cycles. After a Saros cycle finishes, a new Saros cycle begins one Inex later, hence its name: in-ex. A Saros cycle lasts 6,585.3 days (a little over 18 years), which means that after this period a practically identical eclipse will occur. The most notable difference will be a shift of 120° in longitude (due to the 0.3 days) and a little in latitude. A Saros series always starts with a partial eclipse at a pole, then shifts over the globe through a series of annular or total eclipses, and ends on the other pole a couple of millennia later.[12]

Final totality

Due to tidal acceleration, the orbit of the Moon around the Earth is unstable, and becomes approximately 3.8 cm more distant each year. It is estimated that in 600 million years, the distance from the Earth to the Moon will have increased by 23500 km, meaning that it will no longer be able to completely cover the Sun's disk. This will be true even when the Moon is at perigee, and the Earth at aphelion.

A complicating factor is that the Sun will increase in size over this timescale. This makes it even more unlikely that the Moon will be able to cause a total eclipse. We can therefore say that the last total solar eclipse on Earth will occur in slightly less than 600 million years.[13]

Historical solar eclipses

A solar eclipse of 15 June 763 BC mentioned in an Assyrian text is important for the Chronology of the Ancient Orient. This is the earliest solar eclipse mentioned in historical sources that has been identified beyond reasonable doubt. There have been other claims to date earlier eclipses, notably that of Mursili II (likely 1312 BC), in Babylonia, and also in China, but these are highly disputed and rely on much supposition.[14][15]

Herodotus wrote that Thales of Miletus predicted an eclipse which occurred during a war between the Medians and the Lydians. Soldiers on both sides put down their weapons and declared peace as a result of the eclipse. Exactly which eclipse was involved has remained uncertain, although the issue has been studied by hundreds of ancient and modern authorities. One likely candidate took place on May 28, 585 BC, probably near the Halys river in the middle of modern Turkey.[16]

An annular eclipse of the Sun occurred at Sardis on February 17, 478 BC, while Xerxes was departing for his expedition against Greece, as Herodotus recorded.[17] Hind and Chambers considered this absolute date more than a century ago.[18] Herodotus also reports that another solar eclipse was observed in Sparta during the next year, on August 1, 477 BC.[19] The sky suddenly darkened in the middle of the day, well after the battles of Thermopylae and Salamis, after the departure of Mardonius to Thessaly at the beginning of the spring of (477 BC) and his second attack on Athens, after the return of Cleombrotus to Sparta. Note that the modern conventional dates are different by a year or two, and that these two eclipse records have been ignored so far.[20]

It has also been attempted to establish the exact date of Good Friday by means of solar eclipses, but this research has not yielded conclusive results.[21]

Observing a solar eclipse

Looking directly at the photosphere of the Sun (the bright disk of the Sun itself), even for just a few seconds, can cause permanent damage to the retina of the eye, because of the intense visible and invisible radiation that the photosphere emits. This damage can result in permanent impairment of vision, up to and including blindness. The retina has no sensitivity to pain, and the effects of retinal damage may not appear for hours, so there is no warning that injury is occurring. [22]

Under normal conditions, the Sun is so bright that it is difficult to stare at it directly, so there is no tendency to look at it in a way that might damage the eye. However, during an eclipse, with so much of the Sun covered, it is easier and more tempting to stare at it. Unfortunately, looking at the Sun during an eclipse is just as dangerous as looking at it outside an eclipse, except during the brief period of totality, when the Sun's disk is completely covered (totality occurs only during a total eclipse and only very briefly; it does not occur during a partial or annular eclipse). Viewing the Sun's disk through any kind of optical aid (binoculars, a telescope, or even an optical camera viewfinder) is even more hazardous.[23]

Glancing at the Sun with all or most of its disk visible is unlikely to result in permanent harm, as the pupil will close down and reduce the brightness of the whole scene. If the eclipse is near total, the low average amount of light causes the pupil to open. Unfortunately the remaining parts of the Sun are still just as bright, so they are now brighter on the retina than when looking at a full Sun. As the eye has a small fovea, for detailed viewing, the tendency will be to track the image on to this best part of the retina, causing damage.

Viewing partial and annular eclipses

Viewing the Sun during partial and annular eclipses (and during total eclipses outside the brief period of totality) requires special eye protection, or indirect viewing methods. The Sun's disk can be viewed using appropriate filtration to block the harmful part of the Sun's radiation. Sunglasses are not safe, since they do not block the harmful and invisible infrared radiation which causes retinal damage. Only properly designed and certified solar filters should ever be used for direct viewing of the Sun's disk. [24]

The safest way to view the Sun's disk is by indirect projection. This can be done by projecting an image of the disk onto a white piece of paper or card using a pair of binoculars (with one of the lenses covered), a telescope, or another piece of cardboard with a small hole in it (about 1 mm diameter), often called a pinhole camera. The projected image of the Sun can then be safely viewed; this technique can be used to observe sunspots, as well as eclipses. However, care must be taken to ensure that no one looks through the projector (telescope, pinhole, etc.) directly. Viewing the Sun's disk on a video display screen (provided by a video camera or digital camera) is safe, although the camera itself may be damaged by direct exposure to the Sun. The optical viewfinders provided with some video and digital cameras are not safe.

Viewing totality during total eclipses

Contrary to popular belief, it is safe to observe the total phase of a solar eclipse directly with the unaided eye, binoculars or a telescope, when the Sun's photosphere is completely covered by the Moon; indeed, this is a very spectacular and beautiful sight, and it is too dim to be seen through filters. The Sun's faint corona will be visible, and even the chromosphere, solar prominences, and possibly even a solar flare may be seen. However, it is important to stop directly viewing the Sun promptly at the end of totality. The exact time and duration of totality for the location from which the eclipse is being observed should be determined from a reliable source.

Also very beautiful are the effects just before (and just after) totality. When the shrinking visible part of the photosphere becomes very small, Baily beads will occur (see picture). These are caused by the sunlight still being able to reach Earth through lunar valleys, but no longer where mountains are present. Totality then begins with the diamond ring effect, the last bright flash of sunlight. [25] Note that it is not entirely safe to view Baily beads or the diamond ring without proper eye protection (because in both cases the photosphere is still visible).

Other observations

For astronomers, a total solar eclipse forms a rare opportunity to observe the corona (the outer layer of the Sun's atmosphere). Normally this is not visible because the photosphere is much brighter than the corona. According to the point reached in the solar cycle, the corona can appear rather small and symmetric, or large and fuzzy. It is very hard to predict this prior to totality.[26]

During a solar eclipse, special (indirect) observations can also be done with the unaided eye only. Normally the spots of light which fall through the small openings between the leaves of a tree, have a circular shape. These are images of the Sun. During a partial eclipse, the light spots will show the partial shape of the Sun, as seen on the picture. Another famous phenomenon is shadow bands (also known as flying shadows), which are similar to shadows on the bottom of a swimming pool. They only occur just prior to and after totality, and are very difficult to observe. Many professional eclipse chasers have never seen them.[27]

During a partial eclipse, a related effect that can be seen is anisotropy in the shadows of objects. Particularly if the partial eclipse is nearly total, the unobscured part of the sun acts as an approximate line source of light. This means that objects cast shadows which have a very narrow penumbra in one direction, but a broad penumbra in the perpendicular direction.

Parallax, or more accurately motion parallax (Greek: (parallagé) = alteration) is the change of angular position of two stationary points relative to each other as seen by an observer, due to the motion of an observer. Simply put, it is the apparent shift of an object against a background due to a change in observer position.

Lunar Parallax

Jules Verne, From the Earth to the Moon (1865). "Up till then, many people had no idea how one could calculate the distance separating the Moon from the Earth.

The circumstance was exploited to teach them that this distance was obtained by measuring the parallax of the Moon. If the word parallax appeared to amaze them, they were told that it was the angle subtended by two straight lines running from both ends of the Earth's radius to the Moon. If they had doubts on the perfection of this method, they were immediately shown that not only did this mean distance amount to a whole two hundred thirty-four thousand three hundred and forty-seven miles (94,330 leagues), but also that the astronomers were not in error by more than seventy miles (— 30 leagues)."

A primitive way to determine the lunar parallax from one location is by using a lunar eclipse. The full shadow of the Earth on the Moon has an apparent radius of curvature equal to the difference between the apparent radii of the Earth and

the Sun as seen from the Moon. This radius can be seen to be equal to 0.75 degree, from which (with the solar apparent radius 0.25 degree) we get an Earth apparent radius of 1 degree. This yields for the Earth-Moon distance 60 Earth radii or 384,000 km. This procedure was first used by Aristarchus of Samos and Hipparchus, and later found its way into the work of Ptolemy.

Another way to use parallax to determine the distance to the Moon would be to take two pictures of the Moon at exactly the same time from two locations on Earth, and compare the position of the Moon relative to the visible stars. Using the orientation of the Earth, and those two points, and a perpendicular displacement, a distance to the Moon can be triangulated.

Solar Parallax

After Johannes Kepler discovered his Third Law, it was possible to build a scale model of the whole solar system, but without the scale. To fix the scale, it suffices to measure one distance within the solar system, e.g., the mean distance from the Earth to the Sun or astronomical unit (AU). When done by triangulation, this is referred to as the solar parallax, the difference in position of the Sun as seen from the Earth's centre and a point one Earth radius away, i.e., the angle subtended at the Sun by the Earth's mean radius. Knowing the solar parallax and the mean Earth radius allows one to calculate the AU, the first, small step on the long road of establishing the size — and thus the minimum age — of the visible Universe.

A primitive way of determining the distance to the Sun in terms of the distance to the Moon was already proposed by Aristarchus of Samos: if the Sun is relatively close by, the first and last quarters of the Moon will not happen in time precisely in the middle between new and full moon. Unfortunately the method (which unrealistically assumes regular circular motion for the Moon) becomes progressively imprecise for solar distances much larger than the distance of the Moon, and Aristarchus obtained a nonsensical result. It is, however, in essence a parallax method.

It was proposed by Edmund Halley in 1716, that the transit of Venus over the solar disc be used to derive the solar parallax. And so it was done in 1761 and 1769. There is the famous story of the French astronomer Guillaume Le Gentil, who travelled to India to observe the 1761 event, but didn't reach his destination in time due to war. He stayed on for the 1769 event, but then there were clouds blocking the Sun...

The use of Venus transits was less successful than had been hoped due to the black drop effect.

Much later, the solar system was 'scaled' using the parallax of asteroids, some of which, like Eros, pass much closer to Earth than Venus. In a favourable opposition, Eros can approach the Earth to within 22 million kilometres. Both the opposition of 1901 and that of 1930/1931 were used for this purpose, the calculations of the latter determination being completed by Astronomer Royal Sir Harold Spencer Jones.

Also radar reflections, both off Venus (1958) and off asteroids, like Icarus, have been used for solar parallax determination. Today, use of spacecraft telemetry links has solved this old problem completely.

Stellar Parallax

On an interstellar scale, parallax created by the different orbital positions of the Earth causes nearby stars to appear to move relative to the more distant stars. However, this effect is so small it is undetectable without extremely precise measurements.

The annual parallax is defined as the difference in position of a star as seen from the Earth and Sun, i.e. the angle subtended at a star by the mean radius of the Earth's orbit around the Sun. Given two points on opposite ends of the orbit, the parallax is half the maximum parallactic shift evident from the star viewed from the two points. The parsec is the distance for which the annual parallax is 1 arcsecond. A parsec equals 3.26 light years.

The distance of an object (in parsecs) can be computed as the reciprocal of the parallax. For instance, the Hipparcos satellite measured the parallax of the nearest star, Proxima Centauri, as .77233 seconds of arc (±.00242"). Therefore, the distance is 1/0.772=1.29 parsecs or about 4.22 light years (±.01 ly).

The angles involved in these calculations are very small. For example, .772 arcseconds is roughly the angle subtended by an object about 2 centimeters in diameter (roughly the size of a U.S. Quarter) located about 5.3 kilometers away.

The fact that stellar parallax was so small that it was unobservable at the time was used as the main scientific argument against heliocentrism during the early modern age. It is clear from Euclid's geometry that the effect would be undetectable if the stars were far enough away; but for various reasons such a gigantic size seemed entirely implausible.

Measurements of the annual parallax as the earth goes through its orbit was the first reliable way to determine the distances to the closest stars. This method was first successfully used by Friedrich Wilhelm Bessel in 1838 when he measured the distance to 61 Cygni, and it remains the standard for calibrating other measurement methods (after the size of the orbit of the earth is measured by radar reflection on other planets).

In 1989, a satellite called "Hipparcos" was launched with the main purpose of obtaining parallaxes and proper motions of nearby stars, increasing the reach of the method ten-fold. Even so, Hipparcos is only able to measure parallax angles for stars up to about 1,600 light-years away — a little bit more than one percent of the diameter of our galaxy.

Dynamic or moving-cluster parallax

The open stellar cluster 'Hyades' (Rain Stars) in Taurus extends over such a large part of the sky, 20 degrees, that the proper motions as derived from astrometry appear to converge with some precision to a perspective point north of Orion. Combining the observed apparent (angular) proper motion in seconds of arc with the also observed true (absolute) receding motion as witnessed by the Doppler redshift of the stellar spectral lines, allows us to estimate the distance of the cluster and its member stars in much the same way as using annual parallax.

Dynamic parallax has sometimes also been used to determine the distance to a supernova, when the optical wave front of the outburst was seen to propagate through the surrounding dust clouds at an apparent angular velocity, when we know its true propagation velocity to be the speed of light.

Scale of the Universe

All these various astronomical parallax methods allow us to establish the first rungs on the cosmic scale ladder, out to a few hundred light years. Beyond that, other methods must be taken into use: e.g., "spectroscopic parallaxes" — not really parallaxes at all. It is a prototype of a "standard candle" method, where we observe the apparent brightness of an object we know, based on some physical theory, the true brightness of.

Further methods, mostly of the standard candle variety, are the variable stars called Cepheids — the absolute brightness of which depends on their observed period of variation —, supernova brightnesses, globular cluster sizes and brightnesses, complete galaxy brightnesses etc. These are all much more uncertain as they are not based on simple geometry. Yet, parallaxes are the basis of everything, as they allow the calibration of these more uncertain methods in the Solar neighbourhood.

A very modern method which is not a traditional parallax method but also geometric in nature, is "gravitational lensing parallax". It depends on observing the differential time delay of brightness variations from a remote quasar reaching us by two different paths through the gravitational field or "lens" of a foreground galaxy. If the redshifts of both the quasar and the foreground galaxy are known, one can show that the absolute distances of both are proportional to the differential delay, and can in fact be calculated given also the geometry of the gravitational lens on the celestial sphere.

All these independent techniques aim at determining Hubble's constant, the constant describing how the redshift of galaxies, due to the Universe's expansion, depends on these galaxies' distance from us. Knowing Hubble's constant again allows us to determine, by simply running the film of the cosmic expansion backwards, how long ago it was when all these galaxies were collected in a single point -- the Big Bang. Current knowledge puts this at some 13.7 billion years ago, but with considerable uncertainty and dependence on various model assumptions.

Precession refers to a change in the direction of the axis of a rotating object. In physics, there are two types of precession, torque-free and torque-induced, the latter being discussed here in more detail.

In certain contexts, "precession" may refer to the precession that the Earth experiences, the effects of this type of precession on astronomical observation, or to the precession of orbital objects.

Torque-free precession

Only moving objects can be in torque-free precession. For example, when a plate is thrown, the plate may have some rotation around an axis that is not its axis of symmetry. When the object is not perfectly solid, internal vortices will tend to damp torque-free precession.

Torque-induced precession

Torque-induced precession (gyroscopic precession) is the phenomenon by which the axis of a spinning object (e.g. a part of a gyroscope) "wobbles" when a torque is applied to it. The phenomenon is commonly seen in a spinning toy top, but all rotating objects can undergo precession. If the speed of the rotation and the magnitude of the torque are constant the axis will describe a cone, its movement at any instant being at right angles to the direction of the torque. In the case of a toy top, if the axis is not perfectly vertical the torque is applied by the force of gravity trying to tip it over. A rolling wheel will tend to remain upright due to precession. When the wheel tilts to one side, the particles at the top are pushed to one side and the particles at the bottom are pushed the other way. However, since the wheel is rotating, these particles eventually switch places and cancel one another out. Precession or gyroscopic considerations have an effect on bicycle performance at high speed. Precession is also the mechanism

behind gyrocompasses.

This concept is easier to understand by examining the effects of inertia, which is often stated by the phrase "A body in motion tends to stay in motion." In this case the "motion" of a rotating body is in its rotation. If an external force pushes upon the rotating body, the body will resist the force by pushing back against it, but the reaction is delayed.

Gyroscopic precession also plays a large role in the flight controls on helicopters. Since the driving force behind helicopters is the rotor head (which rotates), gyroscopic precession comes into play. If the rotor head is tilted to the right, its counter-clockwise movement forces the aircraft to fly forward. To ensure the pilot's inputs are correct the aircraft has corrective linkages which tilt the rotor head to the right when the pilots push the "cyclic stick" forward, or to the left when the stick is pulled to the back.

The physics of precession

Precession is the resultant of the angular velocity of rotation and the angular velocity produced by the torque. It is an angular velocity about a line which makes an angle with the permanent rotation axis, and this angle lies in a plane at right angles to the plane of the couple producing the torque. The permanent axis must turn towards this line, since the body cannot continue to rotate about any line which is not a principal axis of maximum moment of inertia; that is, the permanent axis turns in a direction at right angles to that in which the torque might be expected to turn it.

Precession of the equinoxes

The Earth goes through one complete precession cycle in a period of approximately 25,800 years, during which the positions of stars as measured in the equatorial coordinate system will slowly change; the change is actually due to the change of the coordinates. Over this cycle the Earth's north axial pole moves from where it is now, within 1° of Polaris, in a circle around the ecliptic pole, with an angular radius of 23 degrees 27 arcminutes [1], or about 23.5 degrees. The shift is 1 degree in 180 years, with the angle is taken from the observer, not from the center of the circle.

This precession was noted by ancient astronomers, and was explained by Newtonian physics. The Earth has a nonspherical shape, being oblate spheroid, bulging outward at the equator. The gravitational tidal forces of the Moon and Sun apply torque as they attempt to pull the equatorial bulge into the plane of the ecliptic. The portion of the precession due to the combined action of the Sun and the Moon is called lunisolar precession.

Precession of planetary orbits

The revolution of a planet in its orbit around the Sun is also a form of rotary motion. (In this case, the combined system of Earth and Sun is rotating.) So the axis of a planet's orbital plane will also precess over time.

The major axis of each planet's elliptical orbit also precesses within its orbital plane, in response to perturbations in the form of the changing gravitational forces exerted by other planets. This is called perihelion precession or apsidal precession (see apsis). Discrepancies between the observed perihelion precession rate of the planet Mercury and that predicted by classical mechanics were prominent among the forms of experimental evidence leading to the acceptance of Einstein's Theory of Relativity, which predicted the anomalies accurately.[2]

It is generally understood that the gravitational pulls of the Sun and the Moon cause the precession of the Earth's orbit which operate on cycles of 23,000 and 19,000 years. These periodic changes of the orbital parameters, as well as that of the inclination of the Earth's axis on its orbit, are an important part of the astronomical theory of ice ages. For precession of the lunar orbit see lunar precession.

An analogous phenomenon to apsidal precession is nodal precession (see orbital node), which affects the orientation of the orbital plane.

Precession is also an important consideration in the dynamics of atoms and molecules.

Nutation

Nutation is a slight irregular motion (etymologically a "nodding") in the axis of rotation of a largely axially symmetric object, such as a gyroscope or a planet.

The nutation of a planet is due to the fact that the tidal forces which cause the precession of the equinoxes vary over time so that the speed of precession is not constant. It was discovered in 1728 by the English astronomer James Bradley, but was not explained until 20 years later.

Because the dynamics of the planets are so well known, nutation can be calculated within seconds of arc over periods of many decades. There is another disturbance of the Earth's rotation called polar motion that can be estimated only a few months ahead, because it is influenced by rapidly and unpredictably varying things such as ocean currents, wind systems, and motions in the Earth's core.

Values of nutation are usually divided into components parallel and perpendicular to the ecliptic. The component which works along the ecliptic is known as the nutation in longitude. The component perpendicular to the ecliptic is known as the nutation in obliquity. Celestial coordinate systems are based on an "equator" and "equinox," which means a great circle in the sky that is the projection of the Earth's equator outwards, and a line, the Vernal equinox intersecting that circle, which determines the starting point for measurement of right ascension. These items are affected both by precession of the equinoxes and nutation, and thus depend on the theories applied to precession and nutation, and on the date used as a reference date for the coordinate system. In simpler terms, nutation (and precession) values are important in observation from Earth for calculating the apparent positions of astronomical objects.

Nutation of Earth

In the case of Earth, the principal sources of tidal force are the Sun and Moon, which continually change location relative to each other and thus cause nutation in Earth's axis. The largest component of Earth's nutation has a period of 18.6 years, the same as that of the precession of the Moon's orbital nodes. However, there are other significant periodical terms which must be calculated depending on the desired accuracy of the result. A mathematical description (set of equations) that represents nutation is called a "theory of nutation" (see,e.g. [1]). Generally, the theory is really a theory, in the sense that it applies physical laws and astronomical measurements; however, there may be parameters which are adjusted in a more or less ad hoc way to obtain the best fit to data. As can be seen from the IERS publication just cited, nowadays simple rigid-body mechanics do not give the best theory; one has to account for deformations of the solid Earth.

Values

The principal term of nutation is due to the regression of the moon's nodal line and has the same period of 6798 days (18.6 years). It reaches 17" in longitude and 9" in obliquity. All other terms are much smaller. The next largest, with a period of 183 days (0.5 year) has amplitudes 1.3" and 0.6" respectively. Interestingly the periods of all terms larger than 0.0001" (about as accurate as one can measure), which lie between 5.5 and 6798 days seem to avoid the range from 34.8 to 91 days. It is therefore customary to split the nutation into long-period and short-period terms. The long-period terms are calculated and mentioned in the almanacs, whilst the additional correction due to the short-period terms is usually taken from a table.

Earth's axis

Viewed from Earth's north pole, the motion of Earth, its moon and their axial rotations are all counterclockwise. The orbital and axial planes are not precisely aligned: Earth's axis is tilted some 23.5 degrees against the Earth–Sun plane (which causes the seasons); and the Earth–Moon plane is tilted about 5 degrees against the Earth-Sun plane (without a tilt, there would be an eclipse every month).

In an inertial reference frame, the Earth's axis undergoes a slow precessional motion with a period of some 25,800 years, as well as a nutation with a main period of 18.6 years. These motions are caused by the differential attraction of Sun and Moon on the Earth's equatorial bulge, due to its oblateness. In a reference frame attached to the solid body of the Earth, its rotation is also slightly irregular due to polar motion. The polar motion is quasi-periodic, containing an annual component and a component with a 14-month period called the Chandler wobble. In addition, the rotational velocity varies, in a phenomenon known as length of day variation.

In modern times, Earth's perihelion is about January 3, and the aphelion is about July 4 (near the solstices, which are on about December 21 and June 21). For other eras, see precession and Milankovitch cycles. The Earth is sometimes referred to as the Third Planet from the Sun because, of the nine planets of our solar system, Earth is the third closest planet to the sun.

Other movements of the Earth

It takes the Earth, on average, 23 hours, 56 minutes and 4.091 seconds (one sidereal day) to rotate around the axis that connects the north and the south poles. From Earth, the main apparent motion of celestial bodies in the sky (except that of meteors within the atmosphere and low-orbiting satellites) is to the west at a rate of 15 °/h = 15'/min, i.e., an apparent Sun or Moon diameter every two minutes.

Earth orbits the Sun every 365.2564 mean solar days (1 sidereal year). From Earth, this gives an apparent movement of the Sun with respect to the stars at a rate of about 1 °/day, i.e., a Sun or Moon diameter every 12 hours, eastward. The orbital speed of the Earth averages about 30 km/s (108,000 km/h), which is enough to cover the planet's diameter (~12,600 km) in seven minutes, and the distance to the Moon.

An observatory is a location used for observing terrestrial and/or celestial events. Astronomy, astrology, climatology, geology, meteorology, oceanography and volcanology are examples of disciplines for which observatories have been constructed. Historically, observatories were as simple as containing a sextant (for measuring the distance between stars) or Stonehenge (which has some alignments on astronomical phenomena).

The largest individual radio telescope is the RATAN-600 (Russia) with 576 meter

diameter of circular antenna (RATAN-600 description). The largest radio telescope in Europe is the 100 meter diameter antenna in Effelsberg, Germany, which also was the largest fully steerable telecope for 30 years until the Green Bank Telescope was opened in 2000. The largest radio telescope in the United States until 1998 was Ohio State University's The Big Ear. Other well known disk radio telescopes include the Arecibo radio telescope located in Arecibo, Puerto Rico, which is steerable within about 20° of the zenith, and the fully steerable Lovell telescope at Jodrell Bank in the United Kingdom . A typical size of the single antenna of a radio telescope is 25 metre, dozens of radio telescopes with comparable sizes are operated in radio observatories all over the world.

An example of the array-type radio telescope is the Very Large Array (VLA), in Socorro, New Mexico, which is an interferometric array formed from 27 individual antennas. The largest exisiting radio telescope array is the Giant Metrewave Radio Telescope, located in Pune, India. A larger array, LOFAR (the 'LOw Frequency ARray') is currently being constructed in western Europe, consisting of 25000 small antennas over an area of several 100s of kilometres in diameter.

The sub-field of astronomy related to observations made through radio telescopes is known as radio astronomy.

Many celestial objects, such as pulsars or active galaxies (like quasars), produce radio-frequency radiation and so are best "visible" or even only visible in the radio region of electromagnetic spectrum. By examining the frequency, power and timing of radio emissions from these objects, astronomers can improve our understanding of the Universe.

Radio telescopes are also the primary means to track space probes (see Deep Space Network), and are used in the SETI project.

The STIS was installed on Hubble during its second servicing mission in

1997 by Mark Lee and Steven Smith, replacing the High Resolution Spectrograph and the Faint Object Spectrograph. It was designed to operate for five years. On August 3, 2004 an electronic failure rendered STIS inoperable, ending its use 2 years after its predicted failure.

Spectrometer

A spectrometer is an optical instrument used to measure properties of light over a specific portion of the electromagnetic spectrum. The variable measured is most often the light's intensity but could also, for instance, be the polarization state. The independent variable is usually the wavelength of the light, normally expressed as some fraction of a meter, but sometimes expressed as some unit directly proportional to the photon energy, such as wavenumber or electron volts, which has a reciprocal relationship to wavelength. A spectrometer is used in spectroscopy for producing spectral lines and measuring their wavelengths and intensities. Spectrometer is a term that is applied to instruments that operate over a very wide range of wavelengths, from gamma rays and X-rays into the far infrared.

In general, any particular instrument will operate over a small portion of this total range because of the different techniques used to measure different portions of the spectrum. Below optical frequencies (that is, at microwave, radio, and audio frequencies), the spectrum analyzer is a closely related electronic device.