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Analemma
In astronomy, an analemma (; ) is a diagram showing the position of the Sun in the sky as seen from a fixed location on Earth at the same mean solar time, as that position varies over the course of a year. The diagram will resemble a figure eight. Globes of Earth often display an analemma as a two-dimensional figure of equation of time vs. declination of the Sun. The north–south component of the analemma results from the change in the Sun's declination due to the tilt of Earth's axis of rotation. The east–west component results from the nonuniform rate of change of the Sun's right ascension, governed by combined effects of Earth's axial tilt and orbital eccentricity. One can photograph an analemma by keeping a camera at a fixed location and orientation and taking multiple exposures throughout the year, always at the same time of day (disregarding daylight saving time, if applicable). Diagrams of analemmas frequently carry marks that show the position of the ...
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Analemma Fishburn
In astronomy, an analemma (; ) is a diagram showing the position of the Sun in the sky as seen from a fixed location on Earth at the same mean solar time, as that position varies over the course of a year. The diagram will resemble a figure eight. Globes of Earth often display an analemma as a two-dimensional figure of equation of time vs. declination of the Sun. The north–south component of the analemma results from the change in the Sun's declination due to the tilt of Earth's axis of rotation. The east–west component results from the nonuniform rate of change of the Sun's right ascension, governed by combined effects of Earth's axial tilt and orbital eccentricity. One can photograph an analemma by keeping a camera at a fixed location and orientation and taking multiple exposures throughout the year, always at the same time of day (disregarding daylight saving time, if applicable). Diagrams of analemmas frequently carry marks that show the position of the Sun at vari ...
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Sundial
A sundial is a horological device that tells the time of day (referred to as civil time in modern usage) when direct sunlight shines by the apparent position of the Sun in the sky. In the narrowest sense of the word, it consists of a flat plate (the ''dial'') and a gnomon, which casts a shadow onto the dial. As the Sun appears to move through the sky, the shadow aligns with different hour-lines, which are marked on the dial to indicate the time of day. The ''style'' is the time-telling edge of the gnomon, though a single point or ''nodus'' may be used. The gnomon casts a broad shadow; the shadow of the style shows the time. The gnomon may be a rod, wire, or elaborately decorated metal casting. The style must be parallel to the axis of the Earth's rotation for the sundial to be accurate throughout the year. The style's angle from horizontal is equal to the sundial's geographical latitude. The term ''sundial'' can refer to any device that uses the Sun's altitude or azi ...
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Position Of The Sun
The position of the Sun in the sky is a function of both the time and the geographic location of observation on Earth's surface. As Earth orbits the Sun over the course of a year, the Sun appears to move with respect to the fixed stars on the celestial sphere, along a circular path called the ecliptic. Earth's rotation about its axis causes diurnal motion, so that the Sun appears to move across the sky in a Sun path that depends on the observer's geographic latitude. The time when the Sun transits the observer's meridian depends on the geographic longitude. To find the Sun's position for a given location at a given time, one may therefore proceed in three steps as follows: # calculate the Sun's position in the ecliptic coordinate system, # convert to the equatorial coordinate system, and # convert to the horizontal coordinate system, for the observer's local time and location. This is the coordinate system normally used to calculate the position of the Sun in terms of ...
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Orthographic Projection
Orthographic projection (also orthogonal projection and analemma) is a means of representing three-dimensional objects in two dimensions. Orthographic projection is a form of parallel projection in which all the projection lines are orthogonal to the projection plane, resulting in every plane of the scene appearing in affine transformation on the viewing surface. The obverse of an orthographic projection is an oblique projection, which is a parallel projection in which the projection lines are ''not'' orthogonal to the projection plane. The term ''orthographic'' sometimes means a technique in multiview projection in which principal axes or the planes of the subject are also parallel with the projection plane to create the ''primary views''. If the principal planes or axes of an object in an orthographic projection are ''not'' parallel with the projection plane, the depiction is called ''axonometric'' or an ''auxiliary views''. (''Axonometric projection'' is synonymous with ...
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Lemniscate
In algebraic geometry, a lemniscate is any of several figure-eight or -shaped curves. The word comes from the Latin "''lēmniscātus''" meaning "decorated with ribbons", from the Greek λημνίσκος meaning "ribbons",. or which alternatively may refer to the wool from which the ribbons were made. Curves that have been called a lemniscate include three quartic plane curves: the hippopede or lemniscate of Booth, the lemniscate of Bernoulli, and the lemniscate of Gerono. The study of lemniscates (and in particular the hippopede) dates to ancient Greek mathematics, but the term "lemniscate" for curves of this type comes from the work of Jacob Bernoulli in the late 17th century. History and examples Lemniscate of Booth The consideration of curves with a figure-eight shape can be traced back to Proclus, a Greek Neoplatonist philosopher and mathematician who lived in the 5th century AD. Proclus considered the cross-sections of a torus by a plane parallel to the axis o ...
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Globe
A globe is a spherical model of Earth, of some other celestial body, or of the celestial sphere. Globes serve purposes similar to maps, but unlike maps, they do not distort the surface that they portray except to scale it down. A model globe of Earth is called a terrestrial globe. A model globe of the celestial sphere is called a ''celestial globe''. A globe shows details of its subject. A terrestrial globe shows landmasses and water bodies. It might show nations and major cities and the network of latitude and longitude lines. Some have raised relief to show mountains and other large landforms. A celestial globe shows notable stars, and may also show positions of other prominent astronomical objects. Typically, it will also divide the celestial sphere into constellations. The word ''globe'' comes from the Latin word ''globus'', meaning "sphere". Globes have a long history. The first known mention of a globe is from Strabo, describing the Globe of Crates from about 1 ...
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Equinox
A solar equinox is a moment in time when the Sun crosses the Earth's equator, which is to say, appears directly above the equator, rather than north or south of the equator. On the day of the equinox, the Sun appears to rise "due east" and set "due west". This occurs twice each year, around 20 March and 23 September. More precisely, an equinox is traditionally defined as the time when the plane of Earth's equator passes through the geometric center of the Sun's disk. Equivalently, this is the moment when Earth's rotation axis is directly perpendicular to the Sun-Earth line, tilting neither toward nor away from the Sun. In modern times, since the Moon (and to a lesser extent the planets) causes Earth's orbit to vary slightly from a perfect ellipse, the equinox is officially defined by the Sun's more regular ecliptic longitude rather than by its declination. The instants of the equinoxes are currently defined to be when the apparent geocentric longitude of the Sun is 0° a ...
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Year
A year or annus is the orbital period of a planetary body, for example, the Earth, moving in its orbit around the Sun. Due to the Earth's axial tilt, the course of a year sees the passing of the seasons, marked by change in weather, the hours of daylight, and, consequently, vegetation and soil fertility. In temperate and subpolar regions around the planet, four seasons are generally recognized: spring, summer, autumn and winter. In tropical and subtropical regions, several geographical sectors do not present defined seasons; but in the seasonal tropics, the annual wet and dry seasons are recognized and tracked. A calendar year is an approximation of the number of days of the Earth's orbital period, as counted in a given calendar. The Gregorian calendar, or modern calendar, presents its calendar year to be either a common year of 365 days or a leap year of 366 days, as do the Julian calendars. For the Gregorian calendar, the average length of the calendar yea ...
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Three-dimensional Space
Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called ''parameters'') are required to determine the position of an element (i.e., point). This is the informal meaning of the term dimension. In mathematics, a tuple of numbers can be understood as the Cartesian coordinates of a location in a -dimensional Euclidean space. The set of these -tuples is commonly denoted \R^n, and can be identified to the -dimensional Euclidean space. When , this space is called three-dimensional Euclidean space (or simply Euclidean space when the context is clear). It serves as a model of the physical universe (when relativity theory is not considered), in which all known matter exists. While this space remains the most compelling and useful way to model the world as it is experienced, it is only one example of a large variety of spaces in three dimensions called 3-manifolds. In this classical example, when the ...
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Perihelion And Aphelion
An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. For example, the apsides of the Earth are called the aphelion and perihelion. General description There are two apsides in any elliptic orbit. The name for each apsis is created from the prefixes ''ap-'', ''apo-'' (), or ''peri-'' (), each referring to the farthest and closest point to the primary body the affixing necessary suffix that describes the primary body in the orbit. In this case, the suffix for Earth is ''-gee'', so the apsides' names are ''apogee'' and ''perigee''. For the Sun, its suffix is ''-helion'', so the names are ''aphelion'' and ''perihelion''. According to Newton's laws of motion, all periodic orbits are ellipses. The barycenter of the two bodies may lie well within the bigger body—e.g., the Earth–Moon barycenter is about 75% of the way from Earth's center to its surface. If, compared to the larger mass, the smaller mass is negligible (e.g., ...
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Local Mean Time
Local mean time (LMT) is a form of solar time that corrects the variations of local apparent time, forming a uniform time scale at a specific longitude. This measurement of time was used for everyday use during the 19th century before time zones were introduced beginning in the late 19th century; it still has some uses in astronomy and navigation. Past use Local mean time was used from the early 19th century, when local solar time or sundial time was last used until standard time was adopted on various dates in the several countries. Each town or city kept its own meridian. This led to a situation where locations one degree of longitude apart had times four minutes apart. This became a problem in the mid 19th century when railways needed clocks that were synchronized between stations, at the same time as people needed to match their clock (or the church clock) to the time tables. Standard time means that the same time is used throughout some region—usually, it was eithe ...
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Local Solar Time
Solar time is a calculation of the passage of time based on the position of the Sun in the sky. The fundamental unit of solar time is the day, based on the synodic rotation period. Two types of solar time are apparent solar time (sundial time) and mean solar time (clock time). Introduction A tall pole vertically fixed in the ground casts a shadow on any sunny day. At one moment during the day, the shadow will point exactly north or south (or disappear when and if the Sun moves directly overhead). That instant is local apparent noon, or 12:00 local apparent time. About 24 hours later the shadow will again point north–south, the Sun seeming to have covered a 360-degree arc around Earth's axis. When the Sun has covered exactly 15 degrees (1/24 of a circle, both angles being measured in a plane perpendicular to Earth's axis), local apparent time is 13:00 exactly; after 15 more degrees it will be 14:00 exactly. The problem is that in September the Sun takes less time (as mea ...
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