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ECLiPSe
ECLiPSe
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ECLiPSe Constraint Logic Programming System
DevelopersEuropean Computer‐Industry Research Centre (ECRC), Munich
Centre for Planning and Resource Control, Imperial College London (IC-Parc)
Cisco Systems
Initial release1992; 34 years ago (1992)
Stable release
7.0 / January 22, 2018; 8 years ago (2018-01-22)
Written inC, Prolog
Operating systemCross-platform
Available inEnglish
TypeConstraint logic programming
LicenseMozilla Public (MPL)
Websiteeclipseclp.org
Repositorysf.net/p/eclipse-clp/git/

ECLiPSe is a software system for the development and deployment of constraint logic programming applications, e.g., in the areas of optimization, planning, scheduling, resource allocation, timetabling, transport, etc. It is also suited for teaching most aspects of combinatorial problem solving, e.g., problem modeling, constraint programming, mathematical programming, and search techniques.[1] It contains constraint solver libraries, a high-level modeling and control language (a superset of Prolog), interfaces to third-party solvers, an integrated development environment and interfaces for embedding into host environments.

ECLiPSe was developed until 1995 at the European Computer‐Industry Research Centre (ECRC) in Munich, and then until 2005 at the Centre for Planning and Resource Control at Imperial College London (IC-Parc). It was purchased by Cisco Systems. In September 2006, it was released as open source software under an equivalent of the Mozilla Public License, and is now hosted on SourceForge

Language

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The ECLiPSe language[2] is largely backward-compatible with Prolog and supports different dialects, including ISO Prolog. Due to being declarative, it can be used both as a modelling language to describe problems, and as a general purpose programming language.

Beyond the basic Prolog data types, the following are available: strings, unlimited precision integer and rational numbers, and floating point intervals. Array syntax and structures with field names are also supported and especially useful in constraint modelling.

A logical iteration construct[3] eliminates the need for most simple recursion patterns.

ECLiPSe provides comprehensive facilities[2] to implement data-driven control behaviour. These include declarative delay-clauses as well as primitives for meta-programmed control like explicit goal suspension, flexible triggering facilities and execution priorities. Together with the attributed variable data type, this is the key to many extensions to the basic logic programming language, including all constraint-based functionality. The system calls user-definable event handlers when it encounters attributed variables in certain contexts, e.g. unification.

The module system controls the visibility of predicates, non-logical stores, source transformations and syntax settings. Module interfaces can be extended and restricted, and modules written in different language dialects can be mixed within one application.

Programs may contain structured comments from which reference documentation can be generated.

Libraries

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ECLiPSe provides several libraries of constraint solvers which can be used in application programs:

Arithmetic constraints over finite domains, finite set constraints, generalized propagation, interval reasoning over non-linear constraints, interfaces to external simplex solvers, constraint handling rules (CHR) and more.

Other libraries implement search methods like branch-and-bound, repair-based search, limited discrepancy search.

ECLiPSe interfaces to external solvers, in particular the COIN-OR, CPLEX, Gurobi, and Xpress-MP linear and mixed-integer programming solvers,[4] and the Gecode solver library.

Compatibility libraries for ISO Prolog[5] and other Prolog dialects (C-Prolog, Quintus, SICStus, SWI-Prolog) enable the reuse of libraries written in those dialects.

Other utility libraries, including a number of popular public domain ones, are included in the distribution.

System architecture

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The system includes an incremental compiler which translates source code into virtual machine code. The compiler optimizes index selection, unification order, inlining of control constructs and can take mode information into account.

The runtime system implements the virtual machine, automatic memory management with garbage collection of stacks and dictionary, event handling and data-driven execution. Versions of ECLiPSe implement OR-parallelism.

ECLiPSe components can be integrated into software via a low-level C or C++ interface, or via high-level interfaces to Java and Tcl.

See also

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References

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[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

ECLiPSe

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from Grokipedia
An eclipse is an astronomical event that occurs when one celestial body moves into the shadow of another, temporarily obscuring its light from observers on a third body. On , the most observable eclipses involve the alignment of the Sun, , and , producing two primary types: solar eclipses, in which the passes between the and the Sun, blocking the Sun's light and casting a shadow on ; and lunar eclipses, in which the passes between the Sun and the , casting a shadow on the Moon's surface. Solar eclipses are classified into three main subtypes based on the Moon's position and apparent size relative to the Sun: total, when the Moon completely covers the Sun's disk, allowing the corona to become visible; annular, when the Moon is too distant to fully cover the Sun, leaving a bright ring of sunlight; and partial, when the Moon covers only a portion of the Sun. Lunar eclipses are similarly categorized as total, when Earth's umbra fully engulfs the , often giving it a reddish hue due to atmospheric of ; partial, when only part of the Moon enters the umbra; and penumbral, when the Moon passes only through Earth's faint outer shadow, causing a subtle dimming. These events occur during eclipse seasons, two periods each year lasting about 35 days when the Moon's aligns with the plane, enabling the necessary configurations. Between two and five solar eclipses happen annually, though total solar eclipses are rarer, occurring roughly every 18 months globally and visible from any specific location only about every 375 years on average. Lunar eclipses also range from two to five per year, but they are visible from anywhere on Earth's night side—roughly half the —making them accessible to more observers than solar eclipses, which are confined to narrow paths or regions of partial visibility. Eclipses have long held scientific, cultural, and navigational significance, aiding in the refinement of astronomical models and calendars throughout history, while modern observations contribute to studies of and Earth's atmosphere.

Fundamentals

Etymology

The word "eclipse" originates from the term ekleipsis (ἔκλειψις), meaning "abandonment" or "forsaking," which derives from the verb ekleipein (ἐκλείπειν), composed of the prefix ek- ("out" or "away") and leipein ("to leave" or "to fail"). This etymology reflects the ancient of a celestial body seemingly abandoning its usual position or light during the event. The term entered Latin as eclipsis, retaining its Greek roots, and was later adopted into as eclipse before appearing in around the 13th century, initially denoting the astronomical obscuration of light. Related terminology includes "," where "solar" stems from the Latin sol ("sun"), referring to the sun's apparent diminishment, and "," with "lunar" from Latin luna ("moon"), describing the moon's temporary darkening. In ancient cultures, eclipses inspired vivid mythological descriptions beyond Greco-Roman ; for instance, Chinese records from as early as the 8th century BCE portrayed solar eclipses as a celestial dragon devouring the sun, reflected in the term shí (食), meaning "to eat." Similarly, Babylonian astronomers in the 7th century BCE documented eclipses in tablets as ominous celestial failures, often interpreting them as divine abandonments without etymological nuance but aligning with themes of forsaking.

Shadow Regions

During an eclipse, the shadow cast by an opaque body on another surface forms distinct regions due to the of rays from an extended source like the Sun. The umbra is the central, fully dark region where the light source is completely obscured by the occluding body, resulting in total blockage of direct illumination. In contrast, the penumbra constitutes the surrounding partial shadow, where the light source is only partially obscured, allowing some rays to graze the edges of the occluder and produce partial illumination with varying degrees of dimming. The antumbra extends beyond the tip of the umbra as a continuation of the shadow cone, where an observer is positioned farther from the occluding body such that the light source appears larger than the occluder, creating an annular appearance around the silhouette. These shadow regions arise from the interaction of rays from an extended source with a smaller opaque object. For a point-like source, such as a , only an umbra forms as all is uniformly blocked behind the occluder. However, with an extended source like the Sun, which has a finite of about 0.5 degrees, rays diverge from different points on the source's disk, leading to the penumbra as a zone of overlap where some rays are blocked while others illuminate the area. The antumbra emerges when the occluder's angular size is smaller than the source's, causing the umbra cone to taper to a point before expanding into this annular shadow region; this configuration is analogous to viewing a smaller held in front of a larger lamp from increasing distances. The shapes and lengths of these shadow cones are determined by the relative angular sizes of the light source and occluder, governed by principles of ray geometry. For instance, the length of the umbra can be approximated using similar triangles formed by the rays to the occluder: if RR is the radius of the light source, ss the distance to the occluder, and rr the occluder's radius, the umbra length dd beyond the occluder satisfies Rs=rd\frac{R}{s} = \frac{r}{d}, yielding d=rsRd = \frac{r s}{R}. This relation highlights how larger source sizes shorten the umbra, as seen in the Sun-Moon system where the Sun's radius (R≈696,000R \approx 696,000 km) and Earth-Moon distances shape the shadow's reach. In eclipses within the Earth-Moon system, these regions dictate visibility patterns, with the umbra enabling total solar eclipses when it intersects Earth's surface.

Geometric Principles

An eclipse requires the precise alignment of three celestial bodies in a straight line, a configuration termed syzygy. In the context of solar and lunar eclipses, this alignment involves the Sun, , and , where the Moon's position relative to and the Sun determines the type of eclipse. The geometry of eclipses is governed by the orbital planes of and the Moon. 's around the Sun defines the plane, while the Moon's around is inclined at an average of 5.145° to this plane. This inclination causes the Moon's path to intersect the at two points, known as the ascending node (where the Moon crosses from south to north) and the descending node (from north to south). Eclipses can only occur when the Moon is positioned near these nodes during syzygy, as the Moon's shadow or 's shadow must project onto the aligned bodies within the plane. Eclipses do not happen every month despite monthly syzygies (new and full moons) because the Moon's typically positions it above or below the plane at those times, preventing shadow overlap. The misalignment of the Moon's line of apsides—the line connecting perigee and apogee—with the line of nodes further restricts eclipse opportunities to specific periods known as eclipse seasons, occurring roughly twice per year when the Sun is near the nodes. For a , syzygy occurs at conjunction, with the between and the Sun (new moon phase); the alignment can be visualized as Sun–Moon–Earth. In contrast, a happens at opposition, with between the Sun and (full moon phase), depicted as Sun–Earth–Moon. These configurations ensure the Moon passes through or casts its shadow on only under the nodal conditions. The nodes themselves are not fixed; they undergo retrograde due to gravitational perturbations, primarily from the Sun. This nodal regression completes a full 360° cycle in approximately 18.6 years, shifting the locations of eclipse seasons over time. The period TT of this cycle is given by T≈18.6T \approx 18.6 years, reflecting the slow westward drift of the nodes at an average rate of about 19.35° per year.

Eclipse Cycles and Prediction

Saros Cycle

The Saros cycle is a recurring astronomical period of exactly 223 synodic months, equivalent to approximately 6585.32 days or 18 years, 11 days, and 8 hours, during which the relative positions of the , , and Sun return closely enough to produce similar eclipses. This alignment allows eclipses to repeat with nearly identical geometry, including the type (partial, annular, total, or hybrid for solar; penumbral, partial, or total for lunar) and the orientation of the Moon's shadow relative to 's surface. The cycle was first documented by Babylonian astronomers around the BCE, who used it to predict eclipse occurrences based on observational records. The Saros cycle functions due to the near-equality of key lunar and solar orbital periods: 223 synodic months (the time between consecutive new or full moons) closely match 242 draconic months (the period for the Moon to return to the same ascending or descending node in its orbit relative to the ) and 239 anomalistic months (the time for the Moon to return to the same point of perigee or apogee). Eclipses occur only when the Moon is near one of its orbital nodes, aligned with the Sun, so this synchronization brings the three bodies back to a configuration conducive to eclipses. The small discrepancies—on the order of hours—arise from the non-perfect commensurability of these periods but are sufficient for practical prediction over centuries. In a Saros series, successive eclipses shift westward by approximately 120 degrees in longitude due to the extra 8 hours in the cycle, which corresponds to one-third of Earth's rotation. This longitudinal displacement occurs because the eclipse timing advances by 8 hours relative to the solar day, requiring Earth to rotate an additional 120 degrees for the geometry to align similarly. Over multiple cycles, such as 8 Saros periods (about 149 years), the paths experience further adjustments of around 120 degrees in longitude influenced by the eccentricity of Earth's orbit around the Sun, altering the exact timing and shadow projection slightly. Latitude also varies gradually within the series, with paths migrating from polar regions toward the equator and back. After three Saros cycles (54 years and about 33 days), the longitude returns nearly to the original position, though latitude differs by roughly 10 degrees due to nodal precession. A representative example is Saros series 134, which features annular solar eclipses, including the event on September 23, 1987, visible across parts of the southern Pacific, , and the Atlantic, and the similar annular eclipse on October 3, 2005, observed in , , , and the —demonstrating the recurring geometry but with the expected longitudinal shift. Each Saros series typically spans 12 to 13 centuries and includes 70 to 80 eclipses, evolving gradually from partial eclipses near one of Earth's poles to central eclipses (annular, hybrid, or total) near the , then back to partials at the opposite pole. This progression reflects changes in the Earth-Moon distance relative to the Sun's apparent , driven by the Moon's elliptical and the slight drift in perigee position over time; for instance, a series may transition from annular (Moon appearing smaller than the Sun) to total (Moon appearing larger) and reverse as the anomalistic alignment evolves. These limitations mean no series produces identical eclipses indefinitely, with the cycle's approximation degrading over millennia, necessitating refinements in modern predictions.

Metonic and Inex Cycles

The is a nearly exact commensurability between the solar year and the , spanning 19 s or 235 synodic months (approximately 6,939.6 days), over which the Moon's phases recur on nearly the same calendar dates. This cycle aligns the with the solar year, indirectly supporting eclipse predictions by synchronizing the dates of new and full moons—conditions necessary for solar and lunar eclipses, respectively—with seasonal positions in the . The mathematical foundation lies in the ratio of 235 synodic months to 19 years, yielding approximately 12.368 lunations per year, which minimizes the drift between lunar phases and solar dates over the period. In , the informed calendar reforms by enabling the insertion of intercalary months to harmonize lunar and solar reckonings, and it was integrated into predictive mechanisms like the Antikythera device to coordinate civil calendars with celestial events, including eclipses. Named after the Athenian Meton around 432 BCE, the cycle's discovery facilitated long-term tracking of lunar-solar alignments essential for anticipating eclipse seasons. The Inex cycle, by contrast, encompasses 358 synodic months (about 10,571 days or 28.94 years), corresponding closely to 388.5 draconic months, and accounts for variations in the latitude of eclipse paths through the regression of the Moon's orbital nodes. This nodal regression, a westward of the Moon's relative to the with an 18.6-year period, causes eclipse tracks to shift progressively northward or southward; the Inex interval effectively returns the Moon to the opposite node, reversing the latitudinal trend and producing eclipses at mirrored latitudes. The cycle's precision stems from the minimal discrepancy of about 4–6 minutes between 358 synodic months and 388.5 draconic months, allowing it to model these positional changes without fully replicating eclipse geometry. Unlike the Saros cycle, which synchronizes both synodic and draconic periods for near-repeats of eclipse type and longitude, the Metonic cycle disregards nodal positions to prioritize phase-calendar alignment, while the Inex focuses solely on latitudinal reversals via half a nodal cycle, omitting full geometric recurrence.

Modern Prediction Methods

Modern eclipse predictions rely on high-precision ephemerides, such as the Jet Propulsion Laboratory's Development Ephemeris DE430, which provides accurate orbital elements for the Earth, Moon, and Sun through numerical integration of the equations of motion, accounting for gravitational perturbations from other bodies. These ephemerides enable forecasts of eclipse timing and paths centuries in advance by solving Keplerian orbits with relativistic and tidal corrections. For solar eclipses, the VSOP87 theory is commonly employed for heliocentric positions of the Sun and major planets, while the ELP2000/82 lunar theory computes the Moon's geocentric coordinates, often combined with a revised lunar secular acceleration to refine predictions. Specialized software tools facilitate these computations for researchers and enthusiasts. NASA's Eclipse Predictions website offers interactive JavaScript-based explorers that calculate local circumstances for solar and lunar eclipses from -1999 to 3000 CE, integrating data to determine visibility, path widths, and durations. Similarly, WinEclipse software solves perturbed Keplerian orbits to generate detailed eclipse maps and timings, supporting analyses over extended historical and future periods. These tools often start from periodic cycles like the Saros as initial approximations before applying full numerical refinements. The core algorithms involve of differential equations describing , such as those in the JPL DE series, which model n-body interactions to predict positions with sub-arcsecond precision. effects are incorporated using standard models like those from the to adjust apparent timings for observers on Earth's surface. Such methods achieve remarkable accuracy, predicting eclipse contacts to within seconds for events up to a ahead, as demonstrated by comparisons between DE430-based forecasts and observed timings. For instance, lunar eclipse predictions using DE430 exhibit errors of less than 0.1 seconds in geocentric conjunction times over the 1550–2650 CE span covered by the .

Eclipses in the Earth-Moon System

Solar Eclipses

A occurs when the passes between and the Sun, temporarily blocking the Sun's light and casting a shadow on 's surface. This alignment happens only during a new moon phase, when the is positioned such that its orbit intersects the ecliptic plane. The resulting shadow on varies in extent and intensity depending on the relative distances and sizes of the Sun and . Solar eclipses are classified into four main types based on the Moon's shadow geometry and its apparent size relative to the Sun. In a total solar eclipse, the Moon's umbra—the darkest central portion of its shadow—reaches 's surface, completely obscuring the Sun from observers within a narrow path. Here, the Moon appears larger than the Sun, fully covering its disk. An annular solar eclipse occurs when the Moon is near apogee, appearing smaller than the Sun, so the antumbra (the extension of the shadow beyond the umbra's tip) touches ; a bright ring of surrounds the silhouetted Moon. A partial solar eclipse takes place when only the Moon's penumbra—the outer, fainter region of the shadow—falls on , blocking only a portion of the Sun's disk. Finally, a hybrid solar eclipse (also called annular-total) arises due to 's curvature, transitioning between annular and total along the path as the shadow's tip grazes the surface. During a total solar eclipse, several striking phenomena become visible. As the Moon advances to cover the Sun, appear: bright points of sunlight streaming through lunar valleys and mountain peaks, creating a string of luminous spots along the 's edge. This effect, lasting mere seconds, culminates in the diamond ring effect, where a single bead persists amid the emerging faint glow of the Sun's corona—the outermost atmosphere—resembling a brilliant diamond set in a ring. Totality allows safe naked-eye viewing of the corona, which is otherwise overwhelmed by the Sun's brilliance; its pearly white streamers extend millions of kilometers, revealing dynamic plasma structures. The maximum duration of totality is theoretically up to 7 minutes and 31 seconds, though most last 2 to 5 minutes. Visibility of solar eclipses is geographically limited. The path of totality for total eclipses is narrow, typically 100 to 200 kilometers wide, sweeping across Earth's surface at over 1,600 kilometers per hour near the equator. Partial phases are observable over a much broader area, often spanning continents, but the full spectacle requires being within the central track. Globally, 2 to 5 solar eclipses occur each year, with at least two being partial; total eclipses visible from any specific location average once every 375 years. The Moon's shadow regions—umbra, penumbra, and antumbra—directly determine these visibility patterns. The type and extent of a solar eclipse are quantified by its magnitude, defined as the fraction of the Sun's diameter occulted by the at greatest eclipse: Magnitude=DMoonDSun\text{Magnitude} = \frac{D_{\text{Moon}}}{D_{\text{Sun}}} where DMoonD_{\text{Moon}} and DSunD_{\text{Sun}} are the apparent angular diameters. A magnitude greater than 1.0 indicates a total eclipse, while values between 0.95 and 1.0 typically produce annular ones; partial eclipses have magnitudes below 1.0. This ratio accounts for the Moon's elliptical orbit and Earth's position, influencing whether the umbra or antumbra contacts the surface.

Lunar Eclipses

A lunar eclipse occurs when the Earth is positioned directly between the Sun and the Moon, with the Moon passing through the Earth's shadow during its full phase. This alignment causes the Moon to be temporarily darkened as it enters the shadow cast by Earth, blocking direct sunlight from reaching its surface. Lunar eclipses are classified into three main types based on the portion of Earth's shadow that the Moon traverses. In a total lunar eclipse, the Moon fully enters the umbra—the darkest central part of Earth's shadow—resulting in the Moon taking on a reddish hue due to the scattering of sunlight by Earth's atmosphere. A partial lunar eclipse happens when only a portion of the Moon passes through the umbra, leaving part of its surface illuminated while the shadowed area darkens progressively. Penumbral lunar eclipses are the most subtle, occurring when the Moon travels entirely within the penumbra—the outer, fainter region of the shadow—causing a slight overall dimming that is often barely noticeable to the naked eye. One striking phenomenon during total lunar eclipses is the "blood moon" effect, where the appears vividly red. This coloration arises from in Earth's atmosphere, which preferentially allows longer-wavelength red light from the Sun to bend around the planet and illuminate the , while shorter blue wavelengths are scattered away. Another rare occurrence is a selenelion, in which both the eclipsed and the Sun are simultaneously visible above the horizon, made possible by that lifts the images of the celestial bodies slightly, allowing observation near sunrise or sunset despite the apparent geometric impossibility. Unlike solar eclipses, lunar eclipses are observable from anywhere on Earth's night side, as the is above the horizon for half the planet at any given time. The entire event can last up to six hours, though the total phase of a total eclipse typically endures for no more than about 100 minutes, during which the is fully immersed in the umbra. Lunar eclipses occur between two and five times annually, including penumbral events, though visible umbral eclipses (total or partial) happen about two to three times per year on average. They are more predictable and easier to observe than solar eclipses because is significantly wider than the , allowing for broader visibility without the need for precise location.

Historical Records

The earliest documented eclipse observations date back to ancient , where Babylonian astronomers recorded a lunar eclipse on March 19, 721 BCE, marking one of the oldest verifiable astronomical records from the region. These tablets preserved timings and descriptions of lunar eclipses, reflecting systematic monitoring for omen interpretation and calendrical purposes. Similarly, Assyrian records include a notable solar eclipse on June 15, 763 BCE, observed in during a period of political instability, which was later correlated with the empire's chronicles. In ancient , oracle bones dating to around 1200 BCE record solar eclipses, such as descriptions of "The Sun has been eaten," reflecting a tradition of eclipse annals starting around that time to track celestial patterns and royal legitimacy, as continued in later texts like the Shiji by . Among key historical events, the Greek philosopher is credited in ancient sources with predicting a total on May 28, 585 BCE, which reportedly halted a battle between the and , though the method—possibly derived from Babylonian saros cycles—remains speculative and unconfirmed by direct evidence. In 1504, , stranded in during his fourth voyage, exploited a predicted total on February 29 to intimidate local indigenous people into providing supplies, using astronomical tables from to forecast the event accurately. A pivotal scientific milestone occurred during the total of May 29, 1919, when British astronomer Arthur Eddington's expeditions to and Sobral, , measured the deflection of starlight by the Sun's gravity, confirming Albert Einstein's general with observations matching the predicted 1.75 arcseconds shift. During the medieval and periods, technological advancements enabled more precise eclipse forecasting. The , an recovered from a dated to around 100 BCE, incorporated gears to predict solar and lunar eclipses using the 223-lunar-month saros cycle, achieving predictions accurate to within hours over 18-year intervals. In the early 18th century, applied and gravitation to forecast the total of May 3, 1715, across , with his published map accurate to within four minutes in timing and 20 miles in path, demonstrating the power of Newtonian mechanics and paralleling his contemporaneous work on periodic comets. In the modern era, the total solar eclipse of April 8, 2024, traversed from through the and , visible to over 30 million people in the path of totality and studied by missions to analyze the Sun's corona and atmospheric effects. In 2025, total lunar eclipses occurred on March 14 (visible in the , , and ) and September 7 (visible in , , and the Pacific), accompanied by partial solar eclipses on March 29 ( and southern ) and September 21 (South Pacific and ). Looking ahead from the 2025 perspective, the next total solar eclipse on August 12, 2026, will cross , , , and parts of , offering opportunities for further solar observations. These events build on the 1919 verification, shifting eclipse records from qualitative omens to quantitative data essential for refining orbital models and geophysical studies. The evolution of eclipse documentation reflects a transition from interpretive omens in antiquity to empirical , culminating in comprehensive catalogs like NASA's Five Millennium Canon of Solar Eclipses (2006), compiled by Fred Espenak, which details 11,898 solar eclipses from 1999 BCE to 3000 CE, including paths, durations, and types to support long-term predictions and historical validations.

Cultural Significance

Eclipses have profoundly shaped mythologies across civilizations, often portrayed as cosmic battles or devourings by mythical creatures. In ancient Chinese lore, a celestial was believed to swallow the Sun during a solar eclipse, prompting people to bang pots, drums, and gongs to frighten it away and restore light. Similarly, depicted the wolves Sköll and Hati perpetually chasing the Sun and Moon, with an eclipse occurring when one caught its prey, symbolizing the precarious balance of the cosmos. In Hindu tradition, the demon , a severed head seeking revenge, attempts to devour the Sun, causing the eclipse until the luminous body emerges from its throat. Religious texts and practices have interpreted eclipses as divine omens or reminders of spiritual truths. The references a darkening of the Sun in Amos 8:9, where declares, "I will make the sun go down at noon and darken the earth in broad daylight," often seen as a portent of judgment. In , eclipses are viewed as signs of Allah's power, not tied to human events like death, but occasions for prayer and reflection, as emphasized in where the Prophet Muhammad instructed believers to perform special salat during such phenomena. The ancient Maya, through the , incorporated eclipse predictions into their religious calendar, using tables to forecast events over centuries, blending astronomy with . Cultural responses to eclipses varied from terror to ritual observance, influencing societal behaviors. Among the , solar eclipses evoked fears of world-ending darkness, leading to human sacrifices to appease the Sun god and prevent catastrophe. In , eclipses prompted purification rituals, such as bathing in sacred rivers like the during lunar events, which drew large gatherings for spiritual renewal despite their inauspicious connotations. Greek philosophers like shifted toward rational inquiry, with his reported prediction of a 585 BCE eclipse fostering early scientific curiosity about natural cycles rather than supernatural fears. In modern times, eclipses inspire tourism and artistic expression, transforming ancient awe into communal celebration. The 2017 total across the was viewed by approximately 215 million people, including an estimated 1.8 to 7.4 million travelers who visited , boosting local economies through events and ; the 2024 event drew up to 4 million travelers to path cities like and Buffalo. has long drawn on eclipses for symbolic depth, as seen in where celestial alignments evoke themes of unity and transience, exemplified in Samuel Taylor Coleridge's lunar imagery in works like "The Rime of the ." In modern manga, Kentaro Miura's Berserk features an event known as the Eclipse, during which Ubik, a member of the God Hand, speaks the quote "ALL I WISH TO SEE ARE HUMANS WITHIN A FIERY APOCALYPSE" while showing visions of despair and destruction to influence Griffith's choice, reflecting Ubik's manipulative nature. Many cultures associate solar eclipses with masculine solar energy overpowering or uniting with the feminine lunar force, reflecting broader gender dualities in cosmology.

Eclipses on Other Solar System Bodies

Inner Planets

Transits of Mercury and , the inner planets of the , manifest as rare alignments where these bodies pass directly between and the Sun, appearing as diminutive against the solar disk and functioning as miniature solar visible from . These events require precise orbital geometry, with the planets' inclinations relative to 's plane allowing such passages only when nodes align near inferior conjunction. Unlike lunar eclipses, transits of the inner planets do not produce totality on but offer opportunities to study planetary atmospheres and solar features through effects. Mercury transits occur approximately 13 to 14 times per century, far more frequently than those of due to Mercury's closer and smaller of about 7 degrees relative to the . From Earth's perspective, Mercury appears as a small black dot traversing the Sun's face over several hours. The most recent transit occurred on November 11, 2019, with the next such events scheduled for November 13, 2032, and November 7, 2039. These transits have been cataloged extensively, with 94 occurrences predicted between 1601 and 2300 CE, clustered around early May and early November dates. Venus transits are considerably rarer, happening in pairs separated by about 8 years, with successive pairs occurring after intervals of either 105.5 or 121.5 years, resulting in roughly four events every 243 years. The most recent pair took place on June 8, 2004, and June 5–6, 2012, each lasting around 6 hours as 's disk, larger than Mercury's but still tiny at about 1 arcminute across, crosses the Sun. Historically, these transits enabled precise measurements of the Sun-Earth distance via the method; for instance, astronomer accurately predicted the December 6, 1631, transit, which was observed despite his death the previous year. In 1769, Captain led a Royal Society-sponsored expedition to to observe the event, using timed observations from multiple global sites to refine solar parallax estimates and advancing astronomical . Neither Mercury nor experiences eclipses on their surfaces, as both lack natural satellites capable of occulting the Sun. Observations of these transits from are challenging due to the planets' small angular diameters—Mercury's silhouette spans only about 12 arcseconds, and Venus's about 58 arcseconds—necessitating solar-filtered telescopes or for safe viewing, as the unaided eye cannot resolve the passages. Atmospheric distortion and the need for precise timing further complicate imaging, though modern spacecraft like NASA's have captured high-resolution footage, revealing atmospheric effects such as the "black drop" phenomenon during ingress and egress.

Terrestrial Planets

The terrestrial planet Mars experiences solar eclipses caused by its two small moons, Phobos and Deimos, which transit the Sun as viewed from the Martian surface. Unlike Earth's , which can produce both total and annular solar eclipses due to its comparable angular size to the Sun, Phobos and Deimos are much smaller relative to the Sun's apparent diameter from Mars—Phobos spans about 0.21 degrees and Deimos about 0.12 degrees, compared to the Sun's 0.35 degrees—resulting exclusively in partial or annular-like events where the moons obscure only a portion of the solar disk, up to roughly 40% in Phobos's case. These eclipses are brief, with Phobos transits lasting 20 to 30 seconds and Deimos transits 50 to 60 seconds, owing to the moons' rapid orbital speeds and proximity to Mars. Phobos, the inner and larger moon with an irregular potato-like shape approximately 22 kilometers across, orbits Mars every 7.65 hours at an average distance of 6,000 kilometers, rising in the west and setting in the east due to its sub-synchronous period relative to Mars's 24.6-hour . This geometry allows for multiple transits per —up to two or three during eclipse seasons—confined to twice-yearly periods lasting about 122 to 228 days when the Sun, Phobos, and observer align properly. Deimos, smaller at about 12 kilometers across, orbits more distantly every 30.3 hours, producing fewer and even less obstructive events, with transits occurring roughly 130 times per year but visible only from specific latitudes. No total eclipses occur on Mars because neither moon's angular size exceeds the Sun's, and their shadows—scaled down dramatically compared to Earth's lunar umbra—project narrow paths across the surface, often just a few kilometers wide for Phobos. Key observations of these events have been captured by Mars missions, providing direct visual records from the surface. The Viking 1 lander in 1977 imaged the shadow of Phobos passing over its site near the equator, confirming the moon's umbral path and aiding early orbital refinements. NASA's Mars Pathfinder in 1997 observed Phobos emerging from Mars's nightside shadow, an event related to the moon's orbital geometry but distinct from a solar transit. More direct solar transits were imaged by the Mars Exploration Rovers Spirit and Opportunity in 2005, capturing six events including both moons silhouetted against the Sun, which revealed their precise timings and shapes. The Curiosity rover recorded Phobos and Deimos transits in 2019 and 2020, with Phobos appearing as a dark, lumpy disc blocking part of the Sun on March 26, 2019. In 2022, the Perseverance rover's Mastcam-Z instrument filmed a high-resolution video of a Phobos transit on April 2, showcasing sunspots and the moon's irregular outline in real time over 40 seconds. More recently, on September 30, 2024, Perseverance captured the silhouette of Phobos as it passed in front of the Sun. These images, taken during favorable alignments, highlight the events' fleeting nature and the challenges of surface-based astronomy on Mars. Scientifically, these eclipses offer valuable data for testing models of the moons' orbital dynamics, as precise timing measurements refine ephemerides and track minute deviations from predicted paths. For instance, observations from rovers have improved Phobos's al parameters by factors of 10 to 100 in accuracy, essential for future missions like sample returns. Additionally, they inform studies of tidal effects, as Phobos's orbit is decaying inward at about 1.8 meters per century due to gravitational interactions with Mars, potentially leading to the moon's disruption in 30 to 50 million years; eclipse timings help quantify this tidal evolution and its implications for . In contrast to Earth's less frequent but longer-lasting eclipses, Mars's events underscore the diversity of solar system shadow phenomena driven by small satellites.

Gas Giants

The gas giants host intricate eclipse phenomena driven by their extensive satellite systems and ring structures, where mutual interactions among moons and planetary shadows create observable events. Jupiter's —Io, Europa, Ganymede, and Callisto—exhibit frequent mutual eclipses and occultations due to their 4:2:1 , in which Io completes four orbits, Europa two, and Ganymede one around in the same interval. This configuration leads to periodic alignments that facilitate a series of mutual events every six years, coinciding with Jupiter's equinoxes when Earth's aligns edge-on to the moons' . These events allow astronomers to study the moons' sizes, albedos, and atmospheres through photometric variations as one passes in front of or behind another. Saturn's system features prolonged eclipses influenced by its prominent rings and major moons, particularly Titan, which casts shadows across the planet's disk in events akin to solar eclipses lasting several hours. The rings themselves produce extended shadows on Saturn and its moons, with Cassini spacecraft imaging a notable backlit view during a 12-hour passage through Saturn's shadow on September 15, 2006, revealing fine ring structures and particle distributions. Titan's orbital geometry results in eclipses by Saturn that can endure up to six hours, enabling detailed observations of the moon's hazy atmosphere during immersion in the planet's umbra. In contrast, and experience fewer mutual eclipses owing to their significant axial tilts—98 degrees for and 28 degrees for —which misalign the orbital planes of their moons relative to the , reducing alignment opportunities. 's retrograde moon Triton undergoes planetary eclipses lasting approximately five hours, as documented during Voyager 2's 1989 flyby, which captured imagery near eclipse phases to analyze surface temperatures and composition. Saturn's ring effects stand out as unique, while Jupiter's mutual event series provide recurrent windows for precise timing and prediction, briefly informed by broader models for event planning. Post-1990s missions, the has imaged multiple moon transits and shadows on , enhancing mutual event analysis, and the has conducted infrared observations of Io during its eclipse by , probing volcanic emissions.

Dwarf Planets

Dwarf planets in the outer Solar System exhibit rare eclipse phenomena, primarily due to their sparse and dynamically unique satellite systems. The Pluto- system stands out as the most prominent example, functioning as a binary dwarf planet pair where mutual eclipses and transits occur because of their synchronous rotation and comparable sizes— is about half of 's diameter. These events take place during seasonal alignments every 124 years, lasting for approximately five years each time, when the of aligns edge-on with respect to the Sun and . During these periods, an observer on would experience a by every 6.4 days, with maximum durations reaching up to 90 minutes, while would similarly eclipse the Sun from 's perspective. Observations of these mutual events have provided critical insights into the system's composition. Ground-based telescopes captured extensive light curves during the 1985–1990 season, revealing surface albedos and thermal properties, with the next season expected to begin in October 2103 and end in January 2117. The spacecraft flyby in 2015 further refined these models through high-resolution imaging and color light curves of and , enabling more accurate predictions for future eclipse timings and durations by accounting for orbital perturbations and surface variations. These eclipses have uniquely allowed separation of the combined light from and , facilitating spectroscopic analysis that detected nitrogen ice on and confirmed the thin nitrogen-methane atmosphere on , with temperature maps indicating regional variations around 40–60 K. Among other dwarf planets, eclipse events are less frequent and more limited. Haumea, with its two small moons Hi'iaka and Namaka, experiences brief mutual occultations and eclipses between Haumea and Namaka due to the moon's 18-day and the system's inclination, as observed in ground-based campaigns from 2008–2011 that lasted only minutes and helped constrain Haumea's triaxial shape and density. In contrast, Eris possesses a single known moon, Dysnomia, but its wide, low-inclination (about 37,000 km semi-major axis) precludes current mutual events; the next predicted season of eclipses and transits is not until around 2239, when the aligns edge-on. The Pluto-Charon system's status as a "double " underscores its uniqueness, as the barycenter lies outside , enabling symmetric mutual eclipses that reveal processes and thermal balances not observable in single-body systems. Post-2015, ground-based stellar occultations by have continued to monitor atmospheric changes, providing data to predict and validate future mutual eclipse light curves expected starting in 2103.

Eclipsing Binary Systems

Characteristics

Eclipsing binary systems consist of two stars orbiting each other such that their is oriented nearly edge-on relative to the observer's , resulting in periodic partial or total obscuration of one star by the other and consequent variability in the system's apparent brightness. The of an eclipsing binary exhibits characteristic periodic dips in brightness corresponding to the , which is determined from the time between successive eclipses. The primary minimum occurs when the hotter, more luminous star is eclipsed by its cooler companion, producing a deeper dip whose depth depends on the relative radii and surface brightnesses of the two stars; the secondary minimum, which is shallower, happens when the cooler star is eclipsed. Eclipses in these systems are classified as total, when the disks of the stars fully overlap and the eclipsed star is completely obscured; partial, when only a portion of the eclipsed star's disk is covered; or annular-like, occurring in cases of unequal star sizes where the smaller eclipsed star appears as a bright ring around the larger eclipsing one without full obscuration. For eclipses to be observable, the ii must be close to 90∘90^\circ, with the minimum inclination given by cos⁡i=(r1+r2)/a\cos i = (r_1 + r_2)/a, where r1r_1 and r2r_2 are the stellar radii and aa is the semi-major axis of the relative . In close binaries, stars may fill or overflow their lobes—the gravitational surfaces defining the region dominated by each star—leading to distorted stellar shapes, , and altered eclipse profiles. The approximate duration of an eclipse, from first to fourth contact, is given by Δt≈(P/π)arcsin⁡(R/a)\Delta t \approx (P / \pi) \arcsin(R / a), where PP is the orbital period, RR is the sum of the stellar radii, and aa is the semi-major axis (valid for near-edge-on orbits and small R/aR/a).

Observational Techniques

Observational techniques for eclipsing binaries primarily rely on photometric and spectroscopic methods to detect periodic brightness variations and orbital motions, enabling the derivation of fundamental stellar parameters. The variability of Algol (β Persei), the first recognized eclipsing binary, was discovered in 1782 by John Goodricke through meticulous visual observations that revealed its 2.87-day period, initially attributed to an eclipsing companion despite prevailing theories of intrinsic pulsation. Systematic studies of such systems began shortly thereafter, with early photometric monitoring establishing the eclipsing nature of additional variables by the mid-19th century. Photometry forms the cornerstone of detection, involving time-series observations to construct light curves that exhibit characteristic V-shaped or U-shaped dips during eclipses, reflecting the geometry and relative sizes of the stellar components. Space-based missions like NASA's Kepler telescope, operational from 2009 to 2013, and its K2 extension until 2018, provided high-precision photometry for over 2,400 eclipsing binaries in targeted fields, revealing light curve morphologies that distinguish detached, semi-detached, and contact systems. The Transiting Exoplanet Survey Satellite (TESS), launched in 2018, has expanded this capability with near-continuous monitoring across the entire sky, cataloging more than 4,500 eclipsing binaries in its first 26 sectors alone through full-frame images and sector-specific observations. Ground-based surveys complement these efforts; for instance, the All Sky Automated Survey (ASAS), initiated in 1997, has monitored millions of bright stars (V < 14 mag) worldwide, identifying thousands of eclipsing binaries via automated photometry from dedicated telescopes in Chile and South Africa. Spectroscopy enhances photometric data by measuring curves, which trace the Doppler shifts in lines due to orbital motion, confirming the binary nature and providing orbital periods, eccentricities, and velocity amplitudes. When combined with analysis, these yield precise es and radii for both components, as the inclination is known to be near 90° from the eclipse geometry; for example, follow-up of Kepler targets has determined masses to within 1-2% accuracy for systems with well-resolved lines. Double-lined spectroscopic binaries, where lines from both are discernible, allow direct mass ratios, while single-lined cases rely on photometric constraints for fuller characterization. Analyzing these observations presents challenges, including , which causes non-uniform surface brightness and distorts eclipse depths, and third-light contamination from unresolved nearby that dilutes the measured variations. Limb darkening effects are modeled using quadratic or nonlinear laws derived from stellar atmosphere theory to fit observed light curves accurately. Third-light contributions, often from cluster members or field , are quantified through high-resolution or multi-wavelength photometry and subtracted iteratively. Software like PHOEBE addresses these issues by integrating Roche geometry, , and to simultaneously model light and curves, accounting for spots, third light, and relativistic effects in a computationally efficient framework.

Astrophysical Importance

Eclipsing binary systems provide direct and precise measurements of fundamental stellar parameters, including masses, radii, and densities, which are otherwise challenging to obtain for individual stars. The radii of the component stars are determined from the durations and depths of eclipses in the light curve, while masses are derived by combining these with radial velocity curves and applying Kepler's third law adapted for binary orbits, which relates the orbital period and semi-major axis to the total mass: (M1+M2)P2=4π2Ga3(M_1 + M_2) P^2 = \frac{4\pi^2}{G} a^3, where M1M_1 and M2M_2 are the stellar masses, PP is the period, aa is the semi-major axis, GG is the gravitational constant, and the individual masses follow from the velocity ratio. Densities can be calculated model-independently from the light curve alone, as the mean density ρ\rho scales with π/(Pτ)\pi / (P \tau), where τ\tau is the ingress/egress duration, offering a key constraint without distance knowledge. These measurements achieve precisions often better than 1-2% for well-observed systems, serving as empirical benchmarks for single-star properties. In stellar evolution studies, contact and overcontact binaries, such as W Ursae Majoris (W UMa)-type systems, offer insights into late-stage interactions like common phases and mergers. These systems feature stars sharing a common convective , with models suggesting they evolve from initially detached binaries through loss via magnetic braking, potentially leading to ejection or direct merger. W UMa stars, in particular, are considered precursors to stellar mergers, as their short periods (typically 0.2-1 day) and mass ratios near unity indicate dynamical instability that can culminate in coalescence, producing rapidly rotating single stars with anomalous chemical abundances. Observations of over 1000 such systems have revealed period oscillations consistent with common dynamics, where the expanding of the primary engulfs the secondary, shrinking the orbit until contact or merger. This process is crucial for understanding the formation of blue stragglers and the efficiency of ejection. Eclipsing binaries have revolutionized exoplanet detection by enabling the identification of circumbinary planets through transit timing variations (TTVs) in eclipse timings, which reveal gravitational perturbations from orbiting bodies. In these systems, the planet's influence causes deviations from the predicted binary eclipse schedule, with TTV amplitudes scaling as Δt≈(Pb/Pbin)(Mp/Mbin)Pbin\Delta t \approx (P_b / P_{bin}) (M_p / M_{bin}) P_{bin}, where PbP_b and MpM_p are the planet's period and mass, and PbinP_{bin} and MbinM_{bin} are the binary's. The first confirmed circumbinary planet, Kepler-16b, discovered in 2011, orbits a 41-day eclipsing binary with a 229-day period, its Saturn-mass body detected via TTVs of up to 0.4 hours; this system exemplifies how eclipsing binaries facilitate precise orbital solutions for planets in ~10% of known circumbinary cases. Approximately 35 such planets have since been confirmed, primarily in Kepler data, providing statistics on their occurrence rate of ~10-20% around close binaries. As benchmarks, eclipsing binaries calibrate models by providing empirical checks on parameters like convective overshooting and mixing length, with detached systems offering radius and mass measurements that test isochrones to ~5% accuracy across 1-20 solar masses. For instance, analyses of 19 well-characterized detached binaries have constrained overshooting parameters in models, reducing discrepancies between predicted and observed radii by up to 10%. Additionally, the surface method uses eclipsing binaries as standard candles for distances, relating the angular radius from eclipse geometry to bolometric corrections via log⁡θ=−0.2mλ+Sλ(T,log⁡g)\log \theta = -0.2 m_\lambda + S_{\lambda}(T, \log g), where θ\theta is the , mλm_\lambda the magnitude, and SλS_{\lambda} the surface brightness-color calibration; this yields distances precise to 3-5% for Galactic systems and has refined the distance to 49.97 kpc. Recent (JWST) observations in 2023-2024 of the white dwarf cooling sequence in the 47 Tucanae have provided an age estimate of 11.8 ± 0.5 Gyr, consistent with ages derived from eclipsing binaries (12.0 ± 0.5 Gyr) and the main-sequence turn-off, confirming the cluster's age around 12 Gyr while probing low-mass .

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