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Heliacal rising
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The heliacal rising (/hɪˈlaɪ.əkəl/ hih-LY-ə-kəl)[1][2][3] of a star or a planet occurs annually, when it becomes visible above the eastern horizon at dawn in the brief moment just before sunrise (thus becoming "the morning star").[a][4] A heliacal rising marks the time when a star or planet becomes visible for the first time again in the night sky after having set with the Sun at the western horizon in a previous sunset (its heliacal setting), having since been in the sky only during daytime, obscured by sunlight.
Historically, the most important such rising is that of Sirius, which was an important feature of the Egyptian calendar and astronomical development. The rising of the Pleiades heralded the start of the Ancient Greek sailing season, using celestial navigation,[5] as well as the farming season (attested by Hesiod in his Works and Days). Heliacal rising is only one of several types of alignment for stars' risings and settings; mostly the risings and settings of celestial objects are organized into lists of morning and evening risings and settings. Culmination in the evening and the culmination in the morning are separated by half a year, while on the other hand risings and settings in the evenings and the mornings are only separated by a half-year at the equator, and at other latitudes set apart by different fractions of the year.
Cause and significance
[edit]
Relative to the stars, the Sun appears to drift eastward about one degree per day along a path called the ecliptic because there are 360 degrees in any complete revolution (circle), which takes about 365 days in the case of one revolution of the Earth around the Sun. The star's heliacal rising will occur when the Earth has moved to a point in its orbit where the star appears on the eastern horizon at dawn. Each day after the heliacal rising, the star will rise slightly earlier and remain visible for longer before the light from the rising sun overwhelms it. Over the following days the star will move further and further westward (about one degree per day) relative to the Sun, until eventually it is no longer visible in the sky at sunrise because it has already set below the western horizon. This is called the acronycal setting.[6]
The same star will reappear in the eastern sky at dawn approximately one year after its previous heliacal rising. For stars near the ecliptic, the small difference between the solar and sidereal years due to axial precession will cause their heliacal rising to recur about one sidereal year (about 365.2564 days) later, though this depends on its proper motion. For stars far from the ecliptic, the period is somewhat different and varies slowly, but in any case the heliacal rising will move all the way through the zodiac in about 26,000 years due to precession of the equinoxes.
Because the heliacal rising depends on the observation of the object, its exact timing can be dependent on weather conditions.[7]
Heliacal phenomena and their use throughout history have made them useful points of reference in archeoastronomy.[8]
Non-application to circumpolar stars
[edit]Some stars, when viewed from latitudes not at the equator, do not rise or set. These are circumpolar stars, which are either always in the sky or never. For example, the North Star (Polaris) is not visible in Australia and the Southern Cross is not seen in Europe, because they always stay below the respective horizons.
The term circumpolar is somewhat localised as between the Tropic of Cancer and the Equator, the Southern polar constellations have a brief spell of annual visibility (thus "heliacal" rising and "cosmic" setting) and the same applies as to the other polar constellations in respect of the reverse tropic.
History
[edit]Constellations containing stars that rise and set were incorporated into early calendars or zodiacs. The Sumerians, Babylonians, Egyptians, and Greeks all used the heliacal risings of various stars for the timing of agricultural activities.
Because of its position about 40° off the ecliptic, the heliacal risings of the bright star Sirius in Ancient Egypt occurred not over a period of exactly one sidereal year but over a period called the "Sothic year" (from "Sothis", the name for the star Sirius). The Sothic year was about a minute longer than a Julian year of 365.25 days.[9] Since the development of civilization, this has occurred at Cairo approximately on July 19 on the Julian calendar.[10][b] Its returns also roughly corresponded to the onset of the annual flooding of the Nile, although the flooding is based on the tropical year and so would occur about three quarters of a day earlier per century in the Julian or Sothic year. (July 19, 1000 BC in the Julian Calendar is July 10 in the proleptic Gregorian Calendar. At that time, the sun would be somewhere near Regulus in Leo, where it is around August 21 in the 2020s.) The ancient Egyptians appear to have constructed their 365-day civil calendar at a time when Wep Renpet, its New Year, corresponded with Sirius's return to the night sky.[9] Although this calendar's lack of leap years caused the event to shift one day every four years or so, astronomical records of this displacement led to the discovery of the Sothic cycle and, later, the establishment of the more accurate Julian and Alexandrian calendars.
The Egyptians also devised a method of telling the time at night based on the heliacal risings of 36 decan stars, one for each 10° segment of the 360° circle of the zodiac and corresponding to the ten-day "weeks" of their civil calendar.
To the Māori of New Zealand, the Pleiades are called Matariki, and their heliacal rising signifies the beginning of the new year (around June). The Mapuche of South America called the Pleiades Ngauponi which in the vicinity of the we tripantu (Mapuche new year) will disappear by the west, lafkenmapu or ngulumapu, appearing at dawn to the East, a few days before the birth of new life in nature. Heliacal rising of Ngauponi, i.e. appearance of the Pleiades by the horizon over an hour before the sun approximately 12 days before the winter solstice, announced we tripantu.
When a planet has a heliacal rising, there is a conjunction with the sun beforehand. Depending on the type of conjunction, there may be a syzygy, eclipse, transit, or occultation of the sun.
Acronycal and cosmic(al)
[edit]The rising of a planet above the eastern horizon at sunset is called its acronycal rising, which for a superior planet signifies an opposition, another type of syzygy. When the Moon has an acronycal rising, it will occur near full moon and thus, two or three times a year, a noticeable lunar eclipse.
Cosmic(al) can refer to rising with sunrise or setting at sunset, or the first setting at morning twilight.[12]
Risings and settings are furthermore differentiated between apparent (the above discussed) and actual or true risings or settings.
Overview
[edit]The use of the terms cosmical and acronycal is not consistent.[13][14] The following table gives an overview of the different application of the terms to the rising and setting instances.
| Daytime | Visibility | Rising (east) | Setting (west) |
|---|---|---|---|
| Morning (matutinal) | True (in daylight) | Cosmical | Acronycal[14]/Cosmical[13] |
| Apparent (in twilight) | Heliacal (first night sky appearance) |
Heliacal[14]/Cosmical[13] (last morning appearance) | |
| Evening (vesper) | True (in daylight) | Acronycal | Cosmical[14]/Acronycal[13] |
| Apparent (in twilight) | Heliacal[14]/Acronycal[13] (first evening appearance) |
Heliacal (last night sky appearance) | |
| [13][14] | |||
See also
[edit]Notes
[edit]- ^ Heliacal risings occur after a star has been behind the Sun for a season, and it is just returning to visibility. There is one morning, just before dawn, when the star suddenly reappears after its absence. On that day it "blinks" on for a moment just before the sunrise and just before it is then obliterated by the [overwhelming light of the] Sun's presence. That one special morning is called the star's heliacal rising.[4]
- ^ The exact date varies with latitude, so that Sirius's return is observed about 8–10 days later on the Mediterranean coast than at Aswan.[11] Official observations were made at Heliopolis or Memphis near Cairo, Thebes, and Elephantine near Aswan.[11] The date at any location also slowly varies within the Gregorian calendar by about three days every four centuries. July 19 of the Julian Calendar occurs on August 1 Gregorian in the 20th and 21st centuries.
References
[edit]
- ^ "heliacal". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)
- ^ "heliacal". Merriam-Webster.com Dictionary. Merriam-Webster.
- ^ "heliacal". Dictionary.com Unabridged (Online). n.d.
- ^ a b "Show me a dawn, or "heliacal", rising". Stanford University.
- ^ "Pleiad". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)
- ^ "rising and setting of stars". sizes.com.
- ^ "Archaic Astronomy and Heliacal Rising". September 10, 2005.
- ^ Schaefer, Bradley E. (1987). "Heliacal Rise Phenomena". Journal for the History of Astronomy. 18 (11). SAGE Publications: S19 – S33. doi:10.1177/002182868701801103. ISSN 0021-8286. S2CID 116923139.
- ^ a b Tetley (2014), p. 42.
- ^ "Ancient Egyptian Civil Calendar", La Via, retrieved 8 February 2017.
- ^ a b Tetley, M. Christine (2014), The Reconstructed Chronology of the Egyptian Kings, Vol. I, p. 43, archived from the original on 2017-02-11, retrieved 2017-02-09.
- ^ Hockey, Thomas A. (January 1, 2012). "Acronical Risings and Settings". American Astronomical Society Meeting Abstracts #219. 219: 150.01. Bibcode:2012AAS...21915001H – via NASA ADS.
- ^ a b c d e f Robinson, Matthew (2009). "Ardua et Astra: On the Calculation of the Dates of the Rising and Setting of Stars". Classical Philology. 104 (3). University of Chicago Press: 354–375. doi:10.1086/650145. ISSN 0009-837X. S2CID 161711710.
- ^ a b c d e f "Understanding - Rising and setting of stars". Encyclopedia FP7 ESPaCE. Retrieved 2022-10-29.
Heliacal rising
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Fundamentals
Definition
The heliacal rising of a celestial body, such as a star or planet, refers to its first visibility in the eastern sky at dawn after a period of invisibility caused by its proximity to the Sun during solar conjunction.[7] This event occurs when the body rises shortly before sunrise, appearing briefly above the horizon before the Sun's glare overwhelms it.[8] The term "heliacal" derives from the Greek word hēliakos, meaning "of the sun," emphasizing the phenomenon's dependence on the Sun's position relative to the celestial body.[9] It was first systematically described in ancient astronomical texts, including Ptolemy's Almagest (Book VIII.6), where it is discussed as the first morning visibility of a star, denoting the star's initial escape from the Sun's rays.[9] Unlike the daily rising of stars due to Earth's rotation, the heliacal rising is an annual event for non-circumpolar bodies, marking the end of their seasonal invisibility period tied to solar interference.[10] Classic examples include the heliacal rising of Sirius, the brightest star in the night sky, which ancient Egyptians observed as a key seasonal marker, and Venus when appearing as the morning star after inferior conjunction.[8][11]Visibility Conditions
The visibility of a celestial object during its heliacal rising hinges on several interconnected environmental and observational factors that determine whether it can be discerned against the brightening dawn sky. The apparent magnitude of the star or planet is paramount: brighter objects like Sirius (magnitude -1.46) become detectable at solar elongations as small as 9°-11°, whereas fainter stars (magnitude +4 or higher) necessitate elongations approaching 18° to overcome twilight glare. Atmospheric extinction, which scatters and absorbs light through the air column, further dims the object, with coefficients typically ranging from 0.2 to 0.35 magnitudes per air mass under standard conditions; drier air reduces this effect, enhancing detectability. Horizon clarity is essential, as obstructions like trees, buildings, or haze can block low-altitude sightings, while the observer's elevation above sea level minimizes the air mass traversed by the light path, thereby lowering extinction and improving visibility thresholds.[12][13][14][15][16] Central to these conditions is the arcus visionis, the minimum solar elongation (angular separation from the Sun) required for the object to emerge from solar glare, often equivalent to the combined altitude of the object above the horizon and the Sun's depression below it. For stars of magnitude 0, this value typically spans 6°-12°, but it scales linearly with increasing faintness; empirical relations derived from ancient observations and modern modeling yield approximations like 10.5° for magnitude 0, decreasing to about 9°-11° for Sirius and rising to 16°-18° for magnitude +3 to +5 stars. This parameter accounts for the interplay of magnitude and extinction, with values varying slightly by azimuth difference between the object and Sun.[12][14][17] Achieving reliable sightings demands optimal atmospheric and site-specific conditions, particularly a unobscured eastern horizon free from local interferences, low humidity to curb aerosol scattering, and negligible light pollution that would otherwise elevate twilight sky brightness and mask faint objects. Such setups are most favorable in mid-latitudes during summer for southern circumpolar stars, where longer nights and stable weather align with peak elongations; urban light pollution can shift effective arcus visionis values upward by several degrees, rendering marginal events unobservable. Observers at higher altitudes, such as mountain sites, benefit from reduced extinction (e.g., 0.03 magnitude less per 1,000 meters), allowing detection at smaller elongations compared to sea-level locations.[14][16][18] On the day of first visibility, the object remains detectable for approximately 30-45 minutes immediately preceding sunrise, as it rises just ahead of the Sun and fades rapidly with increasing daylight; this interval progressively lengthens to over an hour in following days, facilitating easier confirmation.[13][19]Astronomical Mechanisms
Cause
The heliacal rising of a star occurs due to the geometric alignment known as solar conjunction, where the star's right ascension coincides with that of the Sun from Earth's perspective. During this period, the star rises and sets almost simultaneously with the Sun, rendering it invisible amid the intense daylight glare and atmospheric scattering of sunlight.[20] This invisibility persists for several weeks to months, depending on the star's brightness and the observer's latitude, as the star remains too close to the Sun in angular separation.[2] As Earth progresses in its orbit around the Sun, the apparent position of the Sun shifts eastward along the ecliptic relative to the fixed stars, at a rate of approximately one degree per day. This orbital motion gradually increases the star's morning elongation—the angular distance from the Sun in the predawn sky—until the star rises sufficiently earlier than the Sun to become visible low on the eastern horizon just before sunrise, marking the heliacal rising.[2] The process reverses for the heliacal setting in the evening sky, but the morning reappearance is particularly notable for its role in ancient timekeeping. The visibility threshold, typically requiring an elongation of 10–15 degrees for faint stars, determines the exact moment, though detailed conditions are addressed elsewhere.[19] Over millennia, long-term astrophysical effects such as the precession of Earth's rotational axis and the proper motion of stars alter the timing of these events. Precession, a slow wobble completing a cycle every 25,772 years, shifts the vernal equinox westward along the ecliptic, changing when stars align with the Sun relative to seasonal markers. Combined with proper motion—the actual transverse velocity of a star across the sky— these factors cause heliacal rising dates to drift; for Sirius, the brightest star, the combined effects have caused only a minor shift of less than one day in its heliacal rising date in the Julian calendar over the past 5,000 years compared to around 3000 BCE.[21][22] For planets, the causes parallel those for stars but are modulated by their orbital configurations relative to Earth and the Sun. Inferior planets, such as Venus and Mercury, whose orbits lie inside Earth's, experience heliacal risings shortly after inferior conjunction, when they pass between Earth and the Sun and disappear into the solar glare for about 1–2 months. Post-conjunction, Earth's orbital motion carries the Sun away angularly, allowing the planet to reemerge as a morning object.[17] Superior planets, like Mars, whose orbits are outside Earth's, undergo heliacal risings after superior conjunction, when they align behind the Sun from our view following opposition (their point of maximum opposition brightness and eastward motion). The opposition phase indirectly influences the cycle by positioning the planet for approach toward conjunction, after which orbital separation restores morning visibility.[17] These planetary conjunctions thus drive the periodic invisibility and reappearance, with durations varying by synodic period.Calculation
The prediction of a heliacal rising date and time relies on computing the moment when a star rises sufficiently before the Sun to become visible against the dawn sky, accounting for atmospheric effects and observer location. A basic approximation uses the geocentric ecliptic elongation ε between the star and the Sun, defined as ε = |λ_star - λ_sun|, where λ denotes ecliptic longitude; visibility begins when ε exceeds the arcus visionis (AV), a threshold typically around 9°–12° for bright stars like Sirius (visual magnitude m ≈ -1.5), depending on conditions.[17][22] For a rough estimate, AV ≈ 10° + 4° × (m + 1), though more precise models adjust linearly with magnitude, such as AV ≈ 7° + 1.1° × m based on historical Babylonian data.[14] Detailed algorithms incorporate geometric and atmospheric factors for accuracy. Pierre Bretagnon's method, developed for Sirius, computes the event by inverting series expansions of local celestial coordinates (right ascension and declination) as functions of Julian day number, valid from -4400 to +2800; it includes atmospheric refraction (standard valueLimitations
Circumpolar Stars
Circumpolar stars are defined in astronomy as those positioned within an angular distance less than the observer's latitude from the nearest celestial pole, causing their diurnal paths to form circles entirely above the local horizon.[26] For an observer at 40° N latitude, this threshold corresponds to stars closer than 40° to the north celestial pole, such as Polaris (Alpha Ursae Minoris), which maintains a declination of approximately 89.3° and thus never sets.[27] These stars trace continuous loops around the pole due to Earth's rotation, remaining perpetually visible from the horizon upward throughout the year, without ever crossing the horizon line.[28] The concept of heliacal rising does not apply to circumpolar stars because they lack a phase of setting below the horizon, which is essential for the annual cycle of disappearance and reappearance tied to solar conjunction.[29] Instead, their potential invisibility arises solely from atmospheric and solar interference, such as daylight or twilight brightness, rather than positional occultation by the Earth.[30] Although always above the horizon, these stars can be obscured by twilight, especially near solstices when extended twilight periods and varying solar declinations increase sky glow around the poles; for instance, at the summer solstice in the northern hemisphere, the sun's +23.5° declination brings brighter conditions closer to the celestial pole, challenging visibility of fainter circumpolar objects.[31] Observationally, the visibility of circumpolar stars is primarily modulated by their angular distance from the pole—which determines their minimum altitude—and the intensity of solar glare, resulting in continuous presence rather than discrete heliacal events.[32] Stars closer to the pole, like those in Ursa Minor, remain at higher altitudes and are more reliably observable all night in northern latitudes above about 30° N, eliminating any cyclical "reappearance" tied to heliacal risings.[33] This perpetual accessibility contrasts with non-circumpolar stars, where annual invisibility periods enable defined heliacal phenomena, but it underscores the role of polar distance in dictating consistent, glare-limited observability.[30]Latitude Effects
The visibility and timing of heliacal risings for non-circumpolar stars are strongly dependent on the observer's geographic latitude. At the equator, nearly all stars with declinations between -90° and 90° experience an annual heliacal rising, as the celestial equator aligns symmetrically with the horizon, allowing each star to emerge in the morning sky once per sidereal year before being overtaken by the Sun. As latitude increases toward the poles, this symmetry breaks down, limiting the number of southern stars (negative declination) that can achieve sufficient altitude for visibility during their morning apparition. For instance, the bright star Sirius (α CMa, declination δ ≈ -16.7°) has a heliacal rising observable from latitudes up to approximately 70°N, beyond which its path skims the northern horizon too closely for practical detection in twilight; above 50°N, visibility becomes marginal due to the star's low maximum altitude and increased atmospheric extinction.[34][22] The geometry of the horizon plays a key role in these latitude effects, as the point of rising for a star shifts in azimuth depending on the observer's latitude. The azimuth A of a star's rising is given by the formula \cos A = \frac{\sin \delta}{\cos \phi}, where \delta is the star's declination and \phi is the latitude. This shift means that at higher latitudes, southern stars rise farther to the south of due east, altering their angular separation from the Sun's rising point and thus the required arcus visionis (the minimum elongation for visibility). The maximum latitude from which a southern star can rise (and potentially have a heliacal rising) is determined by the condition \sin \phi < \cos \delta; for Sirius, this corresponds to \phi < 73.3^\circ \mathrm{N}, beyond which the star remains below the horizon at all times. These geometric constraints ensure that only stars with declinations satisfying |\delta| < 90^\circ - |\phi| can cross the horizon, excluding extreme southern stars from high northern latitudes.[19] In polar regions, within the Arctic or Antarctic Circles (latitudes >66.5°), the effects are more pronounced due to extended periods of polar day and night. During the summer months, when the Sun remains above the horizon for 24 hours or more, continuous daylight and prolonged civil twilight eliminate the dark skies necessary for distinguishing a star's first appearance just before sunrise, preventing classic heliacal visibility altogether. Similar issues arise in winter polar night, though heliacal risings for southern hemisphere summer events occur then. For example, Sirius's heliacal rising date varies significantly with latitude due to these seasonal and geometric alignments, shifting by approximately 40 days from around June 22 at 30°S to August 1 at 30°N, reflecting changes in the Sun's declination and the star's attainable altitude.[35][22]Historical and Cultural Role
Ancient Observations
In ancient Egypt, the heliacal rising of Sirius, known as Sopdet, served as a critical marker for the annual inundation of the Nile River, signaling the onset of the agricultural season around 3000 BCE during the Old Kingdom period.[36] This event was meticulously recorded in temple inscriptions and calendars, associating the star's reappearance with the goddess Sopdet and the renewal of fertility.[37] Temples such as that of Hathor at Dendera were aligned to facilitate precise observations of this rising, with architectural orientations designed to capture the star's first visibility on the eastern horizon just before dawn.[38] Babylonian astronomers documented heliacal risings in the MUL.APIN tablets, compiled around 1000 BCE, which include lists of approximately 36 stars whose risings defined the months and seasons in their sexagesimal calendar.[39] These cuneiform records from the Neo-Assyrian and Neo-Babylonian periods reflect systematic skywatching practices, integrating stellar phenomena with agricultural and ritual timing.[40] In ancient Greece, Hesiod's Works and Days, composed around 700 BCE, references the heliacal rising of the Pleiades to indicate the start of the harvest season, advising farmers to begin reaping when the cluster appears at dawn while associating its setting with plowing preparations.[41] Chinese oracle bone inscriptions from the Shang Dynasty, dating to approximately 1200 BCE, contain the earliest known records of Venus's heliacal risings, often inscribed during divinations to interpret the planet's visibility as omens for royal decisions.[42] These Shang-era artifacts, primarily shoulder blades and turtle shells, demonstrate ongoing planetary monitoring integrated with ritual practices.[43] Similarly, in Mesoamerica, the Maya tracked Venus's heliacal phases in the Dresden Codex, a Postclassic bark-paper manuscript that details the planet's 584-day synodic cycle, including morning and evening risings, to schedule warfare and ceremonies.[44] The codex's tables emphasize Venus as a harbinger of conflict, with its first appearances linked to ritual sacrifices.[45] Ancient observers across these civilizations employed dedicated techniques for detecting heliacal risings, often conducted by priests during nocturnal vigils on elevated temple roofs to minimize horizon obstructions and ensure clear eastward views.[46] Gnomons—simple vertical rods or obelisks—were used to measure shadows and align sightings with the horizon, aiding in the timing of these fleeting events.[47] For bright stars and planets like Sirius or Venus, such methods achieved an accuracy of 1 to 2 days, accounting for atmospheric conditions and slight annual variations in visibility.[22]Calendrical and Agricultural Uses
In ancient Egypt, the heliacal rising of Sirius formed the basis of the Sothic cycle, a 1460-year period resulting from the annual discrepancy of approximately 0.25 days between the civil calendar and the interval between successive heliacal risings, during which the star's annual reappearance aligned with the civil calendar's New Year after drifting through all 365 days.[48] This cycle, spanning 1460 Egyptian civil years due to the calendar's lack of leap days, allowed the heliacal rising—occurring around late June to early July—to periodically reset the calendar, marking the onset of the Nile's inundation and the agricultural season.[49] The Sothic year, defined as the interval between successive heliacal risings of Sirius, averaged 365.25 days, closely mirroring the tropical year and providing a stable reference for long-term calendrical adjustments.[49] Heliacal risings served as critical signals for agriculture and navigation in the Mediterranean world. In ancient Greece, as described in Hesiod's Works and Days, the heliacal rising of the Pleiades in early May indicated the start of the harvest and the beginning of the safe sailing season across the Aegean, while their heliacal setting in November marked the end of navigation, the completion of harvest, and the time for plowing and sowing winter crops.[41][50] Similarly, in Rome, the heliacal rising of Sirius, known as the Dog Star, warned of the intense summer heat from late July to August, a period termed the dies caniculares, during which farmers anticipated drought and adjusted irrigation and crop management to mitigate its effects on yields.[51][52] Mythological associations amplified the practical role of these risings in seasonal predictions. In Egypt, Sirius, personified as the goddess Sopdet, was linked to Isis, embodying fertility and rebirth, as her heliacal rising heralded the Nile flood that enriched the soil for planting; at times, it was also associated with Anubis, the jackal-headed god, symbolizing renewal tied to the inundation's life-giving waters.[53] In Babylonia, heliacal risings of stars like Sirius guided irrigation timing and crop cycles within the luni-solar calendar, aligning agricultural labor—such as flooding fields—with seasonal shifts to optimize water distribution in the arid Mesopotamian environment.[54] Over centuries, the lack of leap days gradually misaligned the Egyptian calendar with natural cycles, causing the civil New Year to drift from the Nile flood. By the 21st century BCE, this shift had advanced the calendar date of the inundation by roughly 482 days relative to later baselines, positioning the expected flood in what was then early winter rather than summer, necessitating periodic reforms to maintain agricultural synchronization.[55]Related Phenomena
Heliacal Setting
The heliacal setting refers to the final visible appearance of a star or planet in the western sky immediately after sunset, just before it disappears due to conjunction with the Sun, rendering it invisible in the solar glare. This phenomenon marks the conclusion of the object's evening visibility period, as it sets shortly after the Sun on that day, while on subsequent evenings it sets before sunset and cannot be observed.[56] Mechanistically, the heliacal setting arises as the Sun's annual eastward motion along the ecliptic gradually reduces the angular elongation—the separation between the Sun and the celestial object—until it drops below the threshold for naked-eye detection, typically 8–15 degrees depending on the object's magnitude, atmospheric extinction, and observer latitude. For fixed stars, this event occurs roughly opposite the heliacal rising in the seasonal cycle, often separated by several months of visibility, with the exact timing influenced by the arcus visionis, the minimum altitude above the horizon needed for visibility in twilight. Planets like Venus exhibit similar dynamics during their inferior conjunction phases, where decreasing elongation limits post-sunset sightings.[31][17] Historically, the heliacal setting held significant cultural value for demarcating seasonal transitions, particularly in ancient Mediterranean societies. In ancient Greece, the heliacal setting of the Pleiades in late autumn—around October to November—signaled the onset of winter, prompting the cessation of seafaring activities in the Aegean Sea due to worsening weather and guiding agricultural preparations like plowing and sowing winter cereals.[57] Prominent examples include Venus as the evening star, whose heliacal setting occurs when its western elongation shrinks to about 10 degrees, providing the last observable view low in the twilight for roughly 10–20 minutes before it sets, mirroring the brief visibility window of its morning counterpart. For stars like Sirius, the heliacal setting transpires in late spring at mid-northern latitudes, ending its extended evening prominence after months of all-night visibility.[19]Acronycal and Cosmical Events
Acronycal rising refers to the event when a star rises at the same time as the Sun sets, becoming visible in the evening twilight; this phenomenon occurs when the star is at opposition to the Sun, approximately 180 degrees in elongation.[58] Similarly, acronycal setting takes place when a star sets as the Sun rises, visible in the morning twilight and aligned with opposition.[59] These events mark the star's position directly opposite the Sun in the sky, providing a temporal indicator for seasonal changes through their visibility in twilight. Cosmical rising occurs when a star rises simultaneously with the Sun, at true conjunction or 0 degrees elongation, making it invisible amid the dawn light; cosmical setting is the counterpart, where the star sets with the Sun at sunset.[58] Both cosmical events represent exact alignment with the Sun's position, contrasting with the opposition of acronycal phenomena, and they form part of the invisible astronomical alignments that ancient observers noted for calendrical purposes.[60] The key differences between acronycal and cosmical events lie in their solar elongations: acronycal risings and settings happen at roughly 180 degrees, positioning the star for optimal nighttime visibility, including during these events at opposition, while cosmical events at 0 degrees signify conjunction, where the star is lost in the Sun's glare entirely.[60] Unlike heliacal risings, which are the first visible appearances due to slight separation from the Sun, acronycal events are observable in twilight while cosmical events remain unobserved directly, serving instead as theoretical markers in positional astronomy.[58] In classical literature, acronycal and cosmical events underpin "poetical" astronomy, as described by ancient Greek and Roman authors who used these invisible alignments poetically to evoke seasonal or mythical motifs.[59] For instance, the poet Aratus in his Phaenomena (circa 275 BCE) references the acronycal rising of Arcturus to signal agricultural timings, integrating these astronomical oppositions into verse for cultural resonance.[61] Such references highlight how these events, though unseen for cosmical or theoretical, influenced poetic traditions in the Hellenistic world.References
- https://www.[merriam-webster](/page/Merriam-Webster).com/dictionary/heliacal