The Tal-Qadi Sky Pill – Wikibooks, open books for an open world

The Tal-Qadi sky pill in a showcase of the Nationwide Museum of Archeology in Valletta (Malta).

Scale reproduction of the Tal-Qadi sky pill fabricated from beech wooden.

From an astronomical standpoint, the current textual content offers with the archaeological discovery of a roughly 4500-year-old limestone pill from Malta, which clearly exhibits a bit of the starry sky.

On this Wikibook it’s proven that the sky pill of Tal-Qadi could be aligned to the Golden Gate of the Ecliptic within the constellation Taurus to be able to measure the ecliptical latitude of the moon and planets. This was doable 1000’s of years in the past as it’s at this time with none additional gear. With the suitable observations, not solely can the sidereal and draconian intervals of the moon be decided, but in addition star coverages and lunar and photo voltaic eclipses could be predicted. The celestial desk thus proves the excellent astronomical data and expertise already possessed by the Neolithic inhabitants of the island of Malta.

Preface

In historical instances, people may solely take a look at the night time sky with the bare eye. In doing so, nonetheless, they’ve already been in a position to decide that the roughly 5000 seen mounted stars kind an eternally mounted geometric constellation with each other, solely {that a} barely totally different part of the universe could be seen at totally different instances of the day and yr. The impression of wanting on the Milky Method, the open star cluster of the Pleiades or the Andromeda Galaxy has definitely all the time been skilled as chic and mysterious. The brightest mounted stars could be counted on just a few arms and weren’t solely comparatively straightforward to impress however have been even given correct names for identification or communication with different individuals.

Moreover, even at this time, there have been typically unpredictable occasions, comparable to the looks of novae, comets or falling stars, which have been definitely processed mythically. Between these very common and seemingly utterly random appears when wanting on the night time sky, the primary individuals definitely observed that seven particular transferring stars transfer commonly and in addition perpetually in relation to the mounted star sky, above all of the solar and the moon. Generally even two or three of you meet in a single place in heaven, and this unusual, mystical, after which utterly inexplicable behaviour definitely captivated a few of our ancestors in historical instances, and increasingly more myths have lastly grown out of it.

Later within the Center Ages, astronomy, together with arithmetic, geometry and music, was one of many 4 excessive arts of the quadrivium. The processes within the sky are certainly fairly summary and complicated and may solely be understood and associated to one another with in depth prior data. Sadly, this data is more and more being misplaced, because the night time sky hardly permits complete statement because of the sturdy gentle air pollution and curiosity in it decreases accordingly. Maybe these explanations right here assist to arouse curiosity within the topic or to deepen current data.

This Wikibook is a tough translation of the suitable German-speaking Wikibook. Archaeoastronomy is a relatively younger science that has hardly been in a position to set up itself, significantly in German-speaking international locations. The outcomes offered right here might also assist to advance this self-discipline slightly and to carry circles nearer to the astronomical fundamentals for the evaluation of archaeoastronomical information.

Introduction

Badly broken and alienated state of the ruins of Tal-Qadi in 2014.

Tal-Qadi on Malta was already utilized by individuals in 4000 BC, the primary temple buildings of Tal-Qadi have been constructed between 3300 and 3000 BC and have been then in use for a very long time. The interval from 3000 to 2500 BC is named the island’s Tarxien part.

Through the excavations began in 1927, a fan-like limestone plaque with incisions was discovered within the temple advanced. A lot of the markings are clearly harking back to the depiction of stars, which makes the discover one of many oldest archaeoastronomical objects.

The celebs have all the time had a distinguished place within the myths of all peoples. They have been typically seen as manifesting manifestations or because the heavenly “areas” of deities. Whereas the celebrities of the mounted star sky have been of nice significance for the navigation of seafarers or desert hikers, the celestial objects that have been movable in comparison with the mounted star sky have been typically used for astrological interpretations.

On this paper, the emphasis is much less on the archaeological points of the discover. Slightly, the next explanations signify an try to interpret the representations on the stone pill primarily based on the earlier findings from an astronomical, geometrical and geographical standpoint and thus presumably to contribute to having the ability to classify the discover in an expanded context. Based mostly on the celestial phenomena which have been noticed with out telescopes for 1000’s of years, many primary phrases of astronomy are talked about, defined and associated to 1 one other.

Aid map of Malta with the situation of Tal-Qadi.

The temple advanced of Tal-Qadi is positioned ten kilometres northwest of the capital Valletta within the northern a part of the island republic close to at this time’s small city Sàn Pawl il-Baħar. The situation is at 35 ° 56’12 “north latitude and 14 ° 25’14” east longitude. The peak above sea degree of the Mediterranean is round 16 meters.

If visibility is sweet, Etna in Sicily could be seen in a northerly path over the slim bay with salt pans positioned one and a half kilometres east of Sàn Pawl il-Baħar in 200 kilometres. Solely on this path can the Mediterranean Sea be seen from the temple advanced from a place raised by just a few meters.

The alignment of the temple advanced from west to east is uncommon compared to all different Maltese temple complexes, as these are largely aligned alongside the principle axis of the island from northwest to southeast. The constructing was round 30 meters lengthy within the north-south path and round 25 meters within the east-west-east path. Itis not doable to obviously decide the place the doorway to the temple was.[1]

The azimuth (horizontal angle) of the nonetheless recognizable axis within the temple factors east to 76 levels of arc (path to dawn on April 18 and August 24) or in the other way to the west to 256 levels (path to sundown on February 17 and on October 24).
In Malta there are good astronomical statement situations because of the dry and balanced Mediterranean local weather. There, lunar eclipses have been commonly noticed, but in addition complete photo voltaic eclipses, such because the photo voltaic eclipse within the morning hours of Might 18, 2146 BC, with excessive chance.[2]

The particular however largely irregular phenomena within the mounted star sky embrace meteors, supernovae and comets. On common, a supernova might be seen with the bare eye roughly each 200 years over the previous 2000 years. The Halley comet is documented in China as early as 240 BC.[3] The final perihelion passage of the periodic comet C2020 F3 (NEOWISE) is more likely to have taken place throughout the island’s Tarxien part.

Reference of the temple to the sky system

Varied examples are recognized from archaeology of how in historical instances the instructions of the sky might be decided and the rising and setting of the celebrities might be decided and predicted. Examples embrace the Goseck round moat in Saxony-Anhalt (4900 BC) [4], the Nebra sky disc (round 2000BC) or the Belchen system of the Celts within the Vosges, the place the 4 Belchen are seen from Alsace different, extra japanese Belchen within the area have a calendar perform with regard to the sunrises.[5]

Seen from the Tal-Qadi temple ruins, in the direction of the west (270 levels of arc, the path in the direction of sundown originally of spring and autumn), there’s a clearly recognizable path of a pure valley, in the direction of the east there’s a hill over 50 meters excessive that covers the horizon.

The celestial north pole was and is a vital reference level within the northern hemisphere for orientation within the night time sky. In historical instances, due to the precession of the Earth’s axis, the North Star was not on the level of the celestial north pole and will due to this fact not be used immediately to find out the north path. This could simply be recognized from the temple advanced by sighting the ocean bay within the path of Etna. This was all the simpler when the volcano was lively and creating a big column of smoke that might be seen from afar, and even at night time when the corresponding column of fireside was noticeable. Such occasions are documented within the traditions from historical instances for geographical orientation, such because the exodus of the Israelites from the slavery of Pharaoh in Egypt between 1500 and 1000 BC (evaluate Exodus 13.21 + 22).

The limestone slab

Description

Sketch of the incisions on the Tal-Qadi sky pill primarily based on the Institute for Research of the Research of the Historical World at New York College.[6]

The plaque is on show within the Nationwide Museum of Archaeology in Valletta.[7]

It’s unclear whether or not the limestone slab discovered is basically full or only a fragment of a bigger slab, however a number of the sides are noticeably straight and clean.[8] The limestone slab has the form of an irregular hexagon, is 29 centimetres huge, 24centimeters excessive and roughly 5 centimetres thick. Limestone shouldn’t be very arduous and may due to this fact be simply labored and scratched, and quite a few symbols and graphic components are represented on the flat floor. Nonetheless, there are additionally many pure bumps and it isn’t all the time doable to obviously establish whether or not the floor has pure, intentionally man-made, unintentional or damage-related buildings. The provenance of the stone pill has apparently not but been investigated, for instance primarily based on the chemical evaluation of the composition of the rock.

In accordance with the size, the stone pill has an space of virtually 500 sq. centimetres. With a density of two.7 to 2.9 grams per cubic centimetre for limestone [9] the mass of the pill is round six kilograms. This makes it transportable and could be held in your arms for a couple of minutes with a corresponding effort.

The illustration is split radially into 5 roughly equal-sized segments with an angle of 20 arc levels every by 4 straight strains. The strains have a typical level of intersection slightly exterior the board and begin radially from the nook level to the left of the longest and straight edge. Star-shaped symbols are proven within the two segments on the left and proper. A single star image could be seen within the left section, and a number of other star symbols within the different three. The center section exhibits a semi-circular determine, the straight fringe of which is perpendicular to the path in the direction of the centre of the radial rays and on the aspect to this centre. The 2 proper segments are traversed by a way more pronounced furrow.

Interpretation

The three star teams depicted have been related to zodiac indicators early on. It was speculated that the three asterisks stand for the three zodiac indicators Scorpio, Virgo and Leo, or that the present pill is simply a fraction of a bigger pill that has proven a moon-phase calendar. The image within the center section was related to a crescent moon.[1]

It’s doable that the sky area proven on the sky desk with the celebrities that set right here and there was noticed from the temple of Tal-Qadi, particularly within the night and in a westerly path.[10]

Trendy inventive background portray of the night time sky with sections of the neighbouring constellations Orion and Taurus . Under left the arm and the bow of the hunter Orion and within the center the top of the bull with Aldebaran and the Hyades and the physique of the animal with the Pleiades additional above on the correct. The star Omikron Tauri (ο Tauri) is on the decrease proper within the left entrance hoof, and the 2 stars Tien Kuan (ζ Tauri) and Elnath (β Tauri) are on the higher left within the suggestions of the horns. Above the Pleiades on the sting of the image a foot of the constellation Perseus with the 2 stars ζ Persei and Atik (ο Persei) could be seen.

In accordance with latest investigations by the archaeologist Peter Kurzmann, the seven-star-shaped representations on to the left of the centre might be the star Aldebaran (α Tauri) with the celebrities γ, δ, ε and θ Tauri belonging to the open star cluster of the Hyades in at this time’s constellation Taurus (Taurus) in addition to the 2 suggestions of the bull horns and Tien Kuan (ζ Tauri) and Elnath (β Tauri) act. The star ε Tauri can also be known as Ain. The constellation to the correct of the centre might be the seven foremost stars of the open star cluster of the Pleiades, additionally belonging to the constellation Taurus, and to the far proper the constellation Perseus
to the north signify. The only star on the left is related to one of many three brightest stars within the northern sky south of the above-mentioned star clusters:[11]

• The distinctive pink supergiant Betelgeuse within the constellation Orion (α Orionis), the shoulder of the sky hunter (often known as the left shoulder star as a result of it’s on the high left from the viewer).
• The brightest star within the constellation Orion Rigel (β Orionis), the alternative foot of the sky hunter.
• The brightest star of the starry sky Sirius (α Canis Majoris) within the neck and head space of the constellation Canis Main.

In an extra investigation it’s identified that the perimeters of the stone pill should not damaged, however machined and in some instances fairly straight, in order that it may be assumed that the geometry of the stone pill is meant and that it isn’t a fraction from a bigger pill ought to act. A pentagonal construction recognizable within the plaque is analogous with the ground plans of Maltese temples.[8]

In one other temple advanced on Malta, within the south temple of Mnajdra, there are indications of doable statement of the Pleiades in antiquity.[12]

Different researchers assume that the semi-circular image is a chook barge that the individuals of Malta used to sail the Mediterranean on the time. The star constellations are photographs of the Adriatic area, the japanese Mediterranean and the Black Sea.[13] If one follows this strategy, the bottom of the stone pill shouldn’t be within the centre of the rays, however precisely reverse, in order that the boat can be aligned appropriately, specifically swimming within the water. It’s The Chronology of Historical Kingdoms Amended[14] assumed that this could have postulated that constellations have been used for navigation. Within the Chronicle there are references to navigation with stars and to using constellations in historical instances, however this doesn’t apply to the time 4500 years in the past, nor are navigation and constellations introduced right into a direct relationship by Newton. Slightly, he solely factors out that in antiquity, for navigation functions, the rising and setting (morning first and morning final or night first and night final) of particular person stars have been noticed (additionally known as heliacal and acronychical rising and setting). Newton additionally doesn’t converse of correspondences between constellations and geographical situations.[15]

Within the following, a number of the celestial objects talked about in addition to some astronomical information are described in additional element and introduced into context.

The Pleiades with their foremost stars.

After the moon and the 5 planets seen to the bare eye, the Pleiades are essentially the most conspicuous objects within the night time sky. They belong to an open star cluster and should not as massive and as near our photo voltaic system because the star clusters of the Hyades, that are solely 153 gentle years away, however at a distance of round 400 gentle years they’re nonetheless shut sufficient that a number of the brighter stars could be distinguished with the bare eye can.

The Pleiades open cluster consists of over a thousand stars, of which the brightest seven foremost stars are listed under:

The seven foremost stars of the Pleiades
Correct title Obvious
brightness
Alcyone 3,0m
Atlas 3,5m
Electra 3,5m
Maia 4,0m
Merope 4,0m
Taygeta 4,0m
Pleione ≈5,0m
Word: The numerical dimension class of the obvious magnitude is indicated by a subsequent and superscript m (for Latin magnitudo or, for shorter, magazine). A primary dimension class greater means a lower within the obvious brightness by an element of round 2.5. The distinction in brightness between the brightest star within the night time sky Sirius (-1.5m) and the darkest stars (6m) which are barely seen to the bare eye is due to this fact a ratio of 1000 to 1. The obvious brightness says nothing about dimension, distance or absolute brightness of a star.

Two different, considerably darker stars of the star cluster even have correct names, specifically Celaeno (5.5m) and Asterope (6.0m). All different seen stars are considerably darker. The overall obvious magnitude of the star cluster is round 1.5m.

Visibility

Seen from Malta, the Pleiades are at this time each on Might 20th (at the side of the solar they’re invisible) and on November 18th (in opposition to the solar and at midnight with a peak of 78 levels very excessive above the southern horizon) within the meridian. The meridian is the imaginary nice circle that runs by means of the 2 celestial poles in addition to by means of the zenith and the nadir. In winter and spring, the Pleiades could be noticed within the night sky in a westerly path and in summer time and autumn within the morning sky in an easterly path.

The next desk exhibits the instances of the primary and final rising and setting of the Pleiades; Heliacal right here means “belonging to the solar”, i.e. near the rising solar. Nonetheless, this should be under the horizon, and the space to the solar (i.e. the elongation) should be greater than 18 levels in order that the daylight scattered within the environment doesn’t outshine the Pleiades. The acronychical rises (night first) in addition to the heliacal units (morning final) should not vital for the mounted stars (and thus additionally for the Pleiades), as they’re in distinction to the moon, the planets and Comets can all the time be seen within the nights between the primary of the morning and the final of the night:

The place of the Pleiades within the starry sky
Occasion Astronomical title Time Path
Final night Acronychical set April 30 West, on the horizon
Proximity to the solar Conjunction with the solar Mai 20 At midday within the south, near the zenith
First morning Heliacal rise June 10 East, on the horizon
Distant from the solar Opposition to the solar November 18 At midnight within the south, near the zenith

The time of the heliacal rise of the Pleiades in relation to the twelve months decided by the moon phases made them a calendar star within the Babylonian lunisolar calendar. If the rise had shifted to the third calendar month (Simanu), a thirteenth leap month was inserted, with which the calendar months might be synchronized once more with the start of spring of the photo voltaic yr.

The New Zealand Māori additionally used the heliacal rising of the Pleiades as a foundation to set the New 12 months’s date and to start sowing.

Seen from Malta at this time, the Pleiades rise roughly 7 arc levels north of the ecliptic and set 31 arc levels north of the ecliptic. The Pleiades due to this fact rise in Malta at an azimuth of 59 arc levels within the east and set at an azimuth of 301 arc levels within the west.

Seen from Alsatian Belchen at this time the Pleiades rise for instance all the time above Little Belchen, the place the solar on the summer time solstice rises. On Might 1, i.e. on the day on which the Pleiades are gone in our time within the Maltese nightfall, the solar rises above the very best mountain within the Vosges Mountains, the Nice Belchen. This was in all probability devoted to the Celtic god of sunshine Belenus, whose feast day Beltane falls on Might 1st. The Black Forest Belchen is positioned precisely in an easterly path, i.e. on the identical latitude because the Alsatian Belchen (47.82° north latitude). On the 2 days of the equinox originally of spring and autumn, celestial objects which are positioned close to the spring or autumn level of the solar (together with the Pleiades, which have been there4500 years in the past) transfer from Alsatian Belchen as seen precisely within the east above the Black Forest Belchen on or as seen from the Black Forest Belchen precisely within the west above the Alsatian Belchen under.[16]

Representations in antiquity

The Pleiades are in all probability depicted as seven golden discs on the Nebra Sky Disc from the early Bronze Age (round 2000 BC). In Mesopotamia they’re recorded on the cuneiform tablets of the Astrolabe B calendar. However the Celtic iron sword from the third century BC, present in Allach close to Munich in 1891,can also be executed with gold inlays displaying the Pleiades.[17]

It is usually mentioned whether or not the Pleiades throughout the constellation Taurus (Taurus) are already depicted within the Stone Age drawings within the Lascaux cave.[18][19]

Additionally on the Bronze Age disc of Phaistos from the island of Crete, an emblem with seven factors seems a number of instances, which was related to the Pleiades.[20]

Related assumptions exist for an association of seven holes on the calendar stone from Leodagger in Decrease Austria.[21]

Custom

The Pleiades thus had a particular which means in lots of cultures and sometimes seem in pictorial representations. They’re a calendar star, after the rise and fall of which agricultural and seafaring actions have been organized in antiquity, as was the case with the Greek poets Hesiod round 700 BC or
Aratos von Soloi (* approx. 310 BC; † 245 BC) is occupied. The title Pleiades goes again to the seven daughters of the Titan Atlas and his spouse, the Oceanid Pleione from Greek mythology. They’re known as: Alcyone, Electra, Asterope (or Sterope), Celaeno, Maia, Merope und Taygete.

The Pleiades are additionally known as Siebengestirn in German, which makes the direct reference to the magical, mystical and divine quantity seven.[22]

There are numerous German synonyms for the Pleiades:[23][24][25][26]

Regensterne, Schiffersterne, Buschelsterni, Staubkörner, Sieb, Glucke, Henne, Tauben, Weintraube, Frühlingsjungfern, Sieben Schwestern, Töchter des Atlas (additionally Atlantiden, Atlantiaden), …

In lots of languages that they had and nonetheless have a correct title:

Outdated Excessive German thaz sibunstirri (das Siebenstirn), Polish child (crones), Russian baba (crone), Japanese Subaru (meeting), Turkish Ülker, Aztecan Tianquiztli (market place), Sumerian Mul-Mul (stars), Akkadian Zappu (heap), Latin Vergiliae (meshwork), Greek heptasteros (sevenstar), Arabian Al-Thurayya (candelabrum)[27], Hebrew Kimah (little heap), Maori Matariki, Hawaiian Makaliʻi, Aragonesian As Crabetas, Welsh Twr Tewdws, Finnish Seulaset (little sieve or seven forehead), …

The star cluster is talked about thrice within the Outdated Testomony: The ninth chapter “God’s energy and the powerlessness of man” of the Guide of Job mentions the 4 most placing star constellations within the ninth verse: “He makes the constellation of the bear, Orion, the seven stars, the chambers of the south.” Within the 31st verse of the 38th chapter it says: “Do you tie the ties of the seven stars, or do you loosen Orion’s chains?”
Within the ebook of the prophet Amos in chapter 5, verse 8, it says in regards to the two neighbouring constellations: “He created the seven stars and Orion;
it transforms the darkness into the intense morning, it darkens the day into night time.“

The time period quarantine (from French “quarantaine de jours” = “forty days”) is expounded to the Pleiades, as they’re within the subtropical latitudes (at this time) from Might 1st to June ninth, i.e. forty days, from the solar are outshone after which even the brightest star of this constellation, Alcyone (η Tauri), can’t be seen with the bare eye till shortly after sundown after which shortly earlier than dawn. The Babylonians, who know the celebrities, are mentioned to have burned forty reeds when the Pleiades returned within the morning sky for his or her pleasure.

After the invisibility of the Pleiades, in historical Egypt the waters of the Nile started to rise for forty days and to fall once more for simply as lengthy.[28]

Noah opened the window of his ark after forty days [29], and Moses spent forty days on the mountain of God, Sinai.[30] In opposition to this background, it isn’t shocking that within the New Testomony Jesus fasted forty days within the desert[31][32][33], which is why there are forty days of fasting within the lent at this time.

The Inuit inform the legend that a big bear threatened humanity and was chased into the sky by canines. Because the Pleiades, the pack of canines would proceed to pursue this bear at this time.[25]

The Australian aborigines of the Loritja say that whereas the Pleiades are invisible, seven ladies come to earth and carry out a fireplace dance.[34]

In reference to the truth that the cuckoo stops singing in early summer time and that the Pleiades can’t be seen within the latitudes of the climatically temperate zones for for much longer, there’s a German legend a few hard-hearted baker who labored for 72 days till the summer time solstice calls in useless for his spouse and daughters. On this saga it says:

The origin of the Pleiades is advised as follows: Christ walked previous a bakery the place recent bread smelled and despatched his disciples to ask for bread. The baker refused it, however the baker’s spouse was standing within the distance along with her six daughters and was giving the bread secretly. For this they’re moved to the sky as seven stars, however the baker has grow to be a cuckoo and so long as he calls in spring, from Tiburtii (observe: Tiburtii title day of Rome is April 14th) to Midsummer (observe: John the Baptist’s title day is June 24th (St. John’s Day)), the seven stars are [not] seen within the sky.[23]

In North German and East Prussian sagas there are variants of this story during which the cuckoo can’t recall the relations who’ve fled or fears their revenge.[24]

Astronomical reference programs

A historic armillary sphere within the Historic Museum of Basel (Switzerland) with three movable rings that describe the three astronomical planes of the horizon, the celestial equator and the ecliptic. Even the traditional Babylonians noticed occasions within the night time sky with easy designs of such armillary spheres.

Relationship between horizontal and equatorial coordinate system.

When observing the orbits of the mounted stars immediately, there are two pure reference programs, specifically the horizontal and the equatorial. For the statement of the seven transferring celestial objects in relation to the starry sky, it is smart to introduce one other aircraft along with the horizon aircraft and the equatorial aircraft, specifically the ecliptic aircraft.

The horizon

The horizontal coordinate system corresponds to the day by day expertise of the surroundings, for the reason that two eyes of people are often aligned horizontally subsequent to one another. Within the horizon system a stone all the time falls vertically from high to backside in the direction of the centre of the earth. It’s the most incessantly used coordinate system for orientation in on a regular basis life. The perfect horizon is a round horizontal line with the observer within the centre. The plumb line is perpendicular to the corresponding circle, and due to this fact, each level on the earth’s floor has a special horizon system and exhibits a special a part of the sky above it at a sure cut-off date.

The cardinal factors north, east, south and west are used to point instructions. In relation to the north path or alternatively in relation to the south path, the
azimuth may also be used as a clockwise angle the place the north path corresponds to Zero arc levels, the east path to 90 arc levels, the south path to 180 arc levels and the west path to 270 arc levels.

The peak above the horizon is named the elevation angle

${displaystyle h}$

from Zero to 90 levels of arc, with Zero levels of arc on the horizon and 90 levels of arc perpendicular above the observer on the zenith. Adverse angles are under the horizon, and the nadir is strictly under the observer at an elevation angle of -90 levels. The meridian is the good circle that passes the north and south factors in addition to the zenith and nadir.

Because of the rotation of the earth, the horizon system adjustments completely in relation to the starry sky.

The celestial poles

When observing the celebrities at night time, it’s noticeable that inside a sidereal day (from the Latin sideris = the star, i.e. associated to the starry sky) of virtually 24 hours, they’re transferring all the time in the identical circle from east to west across the celestial poles after which stand once more in the identical place in relation to the horizon system. A sidereal day is about 4 minutes shorter than a sunny day, as a result of the solar appears to maneuver slightly to the left in relation to the mounted star sky – because of the rotation of the earth across the solar. After a yr, this distinction provides as much as a complete day, in order that any star rises and units on the identical time of day after a photo voltaic yr and is on the identical level within the horizon system and within the corresponding cardinal path on the identical time of day. This may be simply understood with the next tough calculations:

${displaystyle 4,{frac {textual content{minutes}}{textual content{day}}}cdot 360,{frac {textual content{days}}{textual content{yr}}}=1440,{frac {textual content{minutes}}{textual content{yr}}}}$

${displaystyle {frac {1440,{frac {textual content{minutes}}{textual content{yr}}}}{60,{frac {textual content{minutes}}{textual content{hour}}}}}=24,{frac {textual content{hours}}{textual content{yr}}}}$

${displaystyle {frac {24,{frac {textual content{hours}}{textual content{yr}}}}{24,{frac {textual content{hours}}{textual content{day}}}}}=1,{frac {textual content{day}}{textual content{yr}}}}$

The northern celestial pole is definitely discovered at this time by means of Polaris within the constellation Ursa minor, which lies all night time (and all day) in the identical location just about precisely north of the horizontal reference system. All different stars are continually altering their place within the horizontal reference system.

The celebs shut sufficient to the seen celestial pole are all the time above the horizon for an statement level and are known as circumpolar stars. The circumpolar stars of the alternative, invisible celestial pole can by no means be seen. On the North Pole and on the South Pole of the Earth, all stars within the respective hemisphere are circumpolar, however none is for an observer on the Earth’s equator.

All seen stars that aren’t circumpolar rise sooner or later in the midst of a twenty-four-hour day on the japanese horizon and set on the western horizon. The celebs precisely within the center between the 2 celestial poles lie on the celestial equator, and so they describe the biggest circle (an amazing circle) within the sky. The biggest elevation angle is all the time reached in a southerly path on the meridian, the smallest, presumably damaging elevation angle in a northerly path on the meridian.

The 2 angles within the equatorial coordinate system that outline the place of any celestial physique are the hour angle

${displaystyle tau }$

or the correct ascension

${displaystyle alpha }$

alongside the celestial equator and the declination

${displaystyle delta }$

perpendicular to it within the path of the celestial poles, optimistic to the north and damaging to the south.
The hour angle of a celestial object corresponds to the time that has handed since its final passage of the celestial object by means of the meridian, and the hour angle and proper ascension are due to this fact often given in hours. The proper ascension, nonetheless, is expounded to the vernal equinox, which is within the centre of the solar originally of spring.
The proper ascension and the declination of all mounted stars are fixed other than their slight correct motion and the displacement of the vernal equinox because of the very sluggish precession of the earth’s axis and are due to this fact given in star catalogues that are associated to a specific commonplace epoch.

The pole peak

${displaystyle phi }$

is the smallest angle between the horizon and a celestial pole alongside the meridian, which corresponds precisely to the geographical latitude of the corresponding observer on the globe. The angle between zenith and celestial pole enhances the pole peak to a proper angle with 90 levels of arc and on the identical time it corresponds to the inclination between the horizontal aircraft and the equatorial aircraft. Each reference programs share each the east level and the west level. On the north pole the pole peak is +90 arc levels, on the south pole the pole peak is -90 arc levels, and on the equator, it’s Zero arc levels.

The vernal equinox

The vernal equinox had and nonetheless has an excellent which means in celestial science. When the solar is on the vernal equinox, everywhere in the world it rises at 6 a.m. native time within the morning and units precisely within the west at 6 p.m. native time within the night. For the reason that full moon is all the time reverse the solar as seen from the earth, a full moon that happens originally of spring stands reverse the vernal equinox on the autumn equinox and rises round 6 p.m. within the east and units round 6 a.m. within the west.

Conversely, the solar is on the autumn equinox originally of autumn and rises there within the morning at 6 a.m. native time within the east and units precisely within the west at 6 p.m. native time within the night. A full moon occurring on the identical time is then close to the vernal equinox and rises within the morning at 6 a.m. native time within the east and units within the night at 6 p.m. native time within the west.

The migration of the equinox alongside the ecliptic.

Because of the precession of the earth’s axis, not solely the place of the celestial poles alongside a round path change in a cycle of 25800 years, but in addition the vernal equinox. Throughout this time, it traverses your complete ecliptic with its 360 levels of arc precisely as soon as in a westerly path. In every of the twelve constellations alongside this zodiac with an angle of 30 arc levels per constellation, due to this fact, it’s for 2150 years inside a sure constellation. In different phrases: the vernal equinox shifts by 1.Four arc levels in 100 years, by 8.Four arc minutes in ten years or by 50 arc seconds per yr to the west.

From 4500 years in the past till at this time, the vernal equinox has moved 60 levels to the west from the constellation Taurus, in order that this constellation not units similtaneously the solar originally of spring, however solely 4 hours later than the solar units, and due to this fact, within the west and within the night the constellation is clearly seen as a result of the solar is already nicely under the horizon earlier than the setting of the Hyades and Pleiades. Round 3000 years in the past, the vernal equinox was already within the constellation Aries and at this time it’s within the constellation Pisces.

This migration behaviour was already recognized in antiquity and was represented by the Chaldean scholar Kidinnu (* in all probability round 400 BC; † in all probability 330 BC). Nikolaus Kopernikus
acknowledged and named the precession of the earth’s axis as the reason for the migration of the vernal equinox 500 years in the past, and solely Friedrich Wilhelm Bessel was in a position to decide the precession fixed with excessive accuracy, which was honoured by the Prussian Academy of Sciences in 1813 with the award of a prize.

The spring equinox represents an anchor within the photo voltaic calendars. The Jewish Passover in addition to the Christian Easter feast have all the time taken place after the equinox in spring. For instance, Easter Sunday is the primary Sunday after the primary full moon that follows this equinox. The cultivation of arable land and the sowing of plant seeds have been and are carried out in lots of cultures as regards to the date of the astronomical starting of spring to be able to get hold of good harvest yields.

The ecliptic

The 4 polar and tropic circles throughout the summer time solstice within the northern hemisphere. On this illustration, the ecliptic lies precisely horizontally between the centre of the earth and the solar.

The ecliptic is the imaginary aircraft during which the earth’s orbit strikes across the solar throughout a yr. In relation to the celestial equator it’s inclined by an angle of 23 levels of arc, which can also be known as the obliquity of the ecliptic. This matter of reality is the rationale for 4 digital circles of latitude on the earth’s floor:

• The northern tropic circle, on which the solar is at its zenith at noon on the summer time solstice.
• The southern tropic circle, on which the solar is at its zenith at noon on the winter solstice.
• The northern polar circle, the place the solar does not set on the summer time solstice or the place the solar simply does not rise on the winter solstice.
• The southern polar circle, the place the solar does not set on the winter solstice or the place the solar simply does not rise on the summer time solstice.
 Animation of the obvious day by day motion of the solar originally of the 4 seasons with the three ranges of the horizon (inexperienced), the equator (pink) and the ecliptic (blue). The viewing path runs from the entrance within the east (dawn) to the rear within the west (sundown). The obvious paths of the solar run within the day arcs above and within the night time arcs under the stationary inexperienced horizontal aircraft, that are proven for a geographical latitude of 50 arc levels. Within the south, the day arcs attain their higher vertices at midday, and within the north the night time arcs attain their decrease vertices at midnight. The black pointer standing vertically on the horizontal aircraft is aligned with the zenith.The earth’s brown axis of rotation runs from the underside left (south celestial pole) to the highest proper (north celestial pole). The solar within the vernal equinox is colored inexperienced, and reverse it’s the solar within the autumn equinox when there is similar day and night time. At these two instances, the solar is on the celestial equator proven as a pink circle.The aircraft of the ecliptic is proven as a rotating blue disk. The higher solar represents the scenario on the summer time solstice, and the decrease one on the winter solstice. Through the summer time solstice, the ecliptic is most steeply inclined at midday and least inclined to the horizontal aircraft at midnight, and the opposite manner round throughout the winter solstice.

At any time of the day and yr the ecliptic has a various place and a special arc size above the horizon in comparison with the horizon, however the highest apex is all the time roughly in a southerly path. In Malta, the complete moon on the summer time solstice at midnight solely reaches a horizon peak of round 30 arc levels, however at midday the solar is nearly within the zenith with a horizon peak of over 77 arc levels (horizon peak = 90 arc levels), and thus there’s the longest day of the yr. On the winter solstice it’s the different manner round, and the result’s the bottom place of the solar and thus the shortest day of the yr. On the equinox originally of autumn, the ecliptic reaches its most peak at dawn and the utmost arc size seen above the horizon and the respective minimal at sundown. Within the case of the equinox originally of spring, it’s the different manner round.

The ecliptical size

${displaystyle lambda }$

is often given from the spring equinox as an angle between -180 and +180 levels of arc within the aircraft of the ecliptic, so originally of spring the solar is at zero ecliptical longitude. The ecliptical latitude

${displaystyle beta }$

is set perpendicular to this as an angle between -90 and +90 levels of arc within the path of the poles of the ecliptic. The ecliptical latitude of the solar

${displaystyle beta _{Sonne}}$

is zero by definition. The declination

${displaystyle delta }$

of some extent on the ecliptic all the time lies between

${displaystyle -epsilon }$

and

${displaystyle +epsilon }$

. On the level of spring and autumn the declination of the solar is zero, originally of summer time it’s

${displaystyle +epsilon }$

and originally of winter

${displaystyle -epsilon }$

.

All planetary orbits additionally run close to this aircraft with slight deviations of some levels. As a result of its barely inclined orbit across the earth, the earth’s moon additionally has a deviation from the ecliptic, which ends up in considerably quicker obvious fluctuations round this reference aircraft as a result of its nearer proximity to the earth than the opposite planets. The moon wants a month to finish one orbit across the earth. Provided that the space to the ecliptic (the peak above or under the ecliptic respectively the ecliptic latitude as coordinate) is small enough, it will possibly come to lunar eclipses on the time of full moon or to photo voltaic eclipses on the identical time of latest moon. The 2 inside planets are orbited by the earth and may due to this fact solely be noticed in a comparatively small angular section symmetrical to the solar and with small elongations; within the night within the west after sundown or within the morning within the east earlier than dawn. The elongation of the solar is zero. The outer planets orbit the earth’s orbit and, just like the moon, seem over time on your complete circle of the ecliptic. The elongations of the moon and outer planets can due to this fact attain all values between -180 and +180 arc levels.

The seven-day week

All seven celestial our bodies, which have all the time been seen to the bare eye and are transferring in relation to the starry sky, appear to maneuver alongside the ecliptic across the axis between the 2 ecliptic poles when seen from the earth’s floor. These seven celestial objects, which transfer rapidly in comparison with the starry sky relying on the space from the earth and the solar, are given within the desk under. The truth that they’ll solely be proven in a heptagram ordered by their (sidereal) orbital intervals, which provides the recognized order of the times of the week, is a sign that data of all orbital intervals is a prerequisite for this order. The solar positioned on the high of the diagram:

The seven celestial our bodies which are transferring in relation to the starry sky and their assignments to the times of the week within the illustration of a heptagram, which is organized beginning with the moon in counter-clockwise path and ascending in line with the sidereal orbital intervals. The solar is on the high.
The seven celestial our bodies that transfer throughout the ecliptic
Celestial physique Sideric
interval
in days
Obvious
magnitude
Most
ecliptical
lungitude
Most
elongation
Latin
title of
weekday
Divinity Weekday Quantity Color
Moon 27,3 -13m 5,1° 180° dies lunae Mani Monday 2 2
Mercury 77 -2m 7,0° 28° dies Mercuri Odin / Wotan / Wodan Wednesday 4 7
Venus 225 -5m 3,4° 48° dies Veneris Frija / Frigg / Frigga Friday 6 5
Solar 365 -27m 0,0° dies solis Sol / Sunna Sunday 1 3
Mars 687 -3m 1,9° 180° dies Martis Tiu / Ziu / Tyr Tuesday 3 1
Jupiter 4333 -3m 1,3° 180° dies Iovis Thor / Donar / Thunar Thursday 5 6
Saturn 10760 -0,5m 2,5° 180° dies Saturni Saturn Saturday 7 4

The seven-day week and the names of the seven days of the week return to those seven celestial our bodies. The solar is by far the brightest of those celestial objects, and solely the moon could be seen concurrently with it by the bare eye within the daytime sky all through the entire day.

Observations close to the ecliptic

The Venus crescent in nice brilliancy at a peak of over 30 levels above the western horizon 1 / 4 of an hour earlier than sundown within the day sky.

If the solar is near the horizon and Venus could be very elongated, it may also be noticed with the bare eye within the daytime sky. After the solar and the moon, Venus is by far the brightest planet and is often known as the “morning star” or “night star” in poetic literature due to its sheen. Its rising because the “morning star” and its setting because the “night star” on the ecliptic have been calculated as early because the 17th century BC and recorded on the Venus tablets of the Babylonian king Ammi-saduqa. On a number of the Celtic bronze disks from Monasterevin (Eire, first to second century AD[35]) the obvious course of the Venus positions within the night and morning sky above the horizon in relation to the solar is presumably artistically represented. The opposite planets (generally misleadingly known as strolling or wandering stars) are solely seen between sundown and dawn.

Of the celebrities seen within the northern hemisphere, solely Sirius within the constellation Canis Main, which is simply 8.6 light-years away and was talked about by the Greek poet Homer because the canine star, is -1.5m brighter than Saturn. The subsequent brighter stars Arktur (α Bootis) within the constellation Bootes, Vega (α Lyrae) within the constellation Lyra, Capella (α Aurigae) within the constellation Auriga and Rigel (β Orionis) within the constellation Orion are with a magnitude of round 0m already one and a half orders of magnitude darker than Sirius and half a magnitude darker than Saturn.

There are solely seven shiny objects within the mounted star sky close to the ecliptic. These may even be seen within the daytime sky throughout a complete photo voltaic eclipse[36], as was the case with the English astronomer Edmond Halley (* 1656; † 1742) throughout the photo voltaic eclipse on April 22, 1715 (in line with the Julian calendar, in line with the Gregorian calendar it was Might 3, 1715) in London, when the solar disappeared within the constellation Taurus and its foremost star Aldebaran (α Tauri) in addition to the close by Jupiter and the star Capella (α Aurigae) within the neighbour constellation Auriga turned seen.[37]

The Hyades with the star Aldebaran and the planet Venus within the head of the bull within the constellation Taurus at daybreak over the japanese horizon with all stars with an obvious brightness as much as the fifth magnitude.
The seven brightest objects near the ecliptic
Correct title Astronomical
title
Constellation Obvious
magnitude
Ecliptical
longitude
Ecliptical
latitude
Antares α Scorpii Scorpio 1,0m 250,0° -4,6°
Spica α Virginis Virgo 1,0m 204,1° -2,1°
Regulus α Leonis Leo 1,5m 150,1° 0,5°
Pollux α Geminorum Gemini 1,0m 113,5° 6,7°
Aldebaran α Tauri Taurus 1,0m 70,1° -5,5°
Hyades Open star cluster Taurus 0,5m 66,1° -5,8°
Plejades Open star cluster Taurus 1,5m 60,2° 4,1°

The seven brightest objects near the ecliptic.

The Zodiac

The zodiac describes the twelve constellations alongside the ecliptic, which seem within the following order:

• Spring
• Summer season
• Autumn
• Libra
• Scorpio
• Sagittarius
• Winter
• Capricornus
• Aquarius
• Pisces

Of all of the constellations, solely these twelve are on the ecliptic. The 2 open star clusters of the Pleiades and the Hyades belong to the constellation Taurus and are due to this fact additionally within the space of the ecliptic. All different constellations, specifically Orion and Ursa Main (with the asterism Huge Dipper) are off the ecliptic. A lot of the constellations seen within the northern hemisphere are on or north of the ecliptic.

All twelve constellations of the zodiac occupy their very own 30 arc diploma lengthy part of the complete circle, with adjoining constellations seamlessly merging into each other. It needs to be famous that the constellation Libra, which stands between the 2 constellations Scorpio and Virga, shouldn’t be depicted on the celestial desk of Tal-Qadi in line with the above-mentioned hypothesis. Nonetheless, the constellation Libra is sort of small and relatively inconspicuous. In historical instances it was nonetheless assigned to the claws of the scorpion. Solely the Persians and Babylonians launched twelve zodiac indicators and the common angular construction on the ecliptic with segments of the identical dimension, every with 30 levels of arc. It’s not recognized whether or not and which constellations have been in use 4500 years in the past.

The Golden Gate of the Ecliptic

The place of the equinox earlier than 4500 years within the Golden Gate of the Ecliptic.

4300 years in the past, the vernal equinox was nonetheless within the constellation Taurus, 2150 years in the past within the constellation Aries (the synonym “First Level of Aries” for the vernal equinox comes from this period) and at this time within the constellation Pisces. 2500 BC the spring equinox was precisely between the Hyades and the Pleiades within the Golden Gate of the Ecliptic! Round 4500 years in the past, a full moon that appeared originally of autumn was on the identical time within the equinox and within the golden gate of the ecliptic and set precisely within the west at 6 p.m. native time.

Venus (backside centre) at some point earlier than its passage of the Golden Gate of the Ecliptic because it approaches the Pleiades.

The conspicuous star clusters of the Pleiades and Hyades, that are simply recognizable with the bare eye, kind asterisms within the starry sky. Along with the star Aldebaran within the Hyades (it doesn’t belong to the star cluster itself) these objects signify the three brightest objects within the neighborhood of the ecliptic in a comparatively slim area, i.e. in an angular vary of lower than 10 levels of arc.[38] Collectively they kind the 2 stable posts of the Golden Gate of the Ecliptic within the constellation Taurus. All seven transferring celestial objects transfer roughly incessantly, however commonly very near the ecliptic, by means of this gate and thus between the 2 star clusters, seen from Earth. Solely the Earth’s moon, Venus and Mercury can often hit the posts of the Golden Gate and even go slightly exterior the Pleiades because of the barely bigger deviation from the ecliptic and their relative proximity to the earth.

The constellation Taurus has all the time been some of the vital constellations.[39] Along with the 2 star clusters, the intense pink big Aldebaran is especially placing and is commonly seen because the shining proper eye of the bull. Within the 18th century it was often known as the ox eye in Germany.[40] The title Aldebaran is Arabian and means “the follower” (it follows the Pleiades when rising within the japanese morning sky). This foremost star of the constellation additionally belongs to the asterism of the winter hexagon, which could be seen in Central Europe from September to April. It’s shaped by the six foremost stars of the six neighbouring constellations Taurus, Orion, Canis Main, Canis Minor, Gemini, and Auriga, specifically from the intense stars Aldebaran, Rigel, Sirius, Procyon, Pollux and Capella. The winter hexagon surrounds the intense pink tremendous big Betelgeuse within the constellation Orion – i.e. collectively there are seven very shiny stars on this space.

Within the western night sky of Malta, Aldebaran and the Hyades are slightly south (left under) and the Pleiades slightly north (proper above) of the ecliptic originally of spring. The road connecting the star clusters is roughly parallel to the horizon when it units.

When rising, the Pleiades within the east stand virtually vertically above the Hyades, and the ecliptic then doesn’t run upright, however moderately flat rising alongside the horizon to the south.

The ecliptical longitude is measured from the vernal equinox alongside the ecliptic. For the Golden Gate of the Ecliptic it’s round 64 levels at this time. It also needs to be famous that the road connecting the Hyades and the Pleiades on the ecliptical latitude of Zero levels of arc is minimize virtually precisely within the center by the road of the ecliptic. Moreover, the ecliptic is inclined at an angle of round 45 levels to this connecting line. On this manner, each the place of the ecliptic and its inclination could be simply decided at any cut-off date, from any level on the earth and immediately from the orientation of the Golden Gate of the Ecliptic, with out having to watch the orbits or positions of the solar, the moon or any planets.

For the sake of completeness, it needs to be talked about that 4500 years in the past, yearly originally of spring, the setting solar was on the western horizon within the Golden Gate of the Ecliptic, though this might not be seen itself in any respect due to the intense daylight. At present that is the case on Might 25th, for the reason that vernal equinox has in the meantime shifted by two months (one month corresponds to an angle of 30 levels alongside the ecliptic).

The moon

The photo voltaic yr (additionally the tropical yr from historical Greek τρόπος (tropos) = rotation) describes a whole orbit of the earth across the solar, and it has 365.242 days – that’s virtually 5 and 1 / 4 days greater than 360, the quantity that corresponds to a full circle within the diploma system of angle measurement. Since it’s virtually 1 / 4 day longer than 365 days, February 29th is inserted into the calendar virtually each 4 years as a leap day on the former finish of the calendar yr (September was the seventh month, October the eighth and so forth) in order that the seasons keep in sync with the course of the solar. Which means that the time within the photo voltaic calendar when the solar reaches the spring equinox all the time stays originally of spring.

Lunar intervals

The moon orbits the earth about twelve instances quicker than the earth does the solar, and it takes a month to finish one lunar orbit. The only notion of the course of the moon is obtained by observing the phases of the moon or its elongations. The synodic month (from historical Greek σύνοδος (synodos) = assembly) describes the length between two equivalent moon phases, i.e. from new moon to new moon or from full moon to full moon. Right here, the conjunction of the brand new moon and the solar is usually thought to be a reference cut-off date respectively the beginning of a month. A synodic month lasts about 29.53 days, and twelve synodic months due to this fact final about 354.37 days – that could be a good 5 and a half days lower than 360. This cycle is the premise for a lunar calendar which is round eleven days shorter than a photo voltaic yr. Due to this fact, luni-solar calendars have a thirteenth synodic leap month, which is added on common each three years, in order that the spring equinox of the solar stays roughly in the identical season.

Moreover, the interval could be thought of during which the moon seems once more in the identical place in relation to the mounted star sky. That is often related to its look on the vernal equinox. This time span is named the sidereal month (from Latin sideris = of the star), and its size is 27.322 days. That is additionally the length between two successive appearances of the moon within the Golden Gate of the Ecliptic, since its place is set by stars within the starry sky.

There’s additionally the draconian month (from historical Greek δράκων (drakon) or Latin draco = dragon), which has a length of 27.212 days. This length describes the instances at which the lunar orbit, inclined by 5 arc levels to the ecliptic, crosses the ecliptic; the ecliptical latitude of the moon is then precisely zero. These intersection factors are known as lunar nodes, and they’re reached as soon as a month within the ascending lunar node and as soon as a month within the descending lunar node. If the moon is on the ecliptic, i.e. within the proximity of those lunar nodes, a photo voltaic eclipse happens when it’s near the solar (when the brand new moon is at the side of the solar), and a lunar eclipse happens when it’s removed from the solar (when the complete moon is in opposition to the solar). These factors have been previously often known as dragon factors, which was derived from the concept that a dragon would devour the moon throughout a lunar eclipse or the solar throughout a photo voltaic eclipse.

With the next Java program it’s doable to compute the ecliptical coordinates of the solar and the moon for any cut-off date of a Julian date in Julian centuries associated to the astronomical commonplace epoch J2000: → Java programme EkliptikaleKoordinatenMondSonne[41]

The ecliptical latitudes of the moon throughout a sidereal month with 27-odd days.
Day by day adjustments of the ecliptical latitude of the moon in levels inside a moon quarter
Days after
ascending
node
Change of
ecliptical latitude
after at some point
1 1,2°
2 1,1°
3 1,0°
4 0,9°
5 0,6°
6 0,3°
7 0,0°

The moon, just like the solar, has an obvious angular diameter of roughly 30 minutes of arc or 0.5 levels of arc. When your individual finger with an outstretched arm, this corresponds to a few quarter of the thickness of the finger.

In the middle of time, the moon can cowl all celestial objects near the ecliptic (for the seven brightest see above) on its orbit and launch them once more inside an hour, that are positioned in a band of ± 5 arc levels across the ecliptic.

Sidereal moon intervals

The moon seems 13 or fourteen instances in a tropical yr at a sure level within the mounted star sky, whereby it all the time has a special
moon age (the variety of days for the reason that final new moon) and due to the totally different interval lengths of sidereal months and draconian months all the time has a special ecliptical latitude.

The 2 following diagrams are supposed for instance the temporal course of the moon phases and the ecliptical latitudes of the moon when it appeared within the Golden Gate of the Ecliptic throughout 254 successive sidereal intervals of 27.322 days every (a complete of 6940 days or 19 years):

The phases of the moon in successive appearances of the moon within the Golden Gate of the Ecliptic inside 254 sidereal intervals (a complete of 19 years). For the reason that synodic month (from new moon to new moon) is over two days longer than the sidereal month, there are moon part shifts as a result of the moon has not but absolutely reached its most moon age after a sidereal month when it has reached the identical ecliptical size.

Within the higher half of the diagram waxing moons and within the decrease half waning moons could be noticed. A moon part of Zero % stands for a brand new moon and a moon part of ±100 % for a full moon.

The start line (day Zero in month 0) could be set for instance on Might 22, 2020, when the brand new moon and the solar have been within the Golden Gate of the Ecliptic.

The ecliptical latitudes of the moon throughout successive appearances of the moon within the Golden Gate of the Ecliptic inside 254 successive sidereal intervals (a complete of 19 years). For the reason that draconian month (from one ascending lunar node to the following ascending lunar node) is an efficient two and a half hours shorter than the sidereal month, there are shifts of the longitude as a result of the moon has already left the ascending node behind on the finish of a sidereal month.

At excessive ecliptical latitudes (above) the Pleiades and at low ecliptical latitudes (under) the Hyades or the star Aldebaran are lined by the lunar disk throughout the Golden Gate of the Ecliptic.

The start line (day Zero in month 0) can, for instance, be set on Might 22, 2020, when the brand new moon was at an ecliptical latitude of roughly -2.5 arc levels under the solar, whose ecliptical latitude is all the time Zero arc levels, throughout the Golden Gate of the Ecliptic

After 18.61 years (or 6793.5 days or 230 synodic months, on this determine after 248.6 sidereal months) the moon reaches the identical ecliptical latitude and virtually the identical lunar part however is then at a special ecliptical longitude.

The Meton cycle

Not solely the willpower and prediction of the rising and setting of Venus attracted the eye of historical astronomers, but in addition the lunar cycle with the totally different phases of the moon, in addition to the prevalence of lunar eclipses throughout a full moon and photo voltaic eclipses throughout a brand new moon. There’s a cycle that describes the time after the solar and moon attain the identical constellation. After 19 years (or virtually 6940 days), not solely has the solar reached the identical ecliptical size, but in addition the moon (after 254 sidereal months), and due to this fact, it additionally has the identical moon part (after 235 synodic months). As well as, it has roughly the identical ecliptical latitude (after 255 draconian months), in order that it’s virtually on the identical level of the mounted star sky[42]

The cycle is actually primarily based on the truth that, though solely long-term, however simply observable, that 19 tropical photo voltaic years (6939.6 days), 235 synodic months (6939.6 days), 254 sidereal months (6939.Eight days) and 255 draconian months (6939.1 days) have virtually the identical size. The distinction between the primary two is simply round two hours.

This 19-year-old lunar circle or the Meton cycle named after the traditional Greek astronomer Meton (fifth century BC) in addition to the under talked about Saros cycle have been already recognized to the Babylonians in historical instances and served as the premise for his or her lunar calendar. The 19 megaliths of the Bluestone horseshoe from Stonehenge (2270 to 1930 BC) have additionally been related to it, for instance. By the way, the gold hats from the Bronze Age, for instance, are additionally related to the Meton cycle.[43]

The golden quantity signifies what number of of those 19 years is a sure yr, and it nonetheless performs an vital function in figuring out the Easter date, for instance with the assistance of the formulation for calculating the Easter date by Carl Friedrich Gauß (* 1777; † 1855). The title golden quantity presumably comes from the truth that the calendar (parapegma) of Meton on which this cycle is predicated might be seen in golden letters on the stone partitions of his sundial (heliotropion) on the Pnyx Hill in Athens[44][42]

At present within the months across the winter solstice each 19 years the setting full moon could be seen on the western horizon within the Golden Gate of the Ecliptic, as final in December 2018. The decrease half of the moon is then lined by the horizon throughout setting and the seen shining half thus kinds a semi-circle, as indicated within the center section of the sky desk. On this case, the Hyades and Pleiades lie within the west on a line parallel to the horizon and the intermediate full moon, which remains to be half seen at setting, would correspond to the illustration on the stone pill of Tal-Qadi. 4500 years in the past, this view of the sky arose already across the autumn equinox due to the shift within the spring equinox.

Along with these coincidences, it may also be noticed that the moon after 18.03 years (i.e. after 242 draconian months or 6585.Three days) reaches precisely the identical ascending or descending node, with the solar and moon additionally having the identical ecliptical size (after 223 synodic months). Nonetheless, they’re then at a special level within the mounted star sky, since this length doesn’t coincide with the sidereal intervals. This cycle is named the Saros cycle.

Moreover, there’s an 18.6-year lunar cycle, which is predicated on the truth that, because of the precession of the lunar orbit, the ascending and descending lunar nodes have precisely as soon as utterly handed by means of the ecliptic towards the path of rotation of the moon (retrograde) after this time. The lunar nodes transfer of their ecliptical size at an angle of 19.34 arc levels per yr. This may be noticed, for instance, on the premise of the deviations within the ecliptical latitudes of the moon and thus the azimuths of the moon rises and units on the horizon, which repeat themselves after 18.61 years and thereby oscillate across the factors of the winter and summer time solstices, which by definition lie precisely within the ecliptic at zero ecliptical latitude. The instances at which the corresponding factors between the northern and southern horizon are closest or farthest aside are known as small and huge moon turns. As well as, all doable positions of the moon in relation to the ecliptic on the ecliptical longitudes of -180 to +180 arc levels and the ecliptical latitudes of roughly -6 to +6 arc levels are reached inside this era. Thus, all doable star occultations happen inside this era, particularly these of the Pleiades, the Hyades and of Aldebaran within the constellation Taurus.

The calendar stone of the Mnajdra temple

It’s fascinating to notice that a number of rows of holes seem on the calendar stone from the Maltese temple Mnajdra, which additionally dates from the island’s temple interval, which might be associated to lunar and photo voltaic calendars. On the head of the stone there are a number of hundred holes organized over a big space, which can signify the person months or years of long-term statement. Under that, seven horizontal rows seem proper aligned:

Sketch of the rows of holes on the calendar stone from Mnajdra after Ventura and Hoskin.[12]
Rows of holes on the calendar stone of the Mnajdra temple on Malta
Row Variety of holes Potential use
A 19 The Golden Quantity for the 19 years of the Meton cycle (235 synodic, 255 draconian, 254 sidereal months and 6940 days, respectively). After a tropical yr the solar has reached its ecliptical longitude once more. After a whole Meton interval the moon has the identical moon part and the identical ecliptical latitude and the identical ecliptical longitude (for instance within the Golden Gate of the Ecliptic or within the vernal equinox).
B B2 16 (proper) In complete 29, for the variety of full days in a synodic month (29.5 days). After this time the moon has reached the identical moon part once more. From the outdated gentle of the moon (final morning) to the complete moon there are 16 days after which 13 days till the following outdated gentle. After having accomplished this double row, there shall be a carry over to row E, and if row E is accomplished there shall be a carry over to row A for a brand new tropical yr with the following Golden Quantity.
B1 13 (left above)
C1 3 (above) For the 7 full days of a lunar quarter (7.Four days) or per week.
If this double row is accomplished, there shall be a carry over to row G for a brand new week.
C2 4 (under)
C3 3 (left) For as much as Three accomplished lunar quarters or weeks in a present synodic month after new moon.
At new moon, waxing half-moon, full moon or waning half-moon there shall be a carry over to row D, or if this one can also be accomplished a carry over to row F.
D 25 For the 25 moon quarters within the first half of a tropical yr.
E 11 For the 11 additional days in a photo voltaic yr (365.2 days) in comparison with twelve synodic months (354.Four days).
F 24 + 1 = 25 For the 24 moon quarters within the second half of a tropical yr. The 25th gap is separated since it’s used for a leap moon quarter on the finish of a yr that solely happens about each two years.
G 53 For the began 53 seven-day weeks in a photo voltaic yr (365.2 days) or from one heliacal rise or acronychical set of the Pleiades to the following.

Above the japanese horizon on the final morning the outdated gentle of the waning moon was simply seen 33 hours earlier than new moon.

Relating to double row B, it needs to be famous that within the historical Egyptian lunar calendar, which was used within the Neolithic, the month didn’t start with the invisible new moon, however with the simply seen outdated gentle of the final morning of the moon, i.e. day earlier than new moon.[45] This leads to 16 days till the complete moon after which one other 13 days till the final morning of the moon. The final two holes are set off considerably to the left, which is in step with the next reality: two days earlier than the top of a synodic interval, i.e. after 27 days, a sidereal month is over, after which the moon has reached the identical ecliptical size. Which means that after this time the moon is once more within the Golden Gate of the Ecliptic, for instance, earlier than it reaches the solar, which has apparently already moved two days (or 30 levels) additional to the left.

Alternatively, the 50 holes of rows D and F may signify the 50 full seven-day weeks (350 days) inside twelve synodic intervals lasting 50.6 weeks (354.Four days).

Concerning the quantity seven

So there are seven foremost stars of the Pleiades, seven commonly observable transferring celestial objects and 7 mounted shiny celestial objects close to the ecliptic, which may due to this fact be lined by the moon or be at the side of the planets. It also needs to be famous at this level {that a} lunar quarter lasts seven days. In reference to the quantity seven, often known as divine, mystical or magical, it’s value mentioning that the constellation Orion and the asterism Huge Dipper (generally known as seven stars prior to now) within the constellation Ursa Main and the constellation Ursa Minor with the Polaris at its high every include seven foremost stars:

The seven foremost stars of the asterism Huge Dipper
Astronomical
title
Correct title Obvious
magnitude
ε Ursae Maioris Alioth 1,75m
α Ursae Maioris Dubhe 1,8m
η Ursae Maioris Alkaid 1,9m
ζ Ursae Maioris Mizar 2,2m
β Ursae Maioris Merak 2,3m
γ Ursae Maioris Phekda 2,4m
δ Ursae Maioris Megrez 3,3m
The seven foremost stars of the constellation Orion
Astronomical
title
Correct title Obvious
magnitude
α Orionis Betelgeuse 0,Zero bis 1,5m
β Orionis Rigel 0,0m
γ Orionis Bellatrix 1,5m
ε Orionis Alnilam 1,5m
ζ Orionis Alnitak 1,5m
κ Orionis Saiph 2,0m
δ Orionis Mintaka 2,5m

It’s noticeable that the teams of stars can all be geometrically divided into a bunch of 4 and one group of three. This arithmetic can also be mirrored, for instance, in Christian theology, the place the divine quantity seven from the heavenly trinity of God and the earthly 4 components (or the 4 evangelists, the 4 cardinal factors or the 4 seasons) are added collectively.

The product of the 2 summands three and 4 is twelve. This corresponds to the 4 seasons of spring, summer time, autumn and winter, every lasting three months. The product of the 2 numbers additionally corresponds to the variety of moons or months in a yr in addition to the variety of constellations on the ecliptic during which the solar stays for one month inside a yr.

Conclusions

View of the area of the sky within the western night sky presumably represented on the sky desk of Tal-Qadi.

Based mostly on the speculation that the 2 angular segments to the left and proper of the centre of the sky desk of Tal-Qadi present the asterisms of the Hyades and the Pleiades within the constellation Taurus, which kind the Golden Gate of the Ecliptic, the semi-circular image within the center between them might be a section of the arc of the ecliptic standing above the horizon. All seven transferring celestial our bodies could be seen transferring by means of the Golden Gate of the Ecliptic. Precisely at this level there was the vernal equinox of the solar.

Through the astronomical statement of the Hyades and the Pleiades, the place and inclination of the ecliptic could be learn immediately at any time and at any level within the sky with the assistance of the appropriately aligned and fitted sky desk, with out having to watch the course of the transferring celestial our bodies themselves. With this data, it’s then additionally doable to find out the place of the transferring celestial our bodies that may be noticed on the identical time close to the ecliptic, i.e. to measure their ecliptical size, for instance, from the vernal equinox or from the lengthy proper fringe of the stone pill. With the alignment described, this edge is strictly perpendicular to the ecliptic on the strongly indented level and may due to this fact be used to measure the ecliptical latitude and may thus be used for longer-term statement to find out the
draconian interval between the passages of the moon by means of the lunar nodes on the ecliptic. The latitude above the ecliptic is by definition zero for the solar, and for the seen planets and the moon the deviation is just a few levels. Thus, when aligning the desk, the moon enters the Golden Gate of the Ecliptic each 27 1/Three days between the higher proper nook of the desk and the decrease space on the correct edge. If it hits the higher proper nook of the desk, the Pleiades shall be lined by the moon 12 hours later. If, however, the lunar orbit runs on the intense reverse aspect of the ecliptic, an occlusion of the star Aldebaran is brought on by the moon. Each are extraordinary and particular astronomical occasions.[46][47][48] If the moon is near the ecliptic throughout this statement lunar eclipses can happen round full moon, and photo voltaic eclipses can happen round new moon.

Project of stars to illustration

The sky desk of Tal-Qadi fitted into the triangle Hyades, Pleiades and Omikron Tauri. The dashed pink strains point out the ecliptic, which is perpendicular to the correct fringe of the sky desk, in addition to the 2 excessive ecliptical latitudes of the lunar orbit to the correct and left of the ecliptic. The inexperienced circle marks the equinox 4500 years in the past within the centre of the Golden Gate of the Ecliptic. The dashed inexperienced line is the road connecting Omicron Tauri and the western tip of the Hyades.

Element on the fringe of the sky desk with a full moon proven to scale.

Geometrical relationships when becoming the sky desk into the described constellation throughout statement.

On this constellation, the only star within the left section may match to the brightest star in your complete night time sky Sirius within the constellation Canis Main, which already had a calendar perform in historical Egypt within the third millennium BC, since its look at daybreak introduced the Nile flood. Between Sirius and the Golden Gate of the Ecliptic, nonetheless, lies the placing constellation Orion. The Sumerians noticed a sheep on this constellation, the hunter of Greek mythology Orion and the constellation Orion are solely documented later. From a geometrical standpoint, its placing pink shoulder star Betelgeuse is extra more likely to be displayed on the left aspect of the panel. The six strains proven between the radial centre of the sky desk and Betelgeuse can correspond to the arch of Orion consisting of the six π stars (the central and brightest star π3 Orionis can also be named Tabit after its Arabian title al-thābit), the arm to the shoulder star Bellatrix, the shoulder line to the star of the opposite shoulder Betelgeuse and under it to the belt with the three belt stars Mintaka, Alnilam and Alnitak.

The constellation Taurus at this time consists of the next shiny celestial objects:

• North of the ecliptic:
• Open star cluster of the Pleiades
• Elnath (proper horn tip, additionally belongs to the constellation Auriga)
• South of the ecliptic:
• Open star cluster of the Hyades (head of the bull, together with Ain)
• Aldebaran (pink, proper eye)
• Tien Kuan (left horn tip)

Nonetheless, whether or not and which constellations have been in use 4500 years in the past is unknown, and it’s due to this fact value contemplating the brightest stars within the firmament. The next desk exhibits the brightest objects within the space of the sky area presumably represented on the sky desk of Tal-Qadi:

Potential task of the brightest celestial objects to the celebrities proven within the space of the Tal-Qadi sky desk.
Correct title Astronomical
title
Obvious
magnitude
Sirius α Canis Majoris -1,5m
Capella α Aurigae 0,0m
Rigel β Orionis 0,0m
Betelgeuse α Orionis 0,5m
Aldebaran α Tauri 1,0m
Alnilam ε Orionis 1,5m
Alnitak ζ Orionis 1,5m
Bellatrix γ Orionis 1,5m
Elnath β Tauri 1,5m
Alamak γ Andromedae 2,0m
Algol β Persei 2,0m
Caph β Cassiopeiae 2,0m
Hamal α Arietis 2,0m
Menkalinan β Aurigae 2,0m
Mintaka δ Orionis 2,0m
Mirfak α Persei 2,0m
Saiph κ Orionis 2,0m
Schedir α Cassiopeiae 2,0m
Tsih γ Cassiopeiae 2,0m
Ruchbah δ Cassiopeiae 2,7m

Ecept for the celebrities Sirius, Rigel and Saiph, that are clearly distant in relation to the area described on the left, all different shiny stars could be assigned to the sky desk with out issues.

On the level and within the path the place the thick transverse furrow could be seen within the two right-angled segments, the Milky Method, which is simply weakly seen on this area, runs roughly within the night time sky. Past the Milky Method, within the section to the correct of centre, reverse the Pleiades, there are two stars that may be recognized with the 2 foremost stars Menkalinan (left) and Capella (proper) of the constellation Auriga. Alternatively, the 2 stars Menkib (ζ Persei, 4m) and Atik (ο Persei, 2,7m) may even have been used to suit the sky desk into the sky section.[49] At present they kind the again foot of the constellation Perseus immediately north of the Pleiades. The Babylonians referred to this constellation because the Outdated Man (SU.GI), presumably due to its bowed look.

The far-right section exhibits a star that matches the very shiny star Mirfak within the constellation Perseus, positioned in the midst of the Milky Method. On this aspect of the Milky Method there are the three shiny stars Algol within the constellation Perseus, Alamak within the constellation Andromeda
and on the very backside presumably additionally Hamal within the constellation Aries. Behind it lies the very conspicuous constellation Cassiopeia (the celestial W) with its 5 shiny stars, of which Segin (ε Cassiopeiae, 3,3m) is noticeably darker than Ruchbah, Tsih, Shedar and Caph. This constellation of 4 might be displayed in the correct nook of the celestial desk.

Lastly, it needs to be famous that beneath these situations the radial centre of the sky desk lies within the star ο Tauri (Omicron Tauri), which with an obvious brightness of three,5m shouldn’t be fairly as shiny as the opposite stars described within the constellation Taurus, however remains to be one of many simply recognizable stars within the area and may due to this fact be used for exact adjustment of the desk. The strains between this centre and the Hyades could be traced again to the darker stars within the constellation Taurus (specifically λ Tauri (3,5m) and e Tauri (5m)). There are additionally a number of strains from the centre within the path of the Pleiades, which may point out the corresponding stars there (specifically ξ Tauri (3,5m), s Tauri (5m) and f Tauri (4m)).

Utility

The next photos present utility examples with the fitted sky desk from Tal-Qadi:

The decrease tip of the board fitted on this manner stands precisely on the western horizon throughout the troublesome final, solely short-term alternative to watch the Pleiades within the night sky, on the acronychical setting or final night (at this time on Might 1st) and earlier than it isn’t seen anymore to the bare eye within the northern subtropical latitudes for forty days. If the Pleiades are greater on this night, they are going to be outshone by daylight; if they’re decrease, their gentle shall be obscured on the good distance by means of the environment by sturdy scattered gentle and elevated extinction.

The arc

The ecliptic above the horizon wanting south at sundown originally of spring.

The arch with the straight line in between within the center section of the sky pill of Tal-Qadi shouldn’t be an emblem for a gate. Gates with semi-circular arches weren’t even widespread at the moment. On this context, nonetheless, it should be famous that the ecliptic, seen from the earth, represents an arc of a circle that intersects the horizon at two factors and continues under it. Due to the good similarity, it isn’t unreasonable to imagine that the image proven within the center section of the stone pill, which lies precisely within the Golden Gate of the Ecliptic, represents the arc of the ecliptic above the horizon and in addition slightly under the horizon.

Moonset on the horizon of the western morning sky.

Along with the easy interpretation of the round arc within the center angular section of the sky desk because the arc of the ecliptic above the horizon, there’s one other chance for an evidence: at this time, on the winter solstice, the complete moon could be noticed each 19 years within the Golden Gate of the Ecliptic because it units can then be seen immediately above the horizon or on the higher fringe of the sky desk as an upwardly curved semi-circle.

Aside from that, with common and long-term statement primarily based on the ecliptical latitudes and moon phases occurring within the Golden Gate of the Ecliptic, the 19-year Meton cycle may all the time be traced. For instance, the complete moon seems on November 30, 2020 after midnight within the Golden Gate of the Ecliptic – even then it could be half-hidden behind the aligned sky desk as a semi-circle. On this very day, because of the small enough ecliptical latitude of -1.Eight levels within the morning, there’s a partial penumbral moon eclipse, which is simply seen on the night time aspect of the earth then exterior of Europe.[50]

Ultimate consideration

Each astronomer is aware of how troublesome it’s to function gear and browse or write paperwork at the hours of darkness of night time. A desk that’s straightforward to the touch and, if needed, illuminated by twilight or pink glow in a average manner that’s acceptable for simultaneous statement of the sky, is definitely a useful gizmo on this context.

With the assumptions offered right here and that are apparent, the Tal-Qadi sky desk wouldn’t solely show a traditionally vital picture of the Maltese sky round 4500 years in the past, however may even have been used to find out calendar dates at the moment. This could be proof of the early and certainly not trivial astronomical data of the inhabitants of the island at the moment.

Dedication

The Golden Gate of the Ecliptic as a photomontage with the contour of a useless spruce, which occurs to signify the form of the bull’s head within the constellation Taurus. Within the decrease centre there’s the intense Venus, within the centre the Pleiades and within the higher proper the constellation Perseus.

This compilation is devoted to the German scientist Friedrich Wilhelm Bessel (* 1784; † 1846), who utterly unjustifiably stands unnoticed within the shadow of the distinguished personalities of his time and his surroundings.

The primary writer significantly thanks his college professor Fritz Hinderer (* 1912; † 1991). Together with his all the time pleasant, and affectionate method, in addition to his profound data, he not solely taught him astrophysics, but in addition launched him to the quite a few sides of astronomical statement along with his very in depth set of astronomical instruments.

References

1. ab Chris Micallef: „The Tal-Qadi Stone: A Moon Calendar or Star Map“, The Oracle, Quantity 2, 2001, pages 36 to 44
2. Rita Gautschy: photo voltaic eclipse -2146/05/18, Kanon der Sonnenfinsternisse von 2501 vor Christus bis 1000 nach Christus, Model 2.0, Januar 2012
3. Halley (1986) – Begleiter der Jahrhunderte, Astro Nook
4. 2.000 Jahre vor Stonehenge… – Das Sonnenobservatorium von Goseck, scienexx, 1. Februar 2008
5. Rolf d’Aujourd’hui: Belchen, Historisches Lexikon der Schweiz, 7. Mai 2002, Bern
6. Stone fragment with incised rays, stars, and crescent, New York College, Institute for Research of the Research of the Historical World, Globigerina Limestone. H. 23.5, W. 30.0, D. 4.5 cm Tal-Qadi Temple (Malta) HM–NMA: 21314
7. Nationwide Museum of Archaeology
8. ab Peter Kurzmann: Weitere Untersuchungen zur neolithischen Sternkarte von Tal-Qadi auf Malta, Archäologie on-line, 10. Juli 2016
9. Kalkstein – Eigenschaften, Entstehung und Verwendung, steine-und-minerale.de
10. See additionally Klaus Albrecht: Die „Sternenkarte“ von Tal-Qadi (Malta) und die Ausrichtung des Tempels von Tal-Qadi nach Osten, Kapitel 9 in: Gudrun Wolfschmidt (Herausgeberin): Orientierung, Navigation und Zeitbestimmung – Wie der Himmel den Lebensraum des Menschen prägt, Tagung der Gesellschaft für Archäoastronomie in Hamburg 2017, aus der Reihe Nuncius Hamburgensis – Beiträge zur Geschichte der Naturwissenschaften, Band 42
11. Peter Kurzmann: Die neolithische Sternkarte von Tal-Qadi auf Malta, Archäologie on-line, 25. Juli 2014
12. ab Frank Ventura, Michael Hoskin: Temples of Malta, in: Clive Ruggles (editor), Handbook of Archaeoastronomy and Ethnoastronomy, 7. Juli 2014, Seiten 1421-1430, Springer, New York, ISBN 978-1-4614-6140-1
13. Kai Helge Wirth: „The Zodiac of Malta – The Tal Qadi Stone Enigma – Final proof of Newtons Principle”, 2016, 2. Auflage, ISBN 978-3741250590
14. Isaac Newton: The Chronology of Historical Kingdoms Amended, London, 1728
15. Isaac Newton: A Quick Chronicle from the First Reminiscence of Issues in Europe, to the Conquest of Persia by Alexander the Nice
16. Walter Eichin und Andreas Bohner: Das Belchen-System, Universitätsbibliothek Freiburg im Breisgau, in: Das Markgräflerland: Beiträge zu seiner Geschichte und Kultur, 47, 1985, Heft 2, Seiten 176 bis 185
17. Peter Kurzmann: Die Plejaden in Gold auf einem keltischen Schwert, Archäologische Informationen 39, 2016, 239-246
18. Dirk Lorenzen: Astronomie in der Höhle, Deutschlandfunk, 11. September 2015
19. Sternenkarten in der Eiszeithöhle – Astronomie in den Höhlenmalereien von Lascaux?, scinexx, 1. Februar 2008
20. Angelika Merk-Schäfer: Der Diskos von Phaistos – ein Venus- und Mondkalender im Kontext der minoischen Altpalastzeit auf Kreta. Die mit Symbolen gestempelte Scheibe aus gebranntem Ton ist höchstwahrscheinlich ein Agrar- und Ritualkalender im Dienste der Mond- und Venus-Gottheiten im minoischen Kreta., drmerkschaefer.information.wordpress.com, Juni 2015
21. Irene Hager, Hans Katzgraber, Karl Aigner, Stefan Borovits, Ernst Bellant: Die Darstellung von (konkreten oder symbolischen?) Himmelsobjekten auf dem Plateau des Kalendersteins in Leodagger (Niederösterreich), in: Himmelswelten und Kosmovisionen, Imaginationen, Modelle, Weltanschauungen, Abstractbook 2019, Seite 5 und 6, Gesellschaft für Archäoastronomie, Wien
22. Ferdinand Freiherr von Andrian-Werburg: Die Siebenzahl im Geistesleben der Völker, in: Mittheilungen der Anthropologischen Gesellschaft in Wien, Band 31, Seiten 225 bis 274, 1901
23. ab Jacob Grimm: Kapitel XXII – Himmel und Gestirne, Abschnitt Gestirne / Plejaden, in: Deutsche Mythologie, zweite Ausgabe von 1844
24. ab Siehe auch: Handwörterbuch des deutschen Aberglaubens, Band 9, Sternbilder II, 3. Plejaden, Göschen’sche Verlagshandlung, 1941
27. Emilie Savage-Smith: A Descriptive Catalogue of Oriental Manuscripts at St John’s Faculty, Seite 132, St. John’s Faculty, College of Oxford, Oxford College Press, 2005, ISBN 9780199201952
28. Christian Schulz: Handbuch der Physik: für diejenigen welche Freunde der Natur sind, ohne jedoch Gelehrte zu seyn, Band 2, Kapitel 11, Seite 254, Hilscher, Leipzig, 1791
29. Genesis, Kapitel 8, Vers 6, bibleserver.com, Einheitsübersetzung (2016)
30. Exodus, Kapitel 24, Vers 18, bibleserver.com, Einheitsübersetzung (2016)
31. Evangelium nach Matthäus, Kapitel 4, bibleserver.com, Einheitsübersetzung (2016)
32. Evangelium nach Lukas, Kapitel 4, bibleserver.com, Einheitsübersetzung (2016)
33. Evangelium nach Markus, Kapitel 1, Vers 12 und 13, bibleserver.com, Einheitsübersetzung (2016)
34. Carl Strehlow: Mythen, Sagen und Märchen des Loritja-Stammes, Baer & Firm, 1907
35. Robert David Stevick: The Types of the Monasterevin-Kind Discs, The Journal of the Royal Society of Antiquaries of Eire, Band 136, Seiten 112 bis 140, 2006
36. Richard Anthony Proctor: Mild Science for Leisure Hours – Acquainted Essays on Scientific Topics, Pure Phenomena, third Collection, web page 9 and 10, Longmans, Inexperienced, and Co., London, 1886
37. Edmond Halley: Observations of the late complete eclipse of the solar on the 22d of April final previous, made earlier than the Royal Society at their home in Crane Court docket in Fleet-street, Philosophical Transactions, Quantity 29, Subject 343, Chapter III., pages 245 to 262, London, 1717
38. Carl Friedrich von Klöden: Der Sternenhimmel. Eine vollständige populäre Sternenkunde, mit besonderer Beziehung auf die grosse Sternwandkarte des Landes-Industrie-Comptoirs, Kapitel Anleitung zur Kenntnis der Sterne, Teil II In der Nacht vom 29. März, Abends 10 1/2 Uhr, Abschnitt b Aussicht nach Westen, Seite 93, Weimar, 1848
39. Stierschädel mit Sternenbezug – Himmelswissen der Steinzeit älter als gedacht, scinexx, 1. Februar 2008
40. See “Aldebaran” in: Johann Heinrich Zedlers Grosses vollständiges Common-Lexikon aller Wissenschaften und Künste, 1731-1754, Spalte 1095
41. Utilizing the formulation of: Oliver Montenbruck, Thomas Pfleger: Astronomie mit dem Private Laptop, Springer-Verlag Berlin Heidelberg GmbH, 1989, ISBN 978-3-662-05865-7
42. ab Thomas Rutherforth: “A System Of Pure Philosophy: Being A Course of Lectures In Mechanics, Optics, Hydrostatics, and Astronomy; That are Learn in St Johns Faculty Cambridge”, quantity 2, chapter XIV: “Of the devision of time”, paragraph 388: “The cycle of Metos”, 990 ff.
43. Wilfried Menghin: „Der Berliner Goldhut und die goldenen Kalendarien der alteuropäischen Bronzezeit“, Acta Praehistorica et Archaeologica, Band 32, 2000, ISSN 0341-1184, Seiten 31 bis 108
44. Michael Wright: The Pnyx, Athens, Greece, Portal to the Heritage of Astronomy, August 2011
45. Joachim Friedrich Quack: Zwischen Sonne und Mond – Zeitrechnung im Alten Ägypten, Seite 38, in: Harry Falk (Herausgeber), Vom Herrscher zur Dynastie. Zum Wesen kontinuierlicher Zeitrechnung in Antike und Gegenwart, Bremen 2002
46. Dirk Lorenzen: Aldebaran-Bedeckung am frühen Morgen – Sternbedeckung wie einst bei Copernicus, Deutschlandfunk, 5. November 2017
47. Der Mond im Juli 2009, astronomie.data, Juli 2009
48. Werner Papke: Zwei Plejaden-Schaltregeln aus dem 3. Jahrtausend, Archiv für Orientforschung, 31. Band, 1984, Seiten 67-70
49. Comment: al-Atiq (ζ Persei along with ο Persei) is the shoulder blade of al-Thurayya. See Emilie Savage-Smith: Islamicate Celestial Globes – Their Historical past, Development, and Use, Smithsonian Research in Historical past and Know-how, Nummer 46, Smithsonian Establishment Press, Washington, D.C., 1985
50. Arnold Barmettler: Partielle Halbschattenmondfinsternis am 30. November 2020, astronomie.data, Finsternisse, 30. November 2019