Astronomija

Kako najti koliko stopinj od začetka do konca sončnega zahoda?

Kako najti koliko stopinj od začetka do konca sončnega zahoda?


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Glede na to, kar sem povedal, je od začetka do konca sončnega zahoda 0,5 stopinje.

Žal nisem razumel dveh stvari:

1) Kako lahko na najpreprostejši način dokažem, da je 0,5 stopinje le od začetka do konca sončnega zahoda.

2) Zakaj se ne prilagodi mojim preteklim opazovanjem teh faz (ki so bile veliko daljše (v razponu od 5-7 minut), zaradi česar je med 1-2 stopinjami.


Sonce bi najlažje izmerili z uporabo kamere z luknjami.

Uporabite kos kartice z luknjo za zatič. Dvignite ga tako, da sonce posije skozi luknjo za zatič in na list papirja. (Ne glejte sonca skozi luknjo - poškodbe oči)

Na papirju boste videli krog svetlobe, to je podoba sonca. Če je papir oddaljen 100 cm od kartice in je velikost sončne slike $ x $ cm, potem lahko določite kotno velikost sonca. Gre za $ tan ^ {- 1} (x / 100) $ kar je približno $ frac {180x} {100 pi} $ Morali bi dobiti kot približno 0,5 stopinje.


Povprečni kotni polmer Sonca v radianih je

$$ frac {R_ odot} { mathrm {au}} = frac {6,96 krat 10 ^ 5 ~ mathrm {km}} {1,449 krat 10 ^ 8 ~ mathrm {km}} = 4,65 krat 10 ^ {- 3} $$

in njen srednji kotni premer je dvakrat večji, 0,00930 radiana ali 0,533 °. Ker se oddaljenost Zemlje od Sonca letno spreminja za ± 1,67%, se kotni premer Sonca giblje med 0,524 ° julija in 0,542 ° januarja.

Med sončnim zahodom se nadmorska višina Sonca glede na obzorje zmanjša za isti kot. Če je opazovalec na ekvatorju, gre Sonce naravnost navzdol v dobrih 2 minutah, kot bi pričakovali. V nasprotnem primeru se Sonce spusti pod poševnim kotom $ q $, podaljšuje sončni zahod za faktor $ 1 / sin q $. Na primer, če $ q $ je 30 °, sončni zahod traja dvakrat dlje, kot če bi bil $ q $ znašala 90 °. Če je širina opazovalca $ varphi $ in odklon Sonca je $ delta $, potem

$$ q = cos ^ {- 1} frac { sin varphi} { cos delta} $$

Če $ delta približno 0 ^ circ $, potem $ q približno 90 ^ circ - varphi $.

Kar se spreminja s skoraj konstantno hitrostjo 15 ° / uro, je Sončev urni kot glede na poldnevnik, izmerjen okoli nebesnega ekvatorja. Ena stopinja urnega kota pri deklinaciji $ delta $ obsega samo $ cos delta $ stopinje neba, zato se zdi, da Sonce junija in decembra zahaja za približno 8% počasneje kot marca in septembra.


Kako najti koliko stopinj od začetka do konca sončnega zahoda? - astronomija

Večina urnikov molitev, ki so na voljo na spletu, nima nekaterih pomembnih preudarnih vprašanj in povzroča napačen čas. Moonsighting.com je prevzel pobudo za izobraževanje množic o potrebnih popravkih in za vsako molitev navede "Pravilni urnik molitve", kot je razloženo spodaj:

Fajr: Subh Sadiq (Fajr-al-Mustatir), ko se jutranja svetloba na nebu začne širiti vodoravno. Na visokih zemljepisnih širinah, kjer postane težava prezgodaj moliti Fajrja (Tabayyan), ko se uporablja jutranja svetloba na nebu.
Sončni vzhod: Ko se vrh sončnega diska le prikaže nad obzorjem.
Zuhr: Ko začne sonce padati po doseganju najvišje točke (Zenith) na nebu. 5 minut po Zenithu.
Asr: Ko dolžina sence katerega koli predmeta doseže faktor dolžine predmeta plus dolžina sence tega predmeta opoldne. Faktor je 4/7 za Shi'aa 1 za Shafi'i, Maaliki, Hanbali in 2 za Hanafi.
Sončni zahod: Teoretični čas sončnega zahoda, kot je naveden v časopisih, ko vrh sončnega diska kar izgine pod obzorjem.
Maghrib: Dejanski sončni zahod glede na tri stvari (sprememba loma, območje okoli dejanske upoštevane zemljepisne širine in dolžine ter morebitna nagnjena tla proti smeri sončnega zahoda). Za Sunite je 3 minute po teoretičnem sončnem zahodu za Shi'aas 17 minut po teoretičnem sončnem zahodu.
Isha: Izginotje rdečice Shafaq za Shafi'i, Maaliki in Hanbali in Shi'aa belino za Hanafi. Na visokih zemljepisnih širinah se uporablja kombinacija rdečih in belih meril shafaq.

Fajr & Isha izračunajo drugi z uporabo različnih meril po vsem svetu. Nekateri uporabljajo 15, 18 ali celo 20. Drugi uporabljajo kriterije 75 minut ali 90 minut (kot v Savdski in Indo-Pak). Ta merila ne izračunajo Fajr & Isha na visokih zemljepisnih širinah.

Nad 48,5 ° (npr. Vancouver v Kanadi) sonce ne gre 18 ° pod obzorje najdaljšega dne v letu.

Nad 51,5 ° (npr. Cambridge, Združeno kraljestvo) sonce ne gre 15 ° pod obzorje najdaljšega dne v letu. V drugih dneh bo Isha, izračunana na 15, dala Iši čas 2,5 ure po Maghribu. To postane stiska.

Nad 54,5 ° (npr. V Københavnu na Danskem) sonce najdlje v letu ne gre 12 ° pod obzorje. V drugih dneh bo Isha, izračunana na 12, dala Iši čas 3 ure po Maghribu. To je še večja stiska, zato je nepraktično.

Moonsighting.com je zbral opazovanja za Subha Sadika in izginotje Shafaka iz mnogih krajev po svetu [npr. Rijad (Saudova Arabija), Karači in Tando Adam (Pakistan), Durban (Južna Afrika), Auckland (Nova Zelandija), Sydney NSW ( Avstralija), Miami FL (ZDA), Washington DC (ZDA), Toronto (Kanada), High Wycombe (Velika Britanija), Dewsbury (Velika Britanija) in Blackburn (Velika Britanija)]. Ta opažanja kažejo, da za Fajr in Isha ni mogoče uporabiti fiksnih stopinj. Deset let trajajoča raziskava Moonsighting.com je pokazala, da sta Subh-Sadiq in Shafaq funkcija zemljepisne širine in letnih časov (dnevna številka sončnega leta). Vsa zbrana opazovanja z različnih zemljepisnih širin so bila narisana glede na številko dneva v letu. S tehniko prilagajanja krivulj je moonsighting.com za Fajr & Isha pripravil funkcijo zemljepisne širine in letnih časov. Zato uporabljamo te funkcije. Za Fajrja se uporablja Subh Sadiq, ki velja za (Fajr-al-Mustatir iz Ahadith), ko se jutranja svetloba na nebu širi vodoravno. Za Isho so imeli imam Shafi'i, imam Maalik, imam Ahmad bin Hanbal in dva ugledna učenca imama Abu-Hanife (imam Abu-Yusuf in imam Muhammad) raje Shafaq Ahmerja. Samo imam Abu-Hanifa je imel raje Shafaq Abyad.

Moonsighting.com uporablja Shafaq Ahmer poleti, ko so noči kratke, in Shafaq Abyad pozimi, ko so dnevi kratki. Vendar je general Shafaq izbran, da bi se izognil težavam na višjih zemljepisnih širinah, ko postane Shafaq Abyad poleti prepozno. Shafaq General poleti uporablja Shafaq Abyad, pozimi pa Shafaq Ahmer. Prehod iz Abyada v Ahmer se uporablja spomladi, Ahmer pa v Abyad jeseni. Te formule so dobre do 55 ° zemljepisne širine.

Vsako mesto, kjer trajanje posta presega 18 ur ali je krajše od 6 ur, se mora sklicevati na ure, ki veljajo za najbližjo "uravnoteženo" lokacijo, da se določi trenutek prekinitve posta. Vsekakor ni logično, niti smiselno niti razumno "skočiti" z 18 ur na 14 ur in 54 minut - najdaljši dan v Meki.

Primer takšne lokacije je Hammerfest na Norveškem, mesto s 7000 prebivalci, ki trdi, da je najsevernejše mesto na svetu. Muslimansko prebivalstvo Norveške je približno 300.000, Hammerfesta pa okrog 250. Hammerfest leži na 70.65 S in 23.68 E. V tem kraju sonce ne zaide ali ne vzhaja v višini poletja in sredi zime. Sprejeto pravilo "Aqrabul-Bilad", ki uporablja najbližjo zemljepisno širino, kjer so znaki in časi salah zlahka razločljivi, še vedno daje čas posta več kot 23 ur poleti in manj kot 3 ure pozimi. Zato je treba uporabiti sodno prakso, ki jo je ustanovil Dar al-Ifta, kot je razloženo zgoraj.

Zdaj vzemite Oslo (zemljepisna širina = približno 60 °) in z uporabo pravila Sab'u Lail izračunamo najdaljši dan 19 ur 38 minut in najkrajši dan 7 ur in 43 minut. Seveda presegamo 18-urno omejitev, ki jo določa Fatwa, toda ker se zdi, da prebivalci Osla brez težav priznajo te časovne razporede, bomo 60 ° ohranili kot zemljepisno širino, ki temelji na konceptu "Aqrabul-Bilad".

Moonsighting.com je od svojih uporabnikov prejel številna e-poštna sporočila glede ugovorov glede formul glede na zemljepisno širino in letni čas.

Tukaj je e-sporočilo Abdelkaderja Tayebija iz Windsorja v Kanadi, ki potrjuje čas opazovanja Shafaq Ahmer, ki se ujema z izračuni Moonsighting.com:

V torek, 19. maja 2009, sem bil Abdelkader poslovno v St Joseph, MI. Opazil sem, da je bil Maghrib ob 9:05 in Isha s popolnim izginotjem shafaq ahmar okoli 10:15. Postopek izginotja ni natančen do minute in traja čas, da se v celoti izpelje, morda je odvisen od interpretacije opazovalca, skorajda izginotje se je začelo okoli 10:04 (rdeči odtenki na vrhu teme), nato okoli 10: 11 tam so bili le sledovi temno rdeče in do 10:15 je bila bolj izrazita, edina leva pa je bila bela šafaka, enako so opazili tudi včeraj. Torej so vaši izračuni, ki uporabljajo funkcijo zemljepisne širine in letnih časov, zelo natančni. Nadaljeval bom z opazovanjem, kadar koli imam priložnost v inshAllah.

Tu je še eno e-sporočilo Rafika Ouareda. Pred kratkim sem 23. junija 2016 v Pampignyju v Švici prizorišče imsaka po Surah el baqara, ayat 187. Imsak je bil ob 3:56 zjutraj.

Ugotovil sem, da vaša sposobnost kaže na imsak čas 3:51. Opazil sem, da turška metoda uporablja sončno depresijo pri 12-13 stopinjah, kar daje približno 4:06 AM. Vse druge metode depresije (od 15 do 19 stopinj) so bile pred časom za 20 do 55 minut. Metoda Moonsighting.com je najbližje mojemu opazovanju, posnetemu s kamero.

Zuhr v večini urnikov molitev je prikazan opoldne (pred Zawaalom). Opoldanski čas, ko je sonce na najvišji točki, je Mamnoo '(prepovedano) čas za katero koli molitev. Teoretično sonce ne preide v fazo Zawaal, dokler njegovi robovi niso izven zenitne črte (črta med opazovalcem in središčem sonca, ko je v opoldanski fazi). Sončni disk izstopi iz zenita približno 1,5 minute. Za upoštevanje polmera 30 milj, omenjenega za čas Maghriba, je treba dodati še 1 minuto. Tako je treba za začetek Zuhra šteti najmanj 2,5 minute kot minimalno omejitev po opoldanskem času. Glede na to, da te natančne teoretične opredelitve ne poda noben učenjak, se za začetek Zuhra kot minimalni dejavnik (dodatnih 2,5 minute) šteje kot minimum. Tako je treba opoldne za Zuhra dodati še 5 minut.

Asr časovni izračuni zahtevajo različne interpretacije različnih pravnikov, kot so Hanafi, Šafiji, Maaliki, Hambali ali Ja'friyah (Shi'aa). Za Shafi'i, Maaliki in Hambali se izračuna Asr, ko senca katerega koli predmeta postane enaka njegovi dolžini. Za Hanafija se Asr izračuna, ko senca katerega koli predmeta postane dvakrat večja od njegove dolžine. Za Ja'friyah se Asr izračuna, ko senca katerega koli predmeta postane enaka 4/7 njegove dolžine (kot mi je dal privrženec Ayatullah Sistani).

Maghrib je treba izračunati vsaj 3 minute po teoretičnem sončnem zahodu (ponovno objavljeno v časopisih) zaradi naslednjih razlogov:
1. Učinki dejanske vlažnosti, temperature in tlaka v ozračju lahko povzročijo drugačen lom sončne svetlobe, kot smo predvidevali pri izračunih teoretičnega sončnega zahoda.
2. Na nekaterih območjih bi se lahko proti zahodnemu obzorju spuščala tla navzdol, ki bi opazovalcu povzročala zakasnjen sončni zahod v primerjavi s popolnoma ravnimi tlemi, kot se domneva v izračunih teoretičnega sončnega zahoda.
3. Za večja metropolitanska mesta se bo sončni zahod v radiju 30 milj od točke, predvidene v izračunu, razlikoval. Ker ljudje morda živijo po vsem mestu, lahko to na nekaterih območjih odloži sončni zahod. To so premisleki za štiri glavne sunitske šole misli. Za miselno šolo Ja'friyah se 17 minut po sončnem zahodu šteje za čas Maghriba, kar velja za dovolj, da izgine bronasti sij na obzorju.

Smer Qibla : Vsak dan pride čas, ko je senca katerega koli navpičnega predmeta od sonca v smeri Qibla. Če se to ne zgodi, je čas, ko se obrnete proti soncu, usmerite Qiblo. Vsak ta čas je na voljo za vsak dan v stolpcu Qibla po Iši. Ta metoda za Qiblo je natančnejša od kompasa, ki vključuje napake zaradi prisotnosti magnetnih polj ali kovinskih predmetov in magnetno deklinacijo, zaradi katere igla kompasa prihaja do magnetnega severa, ki bi lahko bil do 100 ° oddaljen od True North za koliko stopinj off odvisno od lokacije.


Velike razlike na severu in jugu

Za vsako stopinjo, ko grete severno od 40 stopinj severne širine, se dolžina mraka okoli junijskega solsticija poveča v povprečju za skoraj 12 minut. Na 48,7 stopinje severne širine mrak traja 3 ure in 44 minut, severno od tam pa se mrak zadržuje skozi celo noč. Iz Londona (51,5 stopinje severne zemljepisne širine) mrak traja celo noč med 23. majem in 18. julijem. Iz Edmontona v Alberti (53,6 stopinje severne zemljepisne širine) traja od 13. maja do 28. julija.

V Fairbanksu na Aljaski (64,8 stopinje severne zemljepisne širine) trajajoči mraki trajajo od 8. aprila do 2. septembra. Pravzaprav od 20. maja do 23. julija nebo ostane tako svetlo, da je malo svetlih zvezd ali planetov, če sploh . Le malo severneje leži arktični krog, južni del "polnočnega sonca". Severno od polarnega kroga sonce vsaj enkrat na leto ostane neprekinjeno 24 ur neprekinjeno.


Civil Twilight & amp Izračunavanje dneva

Kaj je civilni mrak? Ali gre za arhaičen izraz, ki se običajno uporablja v bolj odmevnem kraju in času, ki se je nanašal na čas dneva, ko so moški nagnili klobuke, ženske ukrivile, otroci spoštovali starejše in so bili vsi bolj vljudni? Civil Twlight je pravzaprav bolj znanstveni kot sociološki.

navtični mrak ("Obdobje pred sončnim vzhodom ali po sončnem zahodu, v katerem sonce ni več kot 12 stopinj pod obzorjem") in astronomski mrak (najtemnejši od treh mrakov, s soncem med 12 in 18 stopinjami pod obzorjem). Vsak od teh mrakov lahko uporabimo za opis stanja zjutraj ali zvečer, tako da imamo ves dan šest različnih mrakov.

Če ne verjamete, da gre za nepomembno nepomembnost, upoštevajte, da je poročilo sredi 19. stoletja v publikaciji ameriškega senata med drugim obravnavalo, kaj mrak v resnici je. Zakaj? Po mnenju francoskega fizika Augusteja Bravaisa je "dolžina mraka element, ki ga je treba poznati: s podaljšanjem dneva omogoča nadaljevanje poroda." Zdi se, da razlog za vso to vročinsko zaskrbljenost, kdaj se točno začne mrak začeti in končati, ni bil v tem, da bi pesniki imeli na razpolago natančnejše izraze, mračnike je bolj skrbelo za stvari, kot je "nadaljevanje dela". Treba je opozoriti, da je Bravais tudi ugotovil, da se "filozofi žal ne strinjajo glede njegovega trajanja."

To opažanje je bilo opravljeno sredi 19. stoletja in do začetka 20. stoletja ljudje še vedno niso natančno ugotovili, kdaj civilni mrak končala. Članek v številki iz leta 1916 Mesečni pregled vremena je opozoril, da je "podanih pet ločenih opredelitev konca civilnega mraka." Odvisno od tega, kateri vir iz 19. stoletja je bil eden od avtoritet, civilni mrak bi se lahko končalo, ko je bilo sonce 6, 7, 7 1/2 ali 8 stopinj pod obzorjem.

Državljanski mrak, edini, ki zanima prebivalce mesta in države, se konča v trenutku, ko se sonce spusti šest stopinj pod obzorjem, in takrat se začnejo pojavljati planeti in zvezde prve velikosti.
Times-Picayune (New Orleans, LA), 27. januarja 1895

Praktični ali civilni mrak je čas, ki preteče med trenutkom sončnega zahoda in trenutkom, ko je sedem stopinj velikega kroga pod obzorjem.
Večerna pošta (Charleston, SC), 31. mar. 1899

Kot je bilo že omenjeno, je meja lomne svetlobe, kadar je sonce v 34 'pod obzorjem civilnega mraka, ko je 7 ½ °, in običajnega ali astronomskega mraka, ko je 17 °.
Razni dokumenti senata ZDA, 1857

Lahko se domneva, da se civilni mrak konča, ko je sonce približno 8 ° pod obzorjem, in da se astronomski mrak konča, ko je sonce približno 18 ° pod obzorjem.
—Camille Flammarion (prevedel James Glaisher), Ozračje, 1873

Niso vsi čutili potrebe, da bi natančno določili stopnjo na začetku ali koncu leta civilni mrak. Shirley Palmer leta 1845 Slovar Pentaglota, je opisal kot začetek "po vulgarnem izračunu, v trenutku, ko posameznik ne more več opravljati svojega poklica v hiši brez pomoči umetne svetlobe," in konec ", ko so manjše zvezde zaznavne s prostim očesom. "

Če ste takšna oseba, ki se vam ne zdi treba natančno vedeti, koliko stopinj pod obzorjem je nekaj, ali če se morda ne počutite posebej civilizirano, boste morda želeli imeti besedo, ki se nanaša na posvetlitev sonca na bolj splošen način. Za to imamo antitlight: "Roza ali vijoličast žarek na vzhodnem nebu po sončnem zahodu."

Zelo pogosto lahko opazimo po zahajanju sonca, ko stoji na vzpetini, rdeč lok, definiran na vzhodnem nebu okoli temno modrega prostora. V ugodnih okoliščinah ločitveno črto zaznamuje rumenkast rob. To je pojav, ki je bil oblikovan proti mraku.
—Zurcher in Margolle (prevod William Lackland), Meteorji, 1869

Ne glede na to, kako se imenuje, zamegljeni časi med nočjo in dnevom so odlični časi, da izvlečete druge, bolj poetične izraze, ki opisujejo tisto, kar vidite in čutite ob sončni svetlobi.


Ephemeris.com

Ephemeris zajema gibanje nebesnih teles (planetov, lun itd.) In napove njihov položaj v določenem trenutku. Za kratek pogovor o zgodovini ephemeris teorij glejte razdelek Sodobne teorije na strani Zgodovina na tej strani.

Časovni ukrepi

Drugič
Temeljna enota časa je SI sekunda (glej naslednje poglavje). Običajno mislimo na drugo, kot jo definira dolžina dneva, in sicer 24 ur na dan, 60 minut na uro in 60 sekund na minuto. Vendar zdaj vemo, da se dolžina dneva postopoma krajša. Ker astronomi potrebujejo natančno opredelitev sekunde, ki se nikoli ne spremeni, zdaj uporabljajo atomski čas (glej SI Second spodaj). Še vedno lahko uporabimo običajno definicijo za opazovanje neba, kjer je na dan 86.400 sekund.

SI Drugi
Zemeljsko vrtenje ni konstantno. Nanjo vpliva gravitacijski vlek Lune, Sonca in planetov. To sčasoma počasi pospeši in upočasni vrtenje Zemlje. V začetku 19. stoletja so znanstveniki ugotovili, da ima atom cezija zelo stabilno resonanco. Zgradili so atomske ure, ki so zaznavale prehode v teh atomih. Druga sekunda SI (opredeljena leta 1967) je trajanje 9.192.631.770 obdobij sevanja, ki ustreza prehodu med dvema hiperfinima nivojema osnovnega stanja cezija 133. Dan SI je 86.400 SE sekund, julijansko leto pa 365,25 SI dni. . (Glej Julijski dan spodaj.)

Sončni dan
Sončev dan je čas, ki je potreben, da se Sonce vrne v isti položaj na nebu. To je 24 ur.

Zvezdni dan Če bi se Zemlja v enem letu vrtela natanko enkrat na svoji osi, bi bila ista stran Zemlje vedno obrnjena proti Soncu. Ista stran Zemlje bi bila vedno pri dnevni svetlobi, druga stran pa v temi. Zaradi tega se Zemlja vrti še enkrat, kot se zdi, da se vrti med letom: 366,24-krat (ne 365,24-krat). Zvezdniški dan je čas, ki je potreben, da se zvezde spet pojavijo v istem položaju, zato je to prikladno merilo časa pri izračunu zvezdnih položajev. Zvezdni dan je (365,24 / 366,24) kratnik dolžine sončnega dneva 24 ur. To je približno 0,99727 dni, kar je približno 23 ur in 56 minut. Številne opazovalnice bodo imele uro, ki prikazuje lokalni siderični čas. Če želite izvedeti, zakaj, glejte spodnji razdelek o Kotu ure.

Julijski dan
Astronomi opazujejo stoletja. Potrebujejo enostavno metodo iskanja časa med dvema datumoma, ne glede na prestopne dni v letu, spremembe v načinu izračuna koledarja itd. Leta 1583 je Joseph Justus Scaliger predlagal štetje let v neprekinjenem napredovanju od leta 4713 pr. naprej. S tem smo se izognili skoku iz 1. pr. do 1. stoletja po Kristusu je astronom Herschel ta sistem prilagodil štetju dni. Julijanski dan 0 je določil kot začetek opoldne v ponedeljek, 1. januarja 4713 pr. (Astronomi opazujejo ponoči, zato jim je bilo prav, da začnejo astronomske dneve opoldne.)

V Herschelovem času je bila dolžina tropskega dne stalnica mere. Danes je standardna enota časa SI sekunda. Julijski dan je 86.400 SI sekund.

Besselian Year
Ta ukrep je bil uporabljen pred 100 leti in se je skliceval na "besselijsko" tropsko leto. Beselijske epohe so zapisane z zvezdami z 'B', na primer B1950.0. To se je začelo 1. januarja 1950, to je julijanski datum 2433282.423. Številni starejši efemeridi in zvezdni katalogi so bili omenjeni na B1950, zlasti Zvezdni katalog astronomskega observatorija Smithsonian.

Julijsko stoletje
Julijsko stoletje ima vedno natanko 36525 julijskih dni. Je stalna mera časa, vendar ne odraža sončnega koledarja.

Julian Epoch
Prva zabeležena julijanska epoha je bila J1900.0, to je Julijski dan 2415020.0. To je ustrezalo 0,5. Januarja 1900 (polnoč med 31. decembrom 1899 in 1. Januarjem 1900). Leto 1900 po gregorijanskem koledarju ni bilo prestopno, zato je naslednje julijansko stoletje, J2000.0, Julijski dan 2451545.0 (2415020 + 36525). To je zapisano tudi kot 1. januar 2000 (torej opoldne 1. januarja 2000).

Spremenjen Julijski dan
Namesto da bi pisali cel julijanski dan, lahko zadnje dni pišemo takole. Kot primer vzemimo Julian Epoch J2000.0, ki je JD 2451545.0. Za zadnje dni na začetku izpustimo "24". Ker dneve začnemo ob polnoči po dogovoru, na koncu tudi izpustimo ".0". Epoho J2000.0 lahko zaradi udobja zapišemo kot spremenjeni julijanski dan 51545.

Meritve prostora

Efemeridi pogosto dajejo položaje v Desnem vzponu in deklinaciji. Za zvezde te vrednosti ostajajo dokaj konstantne. Pri planetih se hitro spremenijo. Opazovalec na zemljepisni širini in dolžini na zemeljskem površju lahko s kompasom poišče Azimut nebesnega predmeta in s sekstantom ali podobnim instrumentom, da najde njegovo nadmorsko višino.

Zemljepisna širina in dolžina
Latitude je število stopinj nad ali pod ekvatorjem. Na severni polobli se zemljepisna širina giblje od 0 do 90 stopinj severno. Na južni polobli se zemljepisna širina giblje od 0 do 90 stopinj južno. Ekvator ima zemljepisno širino natanko 0 stopinj. Severni pol ima zemljepisno širino 90 stopinj severno. Južni pol ima zemljepisno širino 90 stopinj južno.

Zemljepisna dolžina je število stopinj vzhodno ali zahodno od prvega poldnevnika (0 stopinj zemljepisne dolžine) v Greenwichu v Angliji. Zahodno od Greenwicha se giblje od 0 do 180 stopinj zahodno. Vzhodno od Greenwicha se giblje od 0 do 180 stopinj vzhodno. Mednarodna datumska črta je na 180 stopinj zemljepisne dolžine (vzhodno ali zahodno).

Desni vzpon in deklinacija
Desni vzpon in deklinacija sta položaj nebesnega predmeta, kot ga lahko vidimo iz središča Zemlje. Ti položaji so pogosti v almanahih, kot je Ameriški pomorski observatorij Astronomski almanah. Od te točke v središču Zemlje lahko izračunamo položaje za katero koli mesto na površini Zemlje. Desni vzpon se meri v urah, pri čemer 24 ur predstavlja 360 stopinj. Desni vzpon se meri proti vzhodu od prve točke ovna (0 stopinj ovna, pomladansko enakonočje). Deklinacija je nadmorska višina nad ali pod ekvatorjem (gledano iz središča Zemlje). Deklinacija se giblje od 90 stopinj severno do 90 stopinj juga.

Azimut in višina
Azimut in nadmorska višina sta položaj nebesnega predmeta, ki ga opazovalec vidi na določenem mestu na površini Zemlje. Običajno izračunamo Azimut in Nadmorsko višino za svojo določeno lokacijo iz Desnega vzpona in deklinacije nebesnega predmeta (glej spodaj). Azimut nebesnega predmeta je stopinja kompasa nad ali pod njim. Azimut se začne pri 0 stopinjah za sever in nadaljuje v smeri urinega kazalca do 360 stopinj za sever, enako kot stopinje na kompasu. Azimut vam pove, v katero smer se morate obrniti, in Nadmorska višina vam pove, koliko stopinj (-90 do +90) je treba pogledati navzdol ali navzgor od obzorja. Opomba: Včasih formule začnejo Azimuth na jugu. Spodnje formule začenjajo Azimut na severu in štejejo stopinje v smeri urinega kazalca, tako kot kompas.

Urni kot
Zgoraj smo videli, da zvezdniški dan traja le približno 23 ur 56 minut. Lokalni urni kot pomladanskega enakonočja je enak lokalnemu zvezdičnemu času. Medtem ko se desno vzpenjanje meri proti vzhodu, se kot stranske ure meri proti zahodu. Kot ure nebesnega predmeta je enak lokalnemu sidričnemu času minus desni vzpon objekta.

Drugi učinki

Poševnost ekliptike
Zemlja je nekoliko nagnjena v primerjavi z ravnino, v kateri kroži okoli Sonca. Ta nagib se imenuje Nagnjenost ekliptike in je za epoho J2000.0 določen kot 23,4392911 stopinj (približno 23,5 stopinj).

Precesija enakonočja
Zemlja se v enem dnevu vrti okoli svoje osi. Vendar ta os ni pritrjena na enem mestu. Os se vrti in se v približno 26.000 letih popolnoma obrne. Čeprav se to morda zdi dolgo, je (360 krat 60 krat 60) ločnih sekund / 26.000 let = približno 50 ločnih sekund na leto. Ker se Zemljina os vrti, se naša zvezda Pole (zvezda, najbližja severu na severni polobli) sčasoma spreminja. Trenutno je naša Pole Star Polaris. Sčasoma se bo to spremenilo. Trenutno je Zemlja najbližje Soncu (v periheliju) januarja in najbolj (v periheliju) julija. Čez 13.000 let bo Zemlja najbližje Soncu januarja, najbolj pa julija. Številne starodavne civilizacije so iz natančnega opazovanja zvezd vedele za precesijo enakonočja.

Nutacija
Tudi Zemlja se nekoliko ziba okoli svoje osi. To povzroča Luna in Sonce, ki vlečeta Zemljino "ekvatorialno izboklino" (Zemlja se rahlo izboči, nekako kot žoga na plaži, ki ima pritisk nad in pod njo). To je periodično nihanje in je znano kot nutacija. Učinki nutacije so majhni (odkrit je bil šele v 17. stoletju), vendar opazen.

Uporaba ephemeris (almanah) za iskanje nebesnega predmeta

Splošno opazovanje
Te formule so formule z nizko natančnostjo za iskanje Azimuta in Nadmorske višine predmeta glede na njegovo desno vzpenjanje in deklinacijo ter zemljepisno širino opazovalca. Ne upoštevajo učinkov precesije in nutacije. So pa dovolj natančni za splošna opazovanja.


Kako najti, koliko stopinj od začetka do konca sončnega zahoda? - astronomija

1.1 Vprašanje: Kako naj poznam čas začetka in konca vsake molitve. Urniki, ki jih dobim, dajejo začetek časa molitve, ne pa tudi konca, po katerem je Salat QAZA. Prav tako želim vedeti čas Zawaala.

1.2 Vprašanje: Na polarnih območjih je dan in noč dolg nekaj mesecev, kako se torej muslimani postijo in molijo v teh regijah?

Odgovor: Časov za Zuhr in Asr je mogoče opazovati na vseh krajih na zemlji in jih je mogoče enostavno izračunati. Za kraje na višjih zemljepisnih širinah v nekaterih mesecih sonce ne zaide ali ne vzhaja. Za izračun Maghriba, Ishe in Fajrja za višje zemljepisne širine, kjer sonce ne zaide ali ne vzhaja, moonsighting.com uporablja fikhski koncept "Aqrabul-Bilaad". Za uporabo tega koncepta se uporablja iterativni postopek izračuna tako, da se zemljepisna širina zmanjša za 0,1 stopinje, pri čemer se zemljepisna dolžina ohrani enaka, in se preračuna čas sončnega zahoda in ta postopek ponavlja, dokler se ne doseže zemljepisna širina, kjer sonce zaide in se uporabi ta zemljepisna širina in enaka dolžina.

1.3 Vprašanje: Če stojite na Luni, vidite Zemljo samo z ene strani Lune. Bi videli, kako sonce vzhaja in zahaja?

1.4 Vprašanje: Kaj je zodiakalna svetloba in kdaj jo je mogoče videti?

2. Fajr & Isha

2.1 Vprašanje: Kaj pa metoda Savdske Arabije za Išo, ki je po mojem vedenju 1–2 / 2 uri po Maghribu vse leto? Ali ni to neupoštevanje spremembe sončnega odklona?

Odgovor: Za zemljepisne širine blizu ekvatorja, kot so Savdska Arabija, Indija, Pakistan, je 1–2 / 2 uri dober približek in tudi praktičen, spreminjanje časa mraka (zaradi kota depresije sonca) pa je v različnih letnih časih majhno. Čas Isha se v nekaterih dneh začne prej kot po 1,5 ure, vendar ni nič narobe, če začnemo moliti po 1,5 ure. Ta 1,5-urna praksa je torej dogovorjena in je seveda v skladu s šeriatskimi smernicami.

2.2 Vprašanje: Kakšno je vaše mnenje o 15 ° v primerjavi z 18 ° za Subh-Sadiq?

Odgovor: Pravi odgovor je, da ni mogoče določiti stopinj za vse zemljepisne širine. Pojav sub-Sadika se bo po stopnjah razlikoval na različnih zemljepisnih širinah in v različnih letnih časih (dan v letu), ker sonce potuje (očitno) vzdolž določene zemljepisne širine na določen datum. Sonce (očitno) potuje med tropom raka in tropom Kozoroga v različnih letnih časih. Ljudje na različnih lokacijah po svetu so opazovali Subh-Sadiq in rezultati so med 9 ° in 18 ° od visokih zemljepisnih širin do ekvatorja. Tukaj je e-poštno sporočilo, ki mi ga je poslal brat Ghulam Dandia ([email & # 160protected]) iz Miamija.

"3. decembra 2000 smo se pet odpravili na območje Miami Beach na Sončnih otokih, da bi opazovali začetek Subh Sadika. Čas, ki ga je moonsighting.com predvidel za 15 °, je bil 100% natančen. Pojav so opazili ob 5:45 Vzhodni standardni čas. Priče so bili jaz (Salam Dandia), Raffia Dandia, Abdul Razz Khanani, Kaiser Perverse in mufti Rafique Ahem (imam bait-ul-mukkram masjid Dhaka, Bangladeš) Jazak Allah. "

Leta 1987 je skupina Uleme v Blackburnu v Angliji, vključno z Molano Yaqub Miftahi iz Velike Britanije, želela rešiti ta problem za ummo v Veliki Britaniji in žrtvovala svoj dragoceni čas, ko si je prizadevala določiti pravilne čase za Subh-e-Sadiq. Izvedli so Mushahado (od septembra 1987 do avgusta 1988) in se odločili, da ne bodo upoštevali časov, ki jih je določil Observatorij, zato so začeli s čistega lista in niso bili psihološko omajani že v času Observatorija. Njihova opažanja torej v nasprotju z opažanji drugih niso poskušala potrditi ali zavrniti nobenega časa iz Observatorija, ampak so zagotovila čas molitve zgolj na podlagi opaženega. Opažanja kažejo, da stopinje za čas Fajrja skozi leto nihajo.

Iz Velike Britanije Maulana Y. Ismail Qasmi (v svoji knjigi Bartaniya me Subh-e-Sadiq ka Sahih Waqt: Dewsbury UK, 1983. Suppl. 1984) omenja več opažanj Ulame v Angliji in navaja, da mora biti molitev Fajrja pri 12 ° ali celo do 16 °.

Limited Observations made in Chicago in 1985 for Subh-Sadiq by Rajaullah Qureshi, Azmatullah Qadri, Mohammad Abdul Hai, Maulana Abdurrahman Sayeed Siddiqi, Maulana Irfan Ahmed Khan and a few others confirms 13 to 15°.

Other individual limited observations made in Buffalo, Toronto, Montreal, San Francisco, Tempe (AZ), Houston (TX), Washington DC show Subh-Sadiq at 12° to 14°.

Limited Observations for Subh-Sadiq in Tando Adam (Pakistan) show 15°.

Some observations made in New Zealand and Australia point Subh-Sadiq between 12° and 15°.

Observations made in Riyadh (Saudi Arabia) in 2004 by a group with Sheikh Abdul-Aziz Fauzan for the whole year shows Subh-Sadiq was observed at 15°.

2.3 Question: Some Ramadan timetables in my area have the sehri end time based at 15° and others at 18°. Which one is the correct one?

2.4 Question: I was very surprised to see a wide difference in timing for Fajr & Isha calculated by assumptions of various organizations. Ali lahko razložite?

2.5 Question: Our local masjid in Chicago publishes Isha timetable at 12°. To date I have not seen a fatwa which establishes 12° as acceptable (most of my reading supported 15 or 18°). In your scientific judgement is 12° for Isha acceptable?

2.6 Question: Is it true that disappearance of Shafaq for Isha, and Subh-Sadiq for fajr cannot be related with any degrees (neither with 18° nor with 15°)?

Answer: Yes, observations made by many ulamaa' and other groups confirm that these phenomena occur at different degrees for different latitudes. Sometimes disappearance of Shafaq for Isha, and Subh-Sadiq for Fajr do not even occur at higher latitudes. This is becuase at higher latitudes the sun does not go much below horizon on some days and its light remains on the horizon for a long time and the phenomenon in Ahadith cannot be observed. So, 15° or 18° is not a solution for all latitudes.

Moonsighting.com have been studying this problem for over 25 years, and with the benefit of Shari'ah knowledge as well as the capability of computer programming to calculate prayer times, a practical solution was found, that other computer programmers have not used because they either did not have Shari'ah knowledge or did not spend enough time to look into this problem.

2.7 Question: Islamicfinder.org gives an option for ISNA prayer Schedule. If that is ISNA's official position, then why moonsighting.com gives a different prayer shcedule compared to Islamicfinder.org's ISNA option?

2.8 Question: Are prayer times given by Islamicfinder.org correct and reliable?

2.9 Question: How long does it take to diasappear Shafaq Ahmer (red), and how long for Shafaq Abyadh (white)?

2.10 Question: What is the relationship of disappearance of Shafaq Ahmer (red), and disappearance of Shafaq Abyadh (white) with degrees?

Answer: There is no fixed relashionship in terms of degrees. Observations from different parts of the world prove that. Moonsighting.com has collected observations done by scholars and other volunteers in many places in the world [Riyadh (S. Arabia), Tando Adam (Pakistan), Cape Town (S. Africa), New Zealand, Buffalo (New York), Toronto (Canada), Sydney, Australia, Phoenix, Arizona, and Trinidad] for few days in a year. More observations were done in Blackburn, Lancashire, England (from September 1987 to August 1988) by a group of Ulamaa'. Although these observations were not for 365 days of the year, but covered almost entire year with a few months missing.

3. Zuhr

3.1 Question: Does Zuhr time begin at noon?

3.2 Question: The terms 'zawwal time' and 'noon time' have been used interchangeably in your web site regarding the prayer timings. I think the term 'noon' generally refers to 12:00pm while the zawwal time keeps on shifting all year round. Could you please tell me what time have you used in your calculations?

3.3 Question: I am a bit confused with the timings of Zuhr time span. Shafi'i Asr time is one hour before us (Hanafi). Due to this can I also say the Zuhr prayer after Shafi'i Asr time starts?

3.4 Question: I heard that one can find true north from the position of shadow at zawal. Is this correct?

4. Asr

4.1 Question: It seems impractical to find the time for Asr based on object's length plus shadow at Zawaal time for Shafi'i, or twice the object's length plus shadow at Zawaal time for Hanafi. How, an individual is supposed to know what is the shadow at Zawaal time. It appears to me that both Shafi'i and Hanafi Fiqh are not practical for this.

Answer: We in the 20th century may feel so much difficulty in knowing the shadow at Zawaal, but the Muslims in early centuries of Islam did not have any such difficulty. That's why, no one ever posed this question in early centuries objecting the Fiqh positions. Those early Muslims knew the time telling by sun's shadows, star's positions and moon phases. However, in the 20th century, we do not have time to observe skies during day or night as much as our ancestors did, but we have the technology to get much of that type of information from our computers, astronomical knowledge, and mathematics. Let us use the tools available in the times we are living in, and not object Fiqh positions.

4.2 Question: What is Asr Shafi'i and Asr Hanafi. I do not know the difference. Could you explain?

Answer: Fiqh (jurisprudence) is the interpretation of Hadith. Since every Muslim in not knowledgeable enough to interpret the Qur'an and Hadith, he/she must rely on some scholar who has done this interpretation. In early Islamic period there were four major scholars, Imam Abu-Hanifah in Iraq, Imam Malik in Madinah, Imam Shafi'i in Egypt, and Imam Ahmad Ibn Hanbal in Baghdad, who did a thorough job for this interpretation. An overwhelming majority of Muslims (Sunni or Ahl-e-Sunnah wal-Jama'ah) have converged to limit the interpretation with-in these four school of thoughts of Fiqh. All, or at least overwhelming majority, of the Fiqh scholars (Fuqahaa') in the later centuries consider themselves either Hanafi, Malikii, Shafi'i, or Hanbali.

5. Maghrib

5.1 Question: Is Maghrib prayer time at sunset or not? What is the definition of sunset in Islam? Is it the time when the solar disc touches the horizon or is the time when the solar disc has completely disappeared below the horizon?

Answer: The definition of sunset in Islam is no different than astronomical definition, i.e. it is the time when the solar disc has completely disappeared below the horizon. It is not the time when the solar disc touches the horizon. However, there is a difference in theoretically calculated sunset and actual sunset. Maghrib time is actual sunset. The calculated sunset is when the sun has just disappeared below horizon to an observer on the surface of the earth assuming earth as perfect sphere and level ground, and assuming some estimated values of temperature, pressure, and humidity conditions in the atmosphere, that affect refraction of light. Maghrib is when looked at the western horizon, the sun just vanishes below horizon with actual effects of refraction, that could change by actual temperature, pressure, and humidity, and the actual ground whether it is sloping downward towards horizon or level ground. Calculations for sunset are done assuming the earth is perfect sphere (which it is not), also assuming that the ground towards western horizon is perfectly level (which may not be), and assuming estimated values of temperature, pressure, and humidity conditions in the atmosphere.

For this purpose at least 3 minutes must be added to the calculated time of astronomical sunset for Islamic sunset or Maghrib. There are 3 reasons for this addition of 3 minutes:
1. The calculations are made at one point by longitude and latitude, and the observer in most cases could be up to 15 miles away from it.
2. The refraction of light through atmosphere whose density keeps on changing due to temperature, pressure and humidity and that changes angle of refraction.
3. There is a possibility of the sloping downward ground towards western horizon, while the calculations are made assuming level ground.

5.2 Question: Some People say that Maghrib time is just for 20 to 30 minutes after sunset. Is that correct?

5.3 Question: Does altitude from mean sea level affecn time of sunset/sunrise?

Answer: The altitude from mean sea level does not affect sunrise/sunset time. What affects sunrise/sunset time is the height of observer from the ground. All scientists of the world agree that the altitude from mean sea level and the height of observer from the ground are two different things.


How to find how many degrees from the beginning to the end of the sunset? - Astronomy

Sunrise and sunset are often defined as the instant when the upper limb of the Sun's disk is just touching the observer's mathematical horizon assuming a spherical earth, and allowing for the atmospheric refraction. This corresponds to an altitude of -0.833 degrees for the Sun. The various 'twilights' are usually defined in terms of the Sun's altitude as follows The limit of astronomical twilight is defined as when the light from the Sun scattered by the atmosphere is roughly the same as that the combined light from the stars, the zodiacal light and the gegenschein. In my inner city area, the sky brightness never drops to such a low level, so I use the nautical twilight to indicate observing times.

The method implemented on this page is taken from the Explanatory Supplement to the Astronomical Almanac section 9.33, and uses a simple iterative scheme which will converge on the times of events. This method may not converge above latitudes of 60 degrees North, or below latitudes of 60 degrees South. The times produced are found to be within seconds of times from a planatarium program, and Dr Ahmed Monsur's Mooncalc. A similar method is explained by Paul Schlyter on his excellent page.

  1. find the number of days from 0h UT on the day in question to J2000.0, and divide this by 36525 to find the number of julian centuries, t
  2. Guess a figure for the UT at which the sunrise occurs
  3. Calculate the Hour angle and declination at the Greenwich meridian for the Sun at the time of the current guess,
  4. Calculate a correction term and use the term to arrive at a new guess for the time of the sunrise, ensuring that the times stay within the range 0 to 24 hours,
  5. Repeat steps 3 and 4 until there is no significant difference between the succesive estimates of times for the sunrise
  6. This time is the time of the sunrise.

You can calculate the rise and set times of the Sun for any day in the past or future 500 years to reasonable accuracy using an ordinary pocket calculator. However, there is a large calculational effort at each repetition of steps 3 and 4, and most people will use a programmable calculator, a spreadsheet or a program function to calculate the times of events.

As a concrete example, I shall calculate the time of the Sunrise on 1998 October 25th at Birmingham UK, latitude 52.5N, longitude 1.9167W.

We start by finding the number of centuries since J2000.0, as all the formulas for the position of the Sun depend on this. As outlined above, we calculate the position of the Sun for 0h on the day in question. We use this position to calculate the time of Sunrise (even though the Sun will have moved a fraction of a degree in the sky), and then recalculate the position of the Sun for the new time. A refined time for the Sunrise can then be calculated.

We find the number of days since J2000.0 (in this case a negative number) and then divide by 36525 to find the number of (julian) centuries. The table below can be used to find the days since J2000.0

In all the calculations below, we measure time in degrees (180 degs = 12h), and we take a crude first guess at the time of sunrise as 12h UT on the day (180).

The 'low precision' formulas below give the Sun's position to an accuracy of about 0.1 degree over a few centuries either side of J2000.0. Taking the figure of t = -0.01186858316 for the number of Julian centuries since J2000.0 as calculated above for our example date

The guts of this iterative algorithm are the two formulas below Formula [1] gives us a way of calculating a better estimate of the time of sunrise, given the current estimate (ut) and the hour angle of the Sun for that time, and the correction term. The quantity GHA + long gives us the Sun's hour angle on the local meridian. Our first guess for the time of sunrise is ut = 180.

For setting events (sunset, end of twilight) we subtract the correction term in formula [1] Formula [2] gives us the value of the correction term for each successive estimate. As we will see in the spreadsheet example below, the correction terms converge rapidly to a single value under most circumstances. You have to calculate the correction term first, before you can use the iteration formula [1] to find your next estimate. I've never really understood why the textbooks list them in this order!

For our example date of 1998 October 25th, at Birmingham (phi = 52.5, long = -1.9167), we have for the correction term [2] and this leads to the refined estimate for the time of Sunrise

  • re-calculating the number of centuries since J2000.0 using the new estimate of UT
  • recalculating the position of the Sun for the new t value,
  • calculating a new correction term [2]
  • using the iteration formula [1] to calculate the new time

When I did this calculation myself (using a basic scientific calculator and rounding answers in a convenient if unsystematic way) I used a column layout, with a new column for the second iteration.

As a 'column based' layout seems so natural for this kind of calculation, I have devised a simple spreadsheet based on the formulas above. I have tried to use 'standard' formulas and so if you follow the instructions below, you should be able to build a working spreadsheet using just about any spreadsheet program you may have.

The sunrise.zip file contains copies of this spreadsheet in .WKS in .SLK formats, as well as the full MS Excel version. One of these should load into most spreadsheet programs.

  • all the trig functions work in radians! I have converted the coefficients in the formulas to give angles in radian measure
  • I can't make assumptions about being able to 'name' certain cells, so I have to use 'absolute cell referencing'
  • =mod(x,y) function changes implementation from program to program, but this does not change the final answers.

To build the spreadsheet, I have an 'input area' with labels in A5 to A12 and corresponding values in B5 to B12, and an 'output area' with labels in D5:D8 and the results of the calculations in E5:E8. The main calculation consists of four successive approximations to the UT of the event, and I put these calculations in the cells B17 to E28, with labels for each term in A17 to A28. It might help if you look at a screenshot of the basic spreadsheet layout.

Put the following labels in A5 to A12 and put the 'test values' in B5 to B12 These values correspond to 1998 October 25th, Birmingham, no zone offset, finding Sunrise (upper limb in contact with mathematical horizon), and a rise event.

Put the following labels into cells D5 to D8 and put the following formulas into E7 and E8, These formulas will give the number of days from J2000.0 in cell E7and the number of Julian centuries from J2000.0 in E8. I get -433.5 and -0.0118685832 in cells E7 and E8 using the 1998 October 25th test date.

Now put the following labels into cells A17 to A28, these names should tie in with the example calculations above

Now we can put the first column of formulas into cells B17 to B28. You should be able to copy and paste the formulas into a spreadsheet as one block Notice the use of 'absolute cell referencing' for $E$7, $E$8, and a few other cells. Note how I have kept a large number of decimal places in the coeficients for the mean longitude (L) calculation. Any rounding here causes trouble. Using our example data for Sunrise on 1998 October 25th, at Birmingham, 52.5 N, 1.9167 W, I get the following values in cells B17 to B28 (output formatted to 6 decimal places)

The next set of formulas in cells C17 to C28 calculates the next approximation to the time of Sunrise, these formulas are slightly different to the first column in that they pick up the new centuries figure from B28 and the new guess for UT from cell B27 And using the test values, I got the following values in cells C17 to C28 You can now copy the formulas from C17:C28 into D17:D28 and into E17:E28 to provide the next iterations in the calculation. I get the following values in D17:D28, and E17:E28 when doing this Four iterations are usually enough to get a reliable result, and as you can see the results in C27 and D27 (1.791597) are identical to 6 dp in this case.

I put the time of Sunrise in cell E5 with the following formula to convert the time from radians to hours Cell E8 now holds the time of the event in decimal hours in the time zone entered in cell B10 originally. For Birmingham on 1998 October 25th, I get 6.843 UT as the decimal hours of Sunrise, which corresponds to 0651 hrs.

  • degree based trig functions
  • days2000(year, month, day, hour, minute, second, optional greg) which returns the number of days since J2000.0 for a given instant. This function is valid for negative years and far into the future, unlike the simple one line function used in the 'portable' spreadsheet above. The optional argument 'greg' uses the Julian calendar if set to 0, and the gregorian if set to 1 or not used. This allows for countries like England and Sweeden, who did not adopt the Gregorian calendar in 1582.
  • sunrise(days, glat, glong, index, optional altitude) which returns the time of a rising or setting event. Index = +1 gives a rising event, index = 2 gives a setting event. The optional argument altitude allows you to specify the altitude you want the Sun to have, i.e. a value of -12 for altitude and +1 for index will give you the time when the night brightens to astronomical twilight.
  • Keep this page open in your browser
  • In the browser window, highlight all the text between the rows of * below
  • Izberite Edit | Kopirati from the browser Edit menu
  • open Excel 95 with a blank workbook
  • click on the Vstavi menu and select Insert | Macro | Modul.
    A new module window should appear
  • click in the new VBA module window, and select Edit | Prilepi from the Excel edit menu
  • Save the new workbook
  • Switch to a blank worksheet, and type the formula =day2000(1998,10,25,0,0,0)/36525 into a cell, then press enter.
    The cell value should be -0.01186858316 , i.e. the number of centuries since J2000.0 for 0h 1998 October 25th
  • latitude (decimal degrees, North positive) of observer
  • longitude (decimal degrees, West negative)
  • time zone offset from Greenwich, West negative
  • rising or setting events (+1 for rise, -1 for set)
  • desired altitude for Sun (i.e. -12 is nautical twilight)
  • Leto
  • Mesec
  • Dan
  • highlight (select) all the code betwen the lines of *******
  • copy this text to the clipboard (cntrol key and C)
  • paste the code into Notepad
  • save, setting the file type to All files (*.*) , and using the file extension .BAS
  • Check the file for broken lines, which occur if the browser window is set less wide than the width of some of the wider lines of BASIC
  • Load resulting file into QBASIC or the FirstBas basic compiler.

Below is the input and output of the program given the example case used throughout this page, sunrise on 1998 October 25th at Birmingham UK.

Seidelmann, P. Kenneth (ed)
Explanatory Supplement to the Astronomical Almanac
University Science Books
1992, completely revised
ISBN 0-935702-68-7

Definitive reference on all aspects of the ephemeris and associated calculations. No hostages taken, no example calculations and modern vectoral notation used throughout. Relevant sections are 9.311 (p484) and 9.33 (p486).

Paul Schlyter's page contains a restatement of a method similar to the one used here, but applicable to his planetary and lunar positions method.


How to find how many degrees from the beginning to the end of the sunset? - Astronomy

The Tropic of Cancer is the circle marking the latitude 23.5 degrees north, where the sun is directly overhead at noon on June 21, the beginning of summer in the northern hemisphere. The Tropic of Capricorn is the circle marking the latitude 23.5 degrees south where the sun is directly overhead at noon on December 21, the beginning of winter in the northern hemisphere. When the lines were named 2000 years ago, the Sun was in the constellation of Capricorn during the winter solstice and Cancer during the summer solstice (hence the names). Now due to the precession of the equinoxes the Sun is no longer in these constellations during these times, but the names remain.

The equator is the circle where the Sun is directly overhead at noon on the equinoxes.

The Arctic and Antarctic Circles are located at ±66.5 degrees latitude. Note that 66.5 + 23.5 equals 90 degrees. This means that on December 21, when the Sun is directly over the Tropic of Capricorn at noon, it will not be visible from the Arctic Circle. So above the Arctic Circle, there is a period during the winter when the sun remains below the horizon. The same is true of the Antarctic Circle during Southern Hemisphere winter. On June 21 st , when the sun is directly over the Tropic of Cancer at noon, it is not visible from below the Antarctic Circle.

This page was last updated on June 27, 2015.

About the Author

Cathy Jordan

Cathy got her Bachelors degree from Cornell in May 2003 and her Masters of Education in May 2005. She did research studying the wind patterns on Jupiter while at Cornell. She is now an 8th grade Earth Sciences teacher in Natick, MA.


The Setting Circles on Your Telescope

By: Alan MacRobert July 28, 2006 0

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Nearly every telescope on an equatorial mount comes with setting circles. In theory, they show the right ascension and declination to which the telescope is pointed, making it simple to aim at any object whose coordinates you look up. In practice, experienced observers generally regard setting circles as decorations to help sell telescopes, as a source of false hope for beginners, and possibly useful as makeshift frisbees.

We're talking here about traditional mechanical setting circles: rings engraved with lines and numbers on the telescope's two axes. More recent "digital setting circles," electronic readouts that tell where a telescope is pointed, can be vastly more accurate and useful they're described at the end of this article.

Conventional setting circles are no substitute for learning to find your way around the sky by looking with your eyes. But having absorbed this lesson, many observers scorn their setting circles forever after, even in situations when they might be quite helpful.

The problem is that many adjustments and alignments have to be done very precisely before the circles will display right ascension and declination accurately enough to find objects "blind." Rarely are all of these adjustments made.

But if you have some knowledge of the sky, you can use the circles for less demanding tasks that have looser accuracy requirements. We will discuss this simpler type of use first, then go on to the more exacting applications.

Offsetting from Stars

Their inherent inaccuracies give less trouble if you use setting circles only to measure your way a few degrees across the sky rather than all around the celestial sphere. To je offsetting method of finding objects from a known star.

This method works even with the oldest-style setting circles that only read hour angle from the celestial meridian instead of right ascension. (These are identified by their 0 to 䔰 hour markings that can't be set to anything but 0 when the scope is pointed at the meridian.)

First check that the telescope is polar-aligned moderately well. The polar axis of the mounting should be aimed at the celestial pole to within a couple of degrees. (Instructions for polar alignment come with most equatorial scopes.)

Look up the coordinates of your target object and any fairly bright star within 10° or so of it. Subtract the right ascension and declination of the star from those of the object. The result tells you how far from the star to swing in declination going north (or south if the value is negative), and how far in right ascension going east (or west if negative).

Most setting circles have rulings every 1° in declination and every 5 minutes of time in right ascension. So express your declination offset in degrees and right ascension in minutes. Try to read the declination dial to a tenth of a degree and the right ascension dial to one minute or better.

Offsetting can be very useful if the normal method of finding objects — star-hopping with the aid of a good map — isn't working. Perhaps you don't have a map that shows enough stars for you to home in on the exact point. Perhaps your finderscope is too small or the light pollution too bad, or you've repeatedly gotten lost in a difficult field and want to try a new tack.

Offsetting is especially efficient when you plan to survey many objects in a small area of sky. Work out your offsets indoors beforehand, and write them in your observing notebook.

If you want to find objects anywhere in the sky by dialing their coordinates, you should understand the many precise adjustments required to your telescope.

Suppose your lowest-power, widest-field eyepiece gives a 1° true field of view, typical of amateur instruments. If the telescope is pointed ½° wrong, your object will be on the edge of the field where it will go unnoticed. Merely to place it closer to the center than to the edge, you have to aim with ¼° accuracy.

What are the adjustments? The axis of the telescope's optical system should be made truly perpendicular to the mount's declination axis. This in turn should be perpendicular to the mount's polar axis. The polar axis must be accurately aligned on the celestial pole. The circles themselves must be positioned just right. Last, you must preberite the circles accurately — usually to a small fraction of their finest gradation.

Some of these adjustments have two degrees of freedom, such as in altitude in azimuth when aligning on the celestial pole. So all told, there are eight variables where error can creep in.

Based on the way simple random errors add up, each of these eight adjustments must be good to 0°.09 accuracy to achieve an povprečno total error of 0°.25 in where the telescope is pointed. Half the time the errors will add up to be better than this, half the time worse. To make them fall consistently on the better side, you should strive for even finer accuracy — say 0°.05 — in each adjustment.

No wonder setting circles have a reputation for never working.

We'll deal with each adjustment in turn.

First, make sure that the optics of the telescope are collimated (aligned) as best you can. Collimation on a reflector is usually just a matter of turning the adjustment screws behind the primary mirror to make a slightly out-of-focus-star image perfectly round when centered. On a Schmidt-Cassegrain telescope, you make tiny adjustments to the screws on the secondary mirror mount. Refractors rarely need collimation. Instructions for collimating a telescope usually come with it.

If you use a star diagonal, such as on a Schmidt-Cassegrain, be sure it too is collimated if it has adjustment screws on its back. Using high power, center the scope on an object while viewing "straight through" without the diagonal. Then insert the diagonal and see if the object is still centered. If it's not, turn the diagonal's adjustment screws until it is.

The reason for getting collimation all squared away first is that when you collimate a telescope, you change its aim point — that is, the direction of its optical axis with respect to the tube. After you collimate you will have to realign the finderscope to match the main telescope's new aim.

Now swing the tube to about 90° declination. While looking through your lowest power eyepiece, swing the mount back and forth in right ascension by turning the polar axis. You will see the field slowly turning. Make slight adjustments to the declination so the motion of the field is minimized when you turn the scope.

Ideally, you will find a declination position where the stars rotate around the exact center of the field. This happy state of affairs means you have gotten the optical axis truly parallel to the mount's polar axis.

Don't expect it to happen. Instead, you will only be able to find a place where the field motion is minimized, not reduced to zero. The point of sky around which the field appears to rotate will be off to one side, perhaps out of view entirely.

You want to shim the telescope tube in its cradle, or adjust the fork arms if the scope has a fork mount, to bring this point to the center of view. While turning the scope in right ascension, form a mental image of where the field's center of rotation lies. Nudge the scope that way to judge which side of the cradle needs to be shimmed, or which fork arm raised.

You can use strips of brass or plastic or folded-up aluminum foil for shimming. Adjust a fork arm on a Schmidt-Cassegrain scope by loosening the bolts that hold it to the drive base and sliding the arm slightly up or down. (This may be limited by the size of the bolt holes) The adjustment may take quite a bit of trial and error, but it's a job you'll only have to do once.

If your telescope tube can rotate in its cradle (a convenience on many reflectors), you may find you can get closer to the ideal after rotating the tube by some amount. Try this first, then do the shimming. Just remember that in actual use, you may need to rotate the tube back to the position it's in right now before the setting circles will work well. Mark the tube so you can do this if the circles later give problems.

Once you've done the best you can, loosen the declination circle, turn it to read precisely 90°, and retighten it permanently.

Now a confession: we've skipped a step. In the case of a German equatorial mount we haven't checked that the declination axis is perpendicular to the polar axis, and with a fork mount we aren't sure if the optical axis is perpendicular to the declination axis. That's because there is little or nothing you can do about it. Trust the manufacturer and cross your fingers.

The next step is accurate alignment on the celestial pole. Some telescopes come with pole-finding reticles for their finderscopes. Another method that is especially precise is described in the article
"Accurate Polar Alignment."

Now, at last, the setting circles are ready for their intended use!

The declination circle need never be touched again. But the right ascension circle does have to be repositioned at the start of each observing session, because the sky is always moving.

Aim at a bright star whose right ascension you know. (It's handy to keep the right ascensions of a dozen bright stars on the inside cover of your observing notebook.) Slide the right ascension circle to read the correct value for that star. On a German equatorial mount, the star should be on the same side of the mount as the objects you'll be looking for.

Now you can dial in the right ascension and declination of any object in the sky. Look in your lowest-power eyepiece, and there it should be.

If your right ascension circle is driven by your telescope's clock drive, as is the case with all Schmidt-Cassegrains we know about and many reflectors, you can dial in object after object all night without touching it again. If the circle is not driven, reposition it to the right ascension of the current object just before swinging to the next.

Technology to the Rescue

New ways have recently been invented to circumvent the problems that make setting circles so error-prone. These methods revolve around the "digital setting circle." In its simplest form, this is nothing more than a readout in little red numbers of what an ordinary setting circle tells you with a dial and pointer. But once this data is electronically encoded, a computer chip can begin to work miracles with it.

In some versions you can simply "initialize" the circles by setting on two or three bright stars at the beginning of a session, and the chip corrects for misalignments of many kinds — even failure to polar-align at all.

The next step up in sophistication is automatically correcting for lack of perpendicularity in the mount's axes — compensating for imperfect mechanics by smart electronics.

Team up good digital setting circles with a computerized data base of celestial objects, and you gain the astounding finding capabilities of a "computer assisted" or "robotic" telescope. These are currently working a revolution in high-end amateur astronomy, finally fulfilling the promise of what many people thought setting circles were supposed to do all along.


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