
samay kaa sameekaran

samay kaa sameekaran dou prakaar key saur samay key beach visangati kaa varnan kartaa haye. sameekaran" shabd kaa upayog "antar key sulah" key madhyayugeen arth mein kiya jaataa haye. dou baar joe bhinn hotey hain way hain spasht saur samay, joe seedhe soorya kii dainik gati koo track kartaa haye, aur saur samay kaa matlab haye, joe khagoliya bhoomadhya rekha key saath samaan gati key saath ack saiddhaantik maadhya soorya koo track kartaa haye. soorya kii vartamaan sthiti (ghante key konn) key maapan seey spasht saur samay praapt kiya jaa sakata haye, jaisa kii soorya kii kiranon dwara (seemit sateekta key saath) sanket diyaa gayaa haye. "iska arth haye" saur samay, ack hii sthaan key liye, ack sthir ghadee sett dwara ingit samay hoga taaki varsh bhar mein spasht saur samay seey isake antar kaa ausat shoonya hoe.
samay kaa sameekaran analema kaa poorv yaa paschim ghatak haye, ack vakr joe khagoliya gole parr apani ausat sthiti seey soorya key koniya offset kaa pratinidhitva kartaa haye jaisa kii prithvi seey dekhaa jaataa haye. khagoliya vedhshaalaaon dwara sankalit varsh key pratyek dinn key liye samay moolyon kaa sameekaran, panchang aur alpakaalik mein vyaapak roop seey soochibaddh kiya gayaa thaa.
samay key sameekaran key ack anuman koo dou shabdon key yog key roop mein likhaa jaa sakata haye (neeche spashteekaran dekhein):
sootra _ 1
sootra _ 2
sootra _ 3 [minut]
saadaa paath praarup menh
eot =-7.659sin (6.24004077 + 0.01720197 (365 * (y-2000) + d)) + 9.863sin (2 (6.24004077 + 0.01720197 (365 * (y-2000) + d)) + 3.5932) [minut]
ack cumm sateek lekin adhik sankshipt aur saral roop haih
eot = 9.87 sin (2b°)-7.77 sin (b° + 78.7°)
jahan b = 360° (d-81)/365
radian mein vyakt tarkon key saathah
eot = 9.87 sin (2b * π/180)-7.77 sin ((b° + 78.7°) * π/180)
"dee" chaalu varsh kii 1 janwari key baad seey dinon kii sankhya kaa pratinidhitva kartaa haye.
avadharana.
ack varsh key dauran samay kaa sameekaran graph parr dikhaae gaye anusaar badalata rahata haye; ack varsh seey dusare varsh mein iska parivartan thodaa hotaa haye. spasht samay aur soorya kii dhoop, 16 minut 33 sekand (lagbhag 3 navambar) taka aage (tej) hoe sakati haye, yaa 14 minut 6 sekand (lagbhag 11 farwari) taka peechhe (dheemi) hoe sakati haye. samay key sameekaran mein 15 aprail, 13 juuna, 1 sitambar aur 25 disambar key karib shoonya hain. prithvi kii kaksha aur ghoornan mein bahut dheemi parivartanon koo nazarandaj karate hue, inn ghatnaaon koo harr ushnakatibandhiya varsh mein ack hii samay parr dohraya jaataa haye. haalaanki, ack varsh mein dinon kii gair-abhinn sankhya key kaaran, yeye tithiyaan saal darr saal ack dinn yaa usase adhik badal sakati hain.
samay key sameekaran kaa graph dou saain vakron key yog seey nikatata seey anumaanit haye, ack varsh kii avadhi key saath aur ack aadhe varsh kii avadhi key saath. vakr dou khagoliya prabhaavon koo darshaate hain, pratyek taaron key saapeksh soorya kii spasht dainik gati mein ack alag gair-ekroopata kaa kaaran banata haih
samay kaa sameekaran kewal shoonya akshiya jhukaav aur shoonya kakshiya vikendrikaran vaale grah key liye gayab hoe jaataa haye. samay key badey samikaranon vaale grahon key dou udaaharan mangal aur uranus hain. mangal grah parr soorya key prakaash key samay aur ghadee key samay key beach kaa antar 50 minut taka hoe sakata haye, kyonki isaki kaksha mein kaafee adhik vikendrikaran haye. uranus grah, jiska akshiya jhukaav bahut badaa haye, kaa samay kaa ack sameekaran hotaa haye joe apane dinon koo kaee ghante pahale yaa baad mein shuru aur samaapt kartaa haye, yeh iss baat parr nirbhar kartaa haye kii yeh apani kaksha mein kahaan haye.
samay key sameekaran kaa sanket.
sanyukt raajya america kii nausena vedhshala kaa kahana haye kii "samay kaa sameekaran antar haye" spasht saur samay "ghataa" ausat saur samay ", i.ee. yadi soorya ghadee seey aage haye tou sanket sakaratmak haye, aur yadi ghadee soorya seey aage haye tou sanket nakaratmak haye. samay kaa sameekaran oopar diye gaye oopari graph mein ack varsh seey thodi adhik kii avadhi key liye dikhaaya gayaa haye. nichale graph (joe thheek ack calender varsh koo cover kartaa haye) key samaan nirpeksh maan hotey hain, lekin sanket ulat jaataa haye kyonki yeh darshaata haye kii ghadee soorya seey kitni door haye. prakaashan kissy bhee praarup kaa upayog curr sakate hain-angreji bolane vaali duniya mein, poorv upayog adhik aam haye, lekin hamesha iska paalan naheen kiya jaataa haye. joe koee bhee prakaashit talika yaa graph kaa upayog kartaa haye, usey pahale isake sanket upayog kii jaanch karni chaahiye. aksar, ack nott yaa caption hotaa haye joe ise samajhaata haye. anyatha, upayog koo yeh jaankar nirdhaarit kiya jaa sakata haye kii pratyek varsh key pahale teen maheenon key dauran, ghadee soorya key prakaash seey aage hoti haye. nae saal, sundial slow" key liye smaraniya "niss" (uchchaaran "achchha") upayogi hoe sakata haye. kuchh prakaashit taalikaaen sanketon kaa upayog naa karke aspashtata seey bachati hain, balki isake bajaay "soorya key prakaash mein teji" yaa "soorya key prakaash mein dheemi gati" jaise vakyanshon koo dikhaati hain.
iss lekh mein, aur angreji wikipedia mein anya, samay key sameekaran key sakaratmak moolya kaa tatparya haye kii ack suryakaksha ack ghadee seey aage haye.
itihas.
vakyansh "samay kaa sameekaran" madhyayugeen lattin "aquatio diarum" seey liya gayaa haye, jiska arth haye "dinon kaa sameekaran" yaa "dinon kaa antar". 
aquatio" (aur madhya angreji "sameekaran") shabd kaa upayog madhyayugeen khagol vigyaan mein ack avalokan moolya aur apekshit moolya key beach key antar koo saaranibaddh karane key liye kiya gayaa thaa (jaisa kii kendra key sameekaran mein, vishuv kaa sameekaran, upapatal kaa sameekaran). 
gerald jey. tommer madhya saur samay aur spasht saur samay key beach tolemy key antar key liye lattin "aquatio" seey madhyayugeen shabd "sameekaran" kaa upayog kartaa haye. sameekaran kii paribhasha johann capler ney "ausat visangati kii degree aur minaton kii sankhya aur sahee visangati kii degree aur minaton key beach kaa antar haye."
khagolvidon dwara pracheen kaal seey hii spasht saur samay aur madhya samay key beach key antar koo pahachaana jaataa thaa, lekin 17veen shatabdi key madhya mein sateek yaantrik ghadiyon key aavishkaar seey pahale, suryaghadi ekmatra vishvasaniya ghadee thee, aur spasht saur samay aam taur parr sweekrit maanak thaa. 19veen shatabdi kii shuruat taka rashtriya panchang aur alpakaalik mein spasht samay kaa sthaan ausat samay ney naheen liya thaa. 
praarambhik khagol vigyaan.
babylone key loga soorya kii aniyamit dainik gati key baare mein jaanate they.
tolemy kii "almagest" (doosari shatabdi) kii pustak III mukhya roop seey soorya kii visangati seey sambandhit haye, aur unhone samay key sameekaran koo apani "upayogi taalikaon" mein saaranibaddh kiya. tolemy soorya key meridian crossing koo saur samay mein badalane key liye aavashyak sudhaar parr charcha karate hain aur soorya key accliptic deshantar key liye accliptic aur meridian sudhaar key saath soorya kii gair-samaan gati koo dhyaan mein rakhate hain. vaha kahata haye kii adhikatam sudhaar samay-degree yaa ack ghante kaa haye (pustak III, adhyaay 9). haalaanki unhone adhikansh gananaon key liye prabhaav koo praasangik naheen maanaa kyonki yeh dheemi gati seey chalane vaale prakaash key liye nagany thaa aur ise kewal sabse teji seey chalane vaale prakaash, chandrama key liye lagu kiya.
almagest" mein tolemy kii charcha key aadhar parr, samay key sameekaran (arabi "taa 'dill all-ayam bee leyleha") key liye moolya madhyayugeen islami khagol vigyaan key karyon mein taalikaon ("jij") key liye maanak they.
praarambhik aadhunik kaal.
neville maskleen ney 1767 key liye "samudri panchang" mein spasht aur ausat samay kaa varnan diyaa thaah "spasht samay vaha haye joe soorya seey turant anuman lagaaya jaataa haye, chaahe vaha meridian seey gujarane key avalokan seey hoe, yaa usake dekhe gaye uday yaa setting seey. yeh samay ghadiyon aur ghadiyon dwara bhoomi parr achchi tarah seey viniyamit kiye gaye samay seey alag haye, jise samaan yaa ausat samay kahaa jaataa haye."unhone aage kahaa kii samudra mein, soorya key avalokan seey paae jaane vaale spasht samay koo samay key sameekaran dwara thheek kiya jaanaa chaahiye, yadi paryavekshak koo ausat samay kii aavashyakta haye.
sahee samay koo mool roop seey vaha maanaa jaataa thaa joe ack soorya key prakaash dwara dikhaaya gayaa thaa. jaba achchi yaantrik ghadiyaan pesh kii jaati theen, tou way harr saal kewal chaar tithiyon key karib soorya key saath sahmat hotey they, isaliye soorya key samay koo praapt karane key liye samay key sameekaran kaa upayog unake reeding koo "sahee" karane key liye kiya jaataa thaa. kuchh ghadiyon, jinhen sameekaran ghadiyaan kahaa jaataa haye, mein iss "sudhaar" koo karane key liye ack aantarik tantra shamil thaa. baad mein, jaise-jaise ghadiyaan pramukh achchi ghadee bunn gaeen, thheek naa kiya gayaa ghadee kaa samay, i.ee.mean time", sweekrit maanak bunn gayaa. suryakakshaon key pathan, jaba unakaa upayog kiya jaataa thaa, taba samay key sameekaran key saath thheek kiye jaate they, aur aksar abhee bhee, ghadee kaa samay praapt karane key liye pahale seey vipareet disha mein upayog kiya jaataa thaa. isaliye, kaee soorya key paton parr samay key sameekaran kii talika yaa graph utkeern hotey hain taaki upayogkarta iss sudhaar koo curr sakey.
samay key sameekaran kaa upayog aitihaasik roop seey ghadiyon koo nirdhaarit karane key liye kiya jaataa thaa. 1656 mein sateek ghadiyon key aavishkaar aur 1900 key aspas vaanijyik samay vitaran sevaaon key aagaman key beach, ghadiyon koo nirdhaarit karane key kaee samanya bhoomi-adharit tareeke they. ack suryakaksha koo samay key sameekaran kii talika yaa graph key saath padhaa aur sahee kiya jaataa thaa. yadi koee pargaman upkaran upalabdh thaa, tou meridian key paar soorya kaa pargaman (jiss kshan soorya paryavekshak key dakshin yaa uttar mein prateet hotaa haye) nott kiya gayaa thaa; ghadee koo dopahar key liye sett kiya gayaa thaa aur usa tarikh key liye samay key sameekaran dwara diye gaye minaton kii sankhya seey offset kiya gayaa thaa. ack teesari vidhi ney samay key sameekaran kaa upayog naheen kiya; isake bajaay, yeh paarshv samay aur ausat saur samay key beach sambandh kaa dohan karate hue, paarshv samay dene key liye taarakiya tippaniyon kaa upayog kartaa thaa.
samay key sameekaran koo anivarya roop seey sahee tareeke seey dene vaali pahali talika 1665 mein christian husense dwara prakaashit kii gaee thee. husense ney tolemy aur samanya roop seey madhyayugeen khagolvidon kii parampara kaa paalan karate hue samay key sameekaran key liye apane moolya nirdhaarit kiye taaki poore varsh sabhi moolyon koo sakaratmak banaaya jaa sakey.
taalikaon kaa ack aur samooh johnn flamstead dwara 1672-73 mein prakaashit kiya gayaa thaa, joe baad mein naee shaahi greenwich vedhshala key pahale khagolshastri shaahi baney. aisaa prateet hotaa haye kii yeye pahali anivarya roop seey sahee taalikaaen theen joe aaj key ausat samay kaa arth detee hain (pahale, jaisa kii oopar ullekh kiya gayaa haye, sameekaran kaa sanket hamesha sakaratmak thaa aur yeh shoonya parr sett kiya gayaa thaa jaba suryodaya kaa spasht samay suryodaya key ghadee samay key saapeksh sabse pahale thaa). flamestead ney sudhaar koo saaranibaddh karane aur namkaran karane kii parampara koo iss arth mein apanaaya kii ise ausat samay dene key liye spasht samay parr lagu kiya jaanaa thaa.
samay kaa sameekaran, soorya kii spasht gati kii aniyamitata key dou pramukh ghatakon parr sahee dhang seey adharit, aam taur parr taba taka naheen apanaaya gayaa thaa jaba taka kii germia horox key karyon key maranoparant sanskaran key saath prakaashit 1672-73 kii flamstead kii taalikaon key baad.
robbert hook (1635-1703), jinhone ganitiya roop seey saarvbhaumik jodd kaa vishleshan kiya, ney sabse pahale dhyaan diyaa kii samay key (gair-dharmnirpeksh) sameekaran aur saarvbhaumik jodd kii jyaamiti aur ganitiya vivaran samaan they, aur ack "yaantrik suryakana" key nirmaan mein ack saarvbhaumik jodd key upayog kaa prastaav rakhaa.
18veen aur 19veen shatabdi kii shuruat.
flamestead kii 1672-1673 aur 1680 kii taalikaon mein kiye gaye sudhaaron ney anivarya roop seey sahee tareeke seey aur aage kii bharpai kii aavashyakta key binaa ganana kiye gaye ausat samay koo diyaa. lekin samay key sameekaran kii taalikaon mein sankhyaatmak maan taba seey kuchh hudd taka badal gaye hain, teen karakon key kaaranah
1767 seey 1833 taka, british "samudri panchang aur khagoliya alpakaalik" ney samay key sameekaran koo iss arth mein saaranibaddh kiya kii 'maadhya samay praapt karane key liye spasht samay seey yaa usase bataae gaye minaton aur sekand kii sankhya koo jodein yaa ghataaen (jaisa kii nirdeshit kiya gayaa haye)'. panchang mein samay spasht saur samay mein thaa, kyonki jahaaj parr samay aksar soorya kaa nireekshan karke nirdhaarit kiya jaataa thaa. yeh operation usa asamanya sthiti mein kiya jaayega jaba ack avalokan key ausat saur samay kii aavashyakta thee. 1834 key baad seey muddon mein, harr samay ausat saur samay mein rhaa haye, kyonki taba taka jahaaj parr savaar samay aksar samudri kaalmaapak dwara nirdhaarit kiya jaataa thaa. parinamswarup nirdesh they kii pratyaksh samay praapt karane key liye madhya samay mein bataae gaye minaton kii sankhya koo jodana yaa ghataana (jaisa kii nirdesh diyaa gayaa haye). tou abb jodd sameekaran key sakaratmak honey key anuroop haye aur ghataav isake nakaratmak honey key anuroop haye.
choonki soorya kii spasht dainik gati prati dinn ack chakkar haye, yaani harr 24 ghante mein 360°, aur soorya swayam akash mein lagbhag 0.5° kii disk key roop mein dikhaai detaa haye, isaliye sadharan suryaghadi koo lagbhag ack minut kii adhikatam sateekta key liye padhaa jaa sakata haye. choonki samay key sameekaran kii seema lagbhag 33 minut haye, isaliye soorya key samay aur ghadee key samay key beach key antar koo nazarandaj naheen kiya jaa sakata haye. samay key sameekaran key alawa, sthaaniya samay kshetra meridian aur grishmakaaleen samay, yadi koee hoe, seey doori key kaaran bhee sudhaar lagu karna padata haye.
prithvi key ghoornan kii dheemi gati key kaaran ausat saur divas kii chhoti vriddhi, prati shatabdi lagbhag 2 ms prati dinn, joe vartamaan mein harr saal lagbhag 1 sekand taka jamaa hoti haye, samay key sameekaran kii paaramparik paribhashaon mein dhyaan mein naheen rakhee jaati haye, kyonki yeh soorya key prakaash kii sateekta key star parr adrishya haye.
sameekaran key pramukh ghatak.
prithvi kii kaksha kii vikendriyata.
prithvi soorya key chaaron or ghoomati haye. jaisa kii prithvi seey dekhaa jaataa haye, soorya ack varsh mein prishthabhoomi key sitaaron key madhyam seey prithvi key chaaron or ack baar ghoomata huaa dikhaai detaa haye. yadi prithvi prithvi kii dhuri key lambavat ack samtal mein ack golakar kaksha mein ack sthir gati seey soorya kii parikrama karati haye, tou soorya harr dinn thheek usee samay parr samaapt hoga, aur ack sahee samay rakshak hoga (prithvi key dheemi gati seey ghoornan key bahut chhote prabhaav koo chhodkar). lekin prithvi kii kaksha ack deerghavritt haye joe soorya parr kendrit naheen haye, aur capler key grahon kii gati key niyamon key anusaar isaki gati 30.287 aur 29.291 kimmy/sekand key beach bhinn hoti haye, aur isaki koniya gati bhee bhinn hoti haye, aur iss prakaar soorya parigh parr (vartamaan mein lagbhag 3 janwari) teji seey (prishthabhoomi sitaaron key saapeksh) aur aadhe saal baad affelian parr dheemi gati seey aage badhata dikhaai detaa haye.
inn charam binduon parr yeh prabhaav spasht saur divas koo apane ausat seey 7.9 sekand/dinn taka badalata haye. natijatan, gati mein anya dinon mein chhote dainik antar inn binduon taka sanchayi hotey hain, joe darshaata haye kii grah ausat kii tulanaa mein kaise gati aur girawat kartaa haye. 
natijatan, prithvi kii kaksha kii vikendrikaranta ack aavadhik bhinnata mein yogdan detee haye joe (pratham-crum key sanniktan mein) ack saain tarang haih
eot key iss ghatak koo uparokt kaarak "aeye" dwara darshaaya gayaa haih
sootra _ 4
a =-7.659 * ganit.paap (6.24004077 + 0.01720197 * (365 * (y-2000) + varsh kaa dinn))
grahan kii tirchhaata.
aggar prithvi kii kaksha golakar bhee hoti, tou bhee hamaare khagoliya bhoomadhya rekha key saath soorya kii kathit gati samaan naheen hoti. yeh prithvi kii parikrama aksh key apani kaksha key tala key sambandh mein jhukaav kaa parinam haye, yaa isake barabar, khagoliya bhoomadhya rekha key sambandh mein grahan key jhukaav (soorya joe maarg khagoliya kshetra mein letaa prateet hotaa haye) kaa parinam haye. hamaare khagoliya bhoomadhya rekha parr iss gati kaa prakshepan, jisake saath "ghadee kaa samay" maapa jaataa haye, sankranti parr adhikatam hotaa haye, jaba soorya kii vaarshik gati bhoomadhya rekha key samanantar hoti haye (kathit gati kaa pravardhan karati haye) aur mukhya roop seey sahee aarohan mein parivartan utpann karati haye. yeh vishuv mein nyuntam hotaa haye, jaba soorya kii spasht gati adhik dhalaan parr hoti haye aur girawat mein adhik parivartan hotaa haye, jisase daahine aarohan mein ghatak key liye cumm chhod diyaa jaataa haye, joe kii saur divas kii avadhi koo prabhaavit karane vaalaa ekmatra ghatak haye. tirchhita kaa ack vyaavhaarik udaaharan yeh haye kii soorya dwara soorya key soorya key prakaash mein, yahaan taka kii bhoomadhya rekha parr bhee, chhaaya kaa dainik parivartan sankranti key karib chhota aur vishuv key karib adhik hotaa haye. yadi yeh prabhaav akele sanchaalit hotaa haye, tou dinn sankranti key paas 24 ghante aur 20.3 sekand (maapa gayaa saur dopahar seey saur dopahar taka) taka lambe honge, aur vishuv key paas 24 ghante kii tulanaa mein 20.3 sekand cumm honge.
daaeen or key chitra mein, humm soorya dopahar mein grahan key tala kii spasht dhalaan kii masik bhinnata dekh sakate hain jaisa kii prithvi seey dekhaa jaataa haye. yeh bhinnata saal bhar ghoomati prithvi kii spasht purvagaman key kaaran haye, jaisa kii soorya seey dopahar mein dekhaa jaataa haye.
samay key sameekaran key sandarbh mein, grahan key jhukaav key parinamswarup saain tarang bhinnata kaa yogdan hotaa haih
eot key iss ghatak koo uparokt kaarak "bee" dwara darshaaya gayaa haih
sootra _ 5
b = 9.863 * ganit.paap (2 * (6.24004077 + 0.01720197 * (365 * (y-2000) + varsh kaa dinn)) + 3.5932)
dharmnirpeksh prabhaav.
uparokt dou karakon kii tarang dairdhya, ayam aur charan alag-alag hain, isaliye unakaa sanyukt yogdan ack aniyamit tarang haye. yug 2000 mein yeye maan hain (minaton aur sekand mein yuu. tii. tithiyon key saath):
cumm samay-seema (hajaaron varsh) parr vishuv aur parigh kii tithiyon mein badalaav adhik mahatvapurna honge. pahala purvagaman key kaaran hotaa haye, aur vishuv koo sitaaron kii tulanaa mein peechhe kii or sthanantarit kartaa haye. lekin vartamaan charcha mein ise nazarandaj kiya jaa sakata haye kyonki hamaare gregorian calender kaa nirmaan iss tarah seey kiya gayaa haye kii vasant vishuv kii tarikh 20 march koo rakhee jaae (cumm seey cumm hamaare uddeshya key liye paryaapt sateekta). perihelian kaa sthanantaran aage haye, harr shatabdi mein lagbhag 1.7 dinn. 1246 mein parigh 22 disambar koo, sankranti key dinn huaa, isaliye dou yogdan dene vaali tarangon mein samaan shoonya bindu they aur samay vakr kaa sameekaran samamit thaah "khagoliya algorithm" mein meeyas farwari aur navambar mein 15 meater 39 sekand kaa charam aur maee aur julaai mein 4 meater 58 sekand kaa charam detaa haye. isase pahale farwari nyuntam navambar key adhikatam seey adhik thaa, aur julaai key nyuntam seey adhik hoe sakata thaa. vaastav mein, 1900 (1901 eesaa poorv) seey pahale key varshon mein maee adhikatam navambar adhikatam seey adhik thaa. varsh-2000 (2001 eesaa poorv) mein adhikatam maee + 12 minut aur kuchh sekand thaa jabaki navambar mein adhikatam 10 minut seey bhee cumm thaa. dharmnirpeksh parivartan taba spasht hotaa haye jaba koee samay key sameekaran (neeche dekhein) key vartamaan graph kii tulanaa 2000 saal pahale key graph seey kartaa haye, jaise.jee., tolemy key aankadon seey nirmit.
vyaavhaarik upayog.
yadi gnomon (chhaaya-casting vastu) ack kinara naheen haye balki ack bindu haye (ee.jee.ack plate mein ack chhed), chhaaya (yaa prakaash kaa sthaan) ack dinn key dauran ack vakr kaa pataa lagaayegi. yadi chhaaya koo samtal satah parr daala jaataa haye, tou yeh vakr ack shanku khand (aamtaur parr ack atidhruviya) hoga, kyonki soorya kii gati kaa vritt gnomon bindu key saath ack shanku koo paribhaashit kartaa haye. vasant aur sharad ritu key vishuv mein, shanku ack samtal mein aur atidhruviya rekha ack rekha mein vighatit hoe jaati haye. pratyek dinn key liye ack alag hyperbola key saath, pratyek hyperbola parr ghante key nishan lagaae jaa sakate hain jisamen koee bhee aavashyak sudhaar shamil hain. durbhagya seey, pratyek hyperbola dou alag-alag dinon key anuroop hotaa haye, varsh key pratyek aadhe mein ack, aur inn dou dinon mein alag-alag sudhaaron kii aavashyakta hogi. ack suvidhajanak samjhauta yeh haye kii "madhya samay" key liye rekha kheenchi jaae aur varsh key dauran dopahar mein chhaaya binduon kii sateek sthiti dikhaane vaalaa ack vakr jodaa jaae. yeh vakr ack aakriti aathh kaa roop legaa aur ise analema key roop mein jaanaa jaataa haye. analema kii tulanaa madhya dopahar kii rekha seey karke, usa dinn aam taur parr lagu kiye jaane vaale sudhaar kii matra nirdhaarit kii jaa sakati haye.
samay key sameekaran kaa upayog naa kewal soorya key prakaash aur isi tarah key upkaranon key sambandh mein kiya jaataa haye, balki saur oorjaa key kaee anuprayogon key liye bhee kiya jaataa haye. saur tracker aur heliostats jaisi machines koo samay key sameekaran seey prabhaavit honey key tareeke seey chalana padata haye.
sivil samay ack meridian key liye sthaaniya ausat samay haye joe aksar samay kshetra key kendra key paas seey gujarta haye, aur sambhavatah dinn key ujaale kii bachat samay dwara aur badala jaa sakata haye. jaba kissy diye gaye nagrik samay key anuroop spasht saur samay paaya jaanaa haye, tou ruchi sthal aur samay kshetra meridian, dinn kii roshni bachaane key samay aur samay key sameekaran key beach deshantar mein antar parr vichaar kiya jaanaa chaahiye.
samay key sameekaran kii ganana karna.
samay kaa sameekaran ack prakaashit talika, yaa ack graph seey praapt kiya jaataa haye. ateet kii tithiyon key liye aisee taalikaaen aitihaasik maapon seey yaa ganana dwara taiyar kii jaati hain; bhavishya kii taarikhon key liye, nishchit roop seey, taalikaon kii ganana kewal kii jaa sakati haye. computer-niyantrit heliostats jaise upkaranon mein computer koo aksar samay key sameekaran kii ganana karane key liye prograam kiya jaataa haye. ganana sankhyaatmak yaa vishleshanatmak hoe sakati haye. poorv gati key vibhedak samikaranon key sankhyaatmak ekikaran parr adharit hain, jisamen sabhi mahatvapurna gurutvaakarshan aur saapeksh prabhaav shamil hain. parinam 1 sekand seey behtar sateek hain aur aadhunik panchang detta key liye aadhar hain. uttaraardh ack aise samadhan parr adharit hain jisamen soorya aur prithvi key beach kewal gurutvaakarshan antahkriya shamil haye, joe pahale vaale kii tulanaa mein saral haye lekin utanaa sateek naheen haye. chhote sudhaaron koo shamil karke isaki sateekta mein sudhaar kiya jaa sakata haye.
nimnalikhit charcha samay key sameekaran key liye ack uchit roop seey sateek (varshon kii ack vistrit shrinkhala mein 3 sekand key bheetar panchang detta key saath sahmat) algorithm kaa varnan karati haye joe khagolvidon key liye achchi tarah seey gyaat haye. yeh yeh bhee darshaata haye kii ack saral anumaanit sootra (ack badey samay antaral parr 1 minut key bheetar sateek) kaise praapt kiya jaae, jiska aasaani seey ack calculator key saath mulyankan kiya jaa sakata haye aur iss lekh mein pahale upayog kii gaee ghatana kaa saral spashteekaran pradaan kartaa haye.
ganitiya vivaran.
samay key sameekaran kii sateek paribhasha haye
iss sameekaran mein honey vaali maatraaen hain
yahaan samay aur konn way maatraaen hain joe karakon seey sambandhit hain jaise kih 2 radian = 360° = 1 dinn = 24 ghante. antar, eot, maapane yogya haye kyonki gha ack konn haye jise maapa jaa sakata haye aur saarvbhaumik samay, yooti, samay key maap key liye ack paimana haye. yuu. tii. seey = 180° = 12 ghante kii offset kii aavashyakta hoti haye kyonki yuu. tii. madhyaraatri mein shoonya hotaa haye jabaki madhya dopahar mein jee. aim. aich. aeye. = 0 hotaa haye. gha aur jee. aim. aich. aeye. donon mein, sabhi bhautik konon kii tarah, ack ganitiya haye, lekin unake sambandhit (spasht aur ausat) dopahar mein ack bhautik visangati naheen haye. isake ghatakon kii ganitiya visangatiyon key bavjood, eot koo gha aur jee. aim. aich. aeye. mein visangatiyon key beach chhote samay antaral mein 24 ghante jodkar (yaa ghataakar) ack nirantar kaary key roop mein paribhaashit kiya jaataa haye.
khagoliya gole parr konon kii paribhashaon key anusaar (ghante kaa konn dekhein) jahaanh
samay key sameekaran mein pratisthaapit karane parr, yeh haye
oopar diye gaye gha key sootra kii tarah, koee bhee likh sakata haye, jahan antim pada ausat soorya kaa sahee aarohan haye. sameekaran koo aksar inn shabdon mein likhaa jaataa haye
kahaan. iss sutrikaran mein samay key ack nishchit moolya parr eot kaa maap yaa ganana usa samay key maap yaa ganana parr nirbhar karati haye. donon aur ack varsh key dauran 0 seey 24 ghante taka bhinn hotey hain. pahale vaale mein ack samay mein ack visangati hoti haye joe yuu. tii. key moolya parr nirbhar karati haye, jabaki baad vaale mein thodi dair baad isaki visangati hoti haye. natijatan, jaba iss tarah seey ganana kii jaati haye tou eot mein dou, kritrim, visangatiyaan hoti hain. inn donon koo ack key ander aur usase pahale key asantulan key baad chhote samay antaral mein eot key moolya seey 24 ghante ghataakar hataaya jaa sakata haye. parinami ee. oh. tii. samay kaa ack nirantar kaary haye.
ack aur paribhasha, jise eot seey alag karane key liye darshaaya gayaa haye, haye
yahaan, greenwich maadhya paarshv samay haye (bhoomadhya rekha key tala mein maadhya vernal vishuv aur maadhya soorya key beach kaa konn). isaliye, jee. aim. aiss. tii. gais kaa ack anuman haye (aur ee. oh. tii. kaa ack anuman haye); aquic koo vishuv kaa sameekaran kahaa jaataa haye aur yeh prithvi kii poorv gati key baare mein ghoornan kii dhuri key hilane yaa nutation key kaaran hotaa haye. choonki poshak gati kaa ayam kewal 1.2 sekand (deshantar kaa 18′) haye, isaliye eot aur isake beach key antar koo taba taka nazarandaj kiya jaa sakata haye jaba taka kii koee upa-dwiteeya sateekta mein ruchi naheen rakhta haye.
ack teesari paribhasha, jise ise eot aur seey alag karane key liye darshaaya gayaa haye, aur abb ise alpakaalik samay kaa sameekaran kahaa jaataa haye (abb eot key beach kiye gaye antar seey pahale, aur baad vaale koo samay key sameekaran key roop mein jaanaa jaataa thaa)
yahaan ausat soorya kaa grahansheel deshantar haye (grahan key tala mein ausat vernal equinox seey ausat soorya taka kaa konn).
1960 seey 2040 taka antar 1.3 sekand haye. isaliye, varshon kii iss pratibandhit seema mein eot kaa ack anuman haye jisaki truti vishuv key sameekaran mein deshantar sudhaar key aadhar parr 0.1 seey 2.5 sekand kii seema mein haye; kaee uddeshyon key liye, udaaharan key liye, ack soorya key dwaar koo thheek karna, yeh sateekta paryaapt achchi seey adhik haye.
sahee aarohan ganana.
sahee aarohan, aur isaliye samay key sameekaran kii ganana neuton key khagoliya gati key dou-pind siddhant seey kii jaa sakati haye, jisamen pind (prithvi aur soorya) apane samanya dravyamaan kendra key baare mein andakar kakshaon kaa varnan karate hain. iss siddhant kaa upayog karate hue, samay kaa sameekaran bunn jaataa haye
jahan nae konn dikhaai dete hain
ganana koo puuraa karane key liye teen atirikt konon kii aavashyakta hoti haih
inn sabhi konon koo daaeen or key chitra mein dikhaaya gayaa haye, joe khagoliya gole aur prithvi seey dekhi jaane vaali soorya kii andakar kaksha koo darshaata haye (soorya seey dekhi jaane vaali prithvi kii kaksha key samaan). iss aakriti mein tirchha haye, jabaki deerghavritt kii vikendriyata haye.
abb ack moolya diye jaane parr, koee bhee nimnalikhit prasiddh prakriya key madhyam seey ganana curr sakata haih
pahale, diye gaye, capler key sameekaran seey ganana keejiyeh
haalaanki iss sameekaran koo bilkul bund roop mein hull naheen kiya jaa sakata haye, lekin isake maan anant (shakti yaa trikonamitiya) shrinkhala, chitraatmak yaa sankhyaatmak tarikon seey praapt kiye jaa sakate hain. vaikalpik roop seey, dhyaan dein kii key liye, aur punaravritti dwaaraah
iss anuman koo phir seey dohrakar, chhote key liye, sudhaar kiya jaa sakata haye,
aur nirantar punaravritti shakti shrinkhala vistaar key kramik roop seey uchch crum key shabdon kaa utpaadan karati haye. (1 seey bahut cumm) key chhote moolyon key liye shrinkhala key dou yaa teen pada ack achchha anuman dete hain; jitna chhota, utanaa hii behtar anuman.
isake baad, yeh jaanate hue kii ack dirghvrittakar kaksha sambandh seey vaastavik visangati kii ganana karein
upayog karane key liye kaee moolyavaan kaary kii sahee shakha vaha haye joe shuru karane kaa ack nirantar kaary karati haye. iss prakaar upayog key liye, aur upayog key liye. usa vishisht moolya parr jiska tark anant haye, upayog karein. yahaan pramukh shakha haye, vaha kaary joe calculator aur computer anuprayogon dwara vaapas kiya jaataa haye. vaikalpik roop seey, iss falan koo isaki teller shrinkhala key sandarbh mein vyakt kiya jaa sakata haye, jisake pahale teen pada hainh
chhote key liye yeh anuman (yaa yahaan taka kii kewal pahale dou shabd) ack achchha haye. isake saath utpaadan key liye anuman kaa sanyojan
sambandh koo kendra kaa sameekaran kahaa jaataa haye; yahaan likhi gaee abhivyakti mein dusare crum kaa sanniktan haye. prithvi kii kaksha kii visheshta key chhote moolya key liye yeh ack bahut achchha anuman detaa haye.
isake baad, isaki paribhasha seey ganana keejiyeh
iska maan gair-raikhik roop seey badalata haye kyonki kaksha andakar haye aur golakar naheen haye. key liye anuman seh
anta mein, oopar dikhaae gaye khagoliya gole parr samkon tribhuj key sambandh seey ganana karna
dhyaan dein kii kaa chaturthansh key samaan haye, isaliye 0 seey 2 kii seema taka cumm karein aur likhein
jahan 0 haye yadi chaturthansh 1 mein haye, yeh 1 haye yadi chaturthansh 2 yaa 3 mein haye aur yeh 2 haye yadi chaturthansh 4 mein haye. una moolyon key liye jinn parr tunn anant haye.
halanki isake liye anumaanit maan katey hue teller shrinkhala seey praapt kiye jaa sakate hain, lekin sameekaran kaa upayog karna adhik prabhaavi haye.
kahaan. dhyaan dein kii dou baar key liye aur dohrate hueh
samay kaa sameekaran.
sahee aarohan ganana key parinam koo samay sootra key sameekaran mein pratisthaapit karke samay kaa sameekaran praapt kiya jaataa haye. yahaan upayog kiya jaataa haye; aanshik roop seey kyonki chhote sudhaar (1 sekand key crum key), joe upayog koo uchit thaharaayenge, shamil naheen hain, aur aanshik roop seey kyonki lakshya ack saral vishleshanatmak abhivyakti praapt karna haye. dou-avadhi key sanniktan kaa upayog karna aur dou shabdon kii spasht abhivyakti key roop mein likhane kii anumati detaa haye, jise naamit kiya jaataa haye kyonki yeh ander aur ander ack pratham crum sanniktan haye.
yeh sameekaran sabse pahale milne dwara vyutpann kiya gayaa thaa, jinhone ise key sandarbh mein likhaa thaa. yahaan likhe gaye sankhyaatmak maan kakshiya mapdand maanon, =, = ° = radian, aur = ° = radian kaa upayog karane key parinamswarup hotey hain joe 1 janwari 2000 key yug key anuroop hotey hain, dopahar 12 baje yuu. tii. 1 parr. jaba oopar diye gaye sankhyaatmak abhivyakti kaa mulyankan kiya jaataa haye, tou ack calculator koo sahee maan praapt karane key liye radian mode mein honah chaahiye kyonki dusare pada key tark mein radians mein likhaa jaataa haye. uchch crum key sanniktan bhee likhe jaa sakate hain, lekin unamen aavashyak roop seey adhik shabd hotey hain. udaaharan key liye, donon mein dusare crum kaa sanniktan aur isamen paanch shabd hotey hain.
iss anuman mein uchch sateekta kii kshamata haye, halanki, ise varshon kii ack vistrit shrinkhala mein praapt karane key liye, mapdand, aur samay key saath badalane kii anumati dee jaani chaahiye. isase atirikt ganana sambandhi jatilataaen paida hoti hain. anya sanniktan prastaavit kiye gaye hain, udaaharan key liye, joe kendra key pratham crum sameekaran kaa upayog kartaa haye lekin nirdhaarit karane key liye koee anya sanniktan naheen haye, aur joe kendra key dwiteeya crum sameekaran kaa upayog kartaa haye.
samay charr koo yaa tou parigh seey pichhale dinon kii sankhya, yaa, ack vishisht tithi aur samay (yug) seey pichhale dinon kii sankhya key sandarbh mein likhaa jaa sakata haih
yahaan chuni hui tarikh aur samay kaa moolya haye. yahaan diye gaye moolyon key liye, radian mein, vaha haye joe yug mein vaastavik soorya key liye maapa jaataa haye, 1 janwari 2000 dopahar 12 baje yuu. tii. 1, aur usa yug seey pichhale dinon kii sankhya haye. periapsis mein, tou hull karna = detaa haye. yeh 4 janwari 2000 koo periapsis koo 00:11:41 parr rakhta haye, jabaki vaastavik periapsis haye, "bahu varsheeya interactive computer panchang" (abhrak key roop mein sankshipt) key parinamon key anusaar, 3 janwari 2000 koo 05:17:30 parr. yeh badee visangati isaliye hoti haye kyonki donon sthaanon parr kakshiya trijya key beach antar duss laakh mein kewal 1 bhaag haye; dusare shabdon mein, trijya periapsis key paas samay kaa ack bahut hii kamjor kaary haye. ack vyaavhaarik mamle key roop mein iska matlab haye kii kissy diye gaye varsh key liye vaastavik periapsis tithi kaa upayog karke aur jodkar samay key sameekaran key liye atyadhik sateek parinam praapt naheen kiya jaa sakata haye. haalaanki, sutrikaran kaa upayog karke uchch sateekta praapt kii jaa sakati haye.
jaba "m" 2 seey badaa hotaa haye aur ise 0 seey 2 kii seema mein laane key liye 2 key gunak (joe varsh parr nirbhar kartaa haye) koo ghataana hotaa haye. isi tarah 2000 seey pahale key varshon key liye 2 key gunak jodana padata haye. udaaharan key liye, varsh 2010 key liye, 1 janwari koo dopahar seey 31 disambar koo dopahar taka bhinn hotaa haye; sambandhit maan kramshah 10 aur 11 gunaa 2 ghataakar 0 seey 2 kii seema mein ghataate hain aur ghataate hain. 
koee bhee hamesha likh sakata haih
5) 
kahanh
2000 key baad key varshon key liye parinami sameekaran, jise dou shabdon key yog key roop mein likhaa gayaa haye, 1), 4) aur 5), haih
sootra _ 1
sootra _ 2
6) sootra _ 3 [minut]
saadaa paath praarup menh
7) eot =-7.659sin (6.24004077 + 0.01720197 (365 * (vaaee-2000) + dee)) + 9.863sin (2 (6.24004077 + 0.01720197 (365 * (vaaee-2000) + dee) + 3.5932) [minut]
aeye" shabd vishishtata key yogdan kaa pratinidhitva kartaa haye, "bee" shabd tiryakta key yogdan kaa pratinidhitva kartaa haye.
gananaon kaa parinam aamtaur parr yaa tou saaranibaddh moolyon key ack samooh key roop mein diyaa jaataa haye, yaa samay key sameekaran key ack graph key roop mein diyaa jaataa haye. varsh 2000 key liye abhrak key bhukhandon aur parinamon kii tulanaa chitra mein dikhaai gaee haye. abhrak dwara utpaadit parinamon key karib dekhaa jaataa haye, poorna truti, poore varsh mein 1 minut seey bhee cumm haye; iska sabse badaa moolya 43.2 sekand haye aur 276 (3 octuber) koo hotaa haye. abhrak key parinamon seey abhedya haye, donon key beach sabse badee poorna truti dinn 324 (20 navambar) koo 2.46 sekand haye.
samay key sameekaran kii nirantarta parr tippani.
falan nirantarta key sambandh mein sambandh kii upayukt shakha key chayan key liye archtangent falan kaa ack sanshodhit sanskaran sahayak haye. yeh ack mapdand dwara apekshit moolya key baare mein poorv gyaan laataa haye. sanshodhit archtangent function koo iss prakaar paribhaashit kiya gayaa haih
yeh ack aisaa moolya utpann kartaa haye joe jitna sambhav hoe utanaa karib haye. falan nikatatam purnank taka chakkar lagaata haye.
iss upaj koo lagu karnaah
parameter yahaan shoonya nikatatam moolya parr sett karane key liye vyavasthit kartaa haye joe vaanchhit haye.
dharmnirpeksh prabhaav.
abhrak aur parinamon key beach antar kii jaanch 1960 seey 2040 taka kii seema mein harr 5 saal mein kii jaati thee. harr mamle mein adhikatam poorna truti 3 sekand seey cumm thee; sabse badaa antar, 2.91 sekand, 22 maee 1965 (dinn 141) koo huaa thaa. haalaanki, varshon kii iss seema mein sateekta key iss star koo praapt karane key liye samay key saath kakshiya maapdandon mein dharmnirpeksh parivartan key liye jimmedaar honah aavashyak haye. iss bhinnata kaa varnan karane vaale sameekaran iss prakaar hainh
inn sambandhon key anusaar, 100 varshon (=) mein, lagbhag 0.5% (1.7°) kii vriddhi hoti haye, lagbhag 0.25% kii kamee hoti haye, aur lagbhag 0.05% kii kamee hoti haye.
natijatan, samay key sameekaran key kissy bhee uchch-crum key sanniktan key liye aavashyak gananaon kii sankhya koo puuraa karane key liye ack computer kii aavashyakta hoti haye, yadi koee samay kii ack vistrit shrinkhala mein apani antarnihit sateekta praapt karna chaahata haye. iss sthiti mein computer kaa upayog karke mulyankan karna isake kissy bhee anuman kii tulanaa mein adhik kathin naheen haye.
iss sub mein, jaisa kii oopar likhaa gayaa haye, mulyankan karna aasaan haye, ack ganak key saath bhee, soorya key prakaash koo thheek karane key liye paryaapt sateek (80 saal kii seema mein 1 minut seey behtar) haye, aur dou shabdon key yog key roop mein achchi bhautik vyakhya haye, ack tirchhaapan key kaaran aur doosara lekh mein pahale upayog kii gaee vilakshanta key liye. yeh yaa tou isake kissy bhee uchch-crum key anuman key kaary key roop mein yaa usake liye sach naheen haye.
vaikalpik ganana.
samay key sameekaran kii ganana key liye ack anya prakriya nimnanusar kii jaa sakati haye. konn degree mein hotey hain; sanchaalan kaa paaramparik crum lagu hotaa haye.
jahan prithvi kaa ausat koniya kakshiya wegg prati dinn degree mein haye, a.key.aeye. "ausat dainik gati.
tarikh kahaan haye, 1 janwari seey shuru honey vaale dinon mein ginaa jaataa haye (i.ee. dinn varsh mein kramik tithi kaa hissa hain). 9 disambar sankranti seey 31 disambar taka key dinon kii anumaanit sankhya haye. yeh vaha konn haye joe prithvi disambar sankranti seey aaj taka apani ausat gati seey apani kaksha mein aage badhegi.
 prithvi kaa konn haye joe prithvi sankranti seey aaj taka aage badhati haye, jisamen prithvi kii kakshiya vikendrikaran key liye pratham crum sudhaar, 0.0167 shamil haye. sankhya 3 31 disambar seey prithvi key parigh kii vartamaan tithi taka key dinon kii anumaanit sankhya haye. iss abhivyakti koo sthirankon koo jodkar saral banaaya jaa sakata haih 
yahaan, bhoomadhyarekhiya tala parr prakshepit sahee gati parr konn key beach kaa antar haye, aur "aadhe modd" mein antar praapt karane key liye 180° seey vibhajit haye. maan 23.44 ° prithvi kii dhuri kaa jhukaav ("tirchha") haye. ghataav samay key sameekaran koo paaramparik sanket detaa haye. kissy bhee diye gaye moolya key liye, (kabhi-kabhi key roop mein likhaa jaataa haye) key kaee maan hotey hain, joe aadhe modd kii purnank sankhya seey ack dusare seey alag hotey hain. calculator yaa computer dwara utpann moolya iss ganana key liye upayukt naheen hoe sakata haye. yeh aadhe modd kii purnank sankhya seey galat hoe sakata haye. samay kaa sameekaran dene key liye ganana key agale charan mein atirikt aadhe modd koo hataa diyaa jaataa haih
abhivyakti kaa arth haye "nikatatam purnank". computer parr, ise prograam kiya jaa sakata haye, udaaharan key liye, key roop mein. varsh key alag-alag samay parr iska moolya 0,1 yaa 2 hotaa haye. ise ghataane seey aadhe modd kii ack chhoti sakaratmak yaa nakaratmak aanshik sankhya nikalati haye, jise 720 seey gunaa kiya jaataa haye, joe samay kaa sameekaran praapt karane key liye soorya key saapeksh ack aadhe modd koo ghumaane mein prithvi koo lagane vaale minaton (12 ghante) kii sankhya haye.
prakaashit moolyon kii tulanaa mein, iss ganana mein kewal 3.7 sekand kii mool ausat varg truti haye. sabse badee truti 6.6 sekand haye. yeh oopar varnit sanniktan kii tulanaa mein bahut adhik sateek haye, lekin vistrit ganana key roop mein sateek naheen haye.
saur patan key baare mein parishisht.
uparokt ganana mein soorya key grahansheel deshantar (90° seey sthanantarit) key liye ack sateek moolya haye, isaliye saur girawat aasaani seey upalabdh hoe jaati haih
joe ack degree key ansh key bheetar sateek haye.

