es# % l`f"V&dUnz dh vk"kZ vo/kkj.kk d xf.krh; izek.k& fou; >k vkfn 'kjkpk;Z d iqjh fLFkr xkso/kZueB d ikdkj

l`f"V&dUnz lEcU/kh vk/kqfud ervk/kqfud oSKkfudksa dks czk.M d dUnz

dk Kku ugha gSAHkkSfrd czk.M dk dksbZ fujis{k dUnz vkbalVkbu d lkis{krkokn fl)kUrkuqlkj gks gh ugha ldrk]D;ksafd ,slk dksbZ fujis{k ns'k&dky dk lUnHkZ ugha gS ftld lkis{k HkkSfrd iz.kkfy;ksa dks ekik tk ldA fdUrq gky esa ^cSdxzkm.M jsfM;s'ku*dh [kkst }kjk ^fcx cS* fl)kUr dks cy feyk gS] ftld vuqlkj czk.M dk vkjEHk dN vjc o"kZ iwoZ gqvk FkkApwWafd orZeku czk.M dky esa vuUr ugha gS] bldk vkjEHk dHkh u dHkh gqvk Fkk] rks bldk ns'k Hkh vuUr ugha gks ldrk] D;ksafd lkis{krkokn d vuqlkj ns'k vkSj dky ijLij vfHkk :i ls tqM+s gq;s gSa tks fnky ;k Lisl&Vkbe&dkW.VhU;we dgykrk gSA vuUr oLrq gh dUnzghu gks ldrh gSApwWafd czk.M ns'k vkSj dky esa lkUr (finite) gS]bldk dksbZ u dksbZ vkdkj gksuk pkfg;s vkSj ml vkdfr dk dgha u dgha dUnz gksuk gh pkfg;s] Hkys gh lkis{krkokn dh dlkSVh ij og dUnz fujis{k vkSj lukru u gksA;g Hkh ugha Hkwyuk pkfg;s fd lkis{krkokn dh dlkSVh doy HkkSfrd fo d fy;s gS] tks Hkkjr dh vk"kZ ekU;rk d vuqlkj 'kkr ugha gSA vc oSKkfud Hkh ekurs gSa fd lw;ZdUnzokn ,oa HkwdUnz &okn vius&vius lUnHkZ d nk;js (frame of reference) esa Bhd gSa] egRo doy bldk gS fd xf.kr lgh gksuk pkfg;sA fjpMZ fQV~txsjYM VsDll fofo|ky; esa HkkSfrdh d izksQlj VkWyseh d vyektsLV dk vk/kqfudhdj.k djus d iz;kl (A Modern Almagest esa fy[krs gSa % the fact that the model described in Almagest is geocentric in nature is a non-issue, since the earth is stationary in its own frame of reference. vk"kZ ekU;rk d vuqlkj l`f"V d dUnz vkSj mld izek.k dh tkWap izLrqr ys[k dk fo"k; gS] tks T;ksfr"k d fl)kUr LdU/k esa vkrk gSA

fl)kUr&T;ksfr"k dh voufr xzgyk?kodkj x.ks'k nSoK }kjk T;k&pkikfn

d fcuk ikfuek.kZ dh yk?ko ;k 'kkVZdV fof/k dk izpkj djus d ikr T;ksfr"k d fl)kUr LdU/k esa yksxksa dh #fp lekIr gks xbZ vkSj dkykUrj esa fl)kUr&xf.kr dh vusd izf;kvksa dk Kku Hkh yksx Hkwy x;sA nqHkkZX;o'k Hkkjrh; fl)kUr&xf.kr dks vU/k;qx esa /kdyus okyh ;g xzgyk?koh; vikfUr ml dky esa gqbZ tc ;wjksi esa iqutkZxj.k vkjEHk gks jgk FkkA fgUnqvksa d nklRo dk dky Fkk] fl)kUr d i{k/kj edjUnkpk;Z vkSj deykdj Hk tSls fo}ku Fks Hkh rks mudh ,d ugha pyhAdeykdj Hk d HkkbZ fnokdj nSoK us deykdj Hk dh ugha lquh vkSj edjUn i)fr ls eUnQyk)Z dks R;kx dj fl)kUr dh vfUre :i ls gR;k dj nh];|fi eUnQyk)Z d fcuk lS)kfUrd xzgd{kk dh O;k[;k lEHko ugha gSA eUnQyk)Z dks R;kxus dh odkyr lcls igys xzgyk?ko us gh vkjEHk dhAxzgyk?ko dk rhljk ;ksxnku Fkk lw;Zfl)kUr d fo#) okrkoj.k rS;kj djuk vkSj Qykns'k d LFkku ij HkkSfrd xzgfi.Mksa d os/k dks izek.k ekuukA xzgyk?ko ls izHkkfor gksdj ewy edjUn lw;Zfl)kUrh; i)fr dks fodr djus okys fnokdj nSoK d ikr lw;Zfl)kUr dh ekSfyd fof/k }kjk ik cuuk cUn gks x;k] ftldk Qy ;g gqvk fd tc izkphu fl)kUr xzUFkksa dh Hkzked O;k[;k;sa fons'kh ys[kdksa vkSj mud ns'kh vuqpjksa us izdkf'kr djuk vkjEHk fd;k rks mudk [k.Mu ugha gks ldkA 'kfr;ksa rd izkphu 'kkksa dh vogsyuk dk nq"ifj.kke ;g gqvk fd tc vaxzstksa us Hkkjrh; fo|kvksa dks fodr djd >qBykus dk "kM;U= vkjEHk fd;k rks muls yksgk ysus dk ckSf)d lkeF;Z Hkkjr [kks pqdk FkkA jktuSfrd LorU=rk izkIr djus d ikr Hkh 'kk d {ks= esa [kks;k gqvk ckSf)d lkeF;Z ugha ykSVk] D;ksafd ftu izkphu fo|kvksa dk yksi gks pqdk Fkk mudh iquizkZfIr vkSj iquLFkkZiuk d iz;kl ugha fd;s x;sA Hkkjr dh es/kk ikkR; fo|kvksa dh Js"Brk esa fo'okl djus yxh] dN eqh Hkj yksx izkphu

fo|kvksa ls fpid jgs] fdUrq jkT;kJ; d vHkko vkSj izkphurk d izfr fodklokfn;ksa dh _.kkRed eukso`fr d dkj.k izkphu fo|kvksa d iqu#RFkku gsrq bZekunkjh ls lqfu;ksftr vkSj lfBr iz;kl ugha fd;k x;kA fdUrq ,sls lk{;ksa dh deh ugha tks vk"kZ Kku dks iquthZfor djus esa l{ke gSaA vko';drk doy bldh gS fd bu lk{;ksa dh fu"i{k :i ls tkWap dh tk;A ,sls ,d lk{; dk izLrqr ys[k esa Li"Vhdj.k fd;k x;k gSA

vk"kZ es#dUnzokn ife esa DykmfM;l VkWyseh dk opZLo 14 'kfr;ksa rd jgkAikkR; ys[kdksa ,oa mud Hkwjs f'k";ksa dh ftn gS fd VkWyseh vkSj vU; ikkR; fo}kuksa ls gh Hkkjr us T;ksfr"k lh[kkA ,sls yksx vkt Hkh vlR; izpkj dj jgsa gSa fd Hkkjrh; T;ksfr"k HkwdfUnzr Fkk vkSj VkWyseh d vk/kkj ij gh lw;Zfl)kUr dh jpuk gqbZA izLrqr ys[k esa ,sls xf.krh; izek.k fn;s x;s gSa tks fl) djrs gSa fd lPpkbZ m izpkj d foijhr gS % Hkkjrh; ikSjkf.kd&lS)kfUrd T;ksfr"k iw.kZr;k ekSfyd gS rFkk VkWyseh tSls ijorhZ ys[kdksa d fl)kUr blh ij izR;{k ok ijks{k :i ls vk/kkfjr FksA

ikkR; ys[kdksa ,oa mud vuqpjksa }kjk es# dh ppkZ Hkh ugha dh tkrh] ;|fi iqjk.kksa vkSj egkdkO;ksa rFkk tSu lkfgR; esa czk.M dk dUnz es# ioZr ij gksus dh ckr ckjEckj dgh xbZ gSA bu lkfgfR;d lk{;ksa dks diksj dYiuk dgdj gWalh esa mM+k fn;k tkrk gS] izkphu xf.kr dks le>us dk iz;kl Hkh ugha fd;k tkrkAlkSji{k cuke Di{k % lw;ZkfUrlw= dk izek.k lw;Zfl)kUr d v/;k;&3^f=izkf/kdkj* esa yXuku;u ,oa lEcfU/kr fo"k;ksa dk o.kZu gSA yXu d lw= dh lgh O;k[;k Hkk";dkjksa us dh] fdUrq bl lw= dh T;kferh; miifk

kkslkokfnR;siq#"klkslkoge~[kEecz;g 'kq ;tqosZn ek/;fUnu 'kk[kk dk

vfUre eU= gS ftl dkj.k bl fopkj/kkjk dk uke^osnkUr*iM+kAlkSji{k ls rkRi;Z gS vHkkSfrd Hkqoyksd dk ftldk Kku bfUnz;ksa }kjk izkIr ugha fd;k tk ldrk]ftld doy rhu gh mik; gSa % 'kk fnO; vk"kZ xzUFk] ;Fkk T;ksfr"k d {ks= esa lw;Zfl)kUr] vkIr opu vkSj riA mkhloha 'krh esa ,f'k;kfVd lkslkbVh d v/;{k dksyczqd] fofYdUlu] LikWfVloqM] ctsZl] tSls ikkR; ^Hkkjrfonksa* us euxwBk izpkj vkjEHk fd;k fd lw;Zfl)kUr izkphu dky esa HkkSfrd xzgksa dk LFkwy eku n'kkZrk Fkk fdUrq vc vkmV&vWo&MsV gks pqdk gSA lPpkbZ ;g gS fd Di{k vkSj lkSji{k esa vUrj izkphure dky ls gh _f"k;ksa dks Kkr Fkk] ftldk ,d mnkgj.k gS fo".kq/keksZkjiqjk.k esa egf"kZ osn O;kl dk opu %

;U=os/kkfnuk Kkra ;n~ chta x.kdLrr%Axzg.kkfn ijh{ksr u frF;kfn dnkpu

;U=kfn }kjk chtx.kuk ls xzg.kkfn tSls '; ?kVukvksa dk ijh{k.k djsa] fdUrq frF;kfn gsrq ,sls DrqY; ijh{k.k u djsaA T;ksfr"k d v"V Qy gsrq ikksi;ksxh frF;kfn d fu.kZ; esa Xxf.kr dk _f"k;ksa us fu"ks/k fd;k FkkA vr% Li"V gS fd oSfnd&ikSjkf.kd dky esa Hkh Di{k rFkk lkSji{k esa vUrj dk Kku _f"k;ksa dks Fkk] ijUrq _f"k;ksa us T;ksfr"k esa lkSji{k d gh iz;ksx dk vkns'k fn;k] ;|fi '; txr gsrq Xxf.kr dh mi;ksfxrk dk Kku mUgsa FkkA fu.kZ; flU/kq esa blij Li"V opu gS %

v"VQyfl/;FkZ ;Fkkdxf.kra d#Axf.kra ;fn "VkFkZ rn"V~;qn~HkorLlnk

v"V Qy dh flf) gsrq vdxf.kr lw;Zfl)kUr dk iz;ksx djas---A Li"V gS fd ck p{kq ls "V HkkSfrd xzg&fi.Mksa dk T;ksfr"k d v'; xzgnsofcEcksa ls vUrj ekuk tkrk FkkA ikjk'kjh gksjk'kk esa mYys[k gS fd T;ksfr"k d xzg izkf.k;ksa dks deZQy nsus d fy;s ijekRek d vorkj gSaA ck p{kq }kjk nsoksa dk n'kZu lEHko ughaA vr% vHkkSfrd Hkqoyksdh; xzgksa dks HkkSfrd xzg le>uk vk"kZ ijEijk d fo#) gSA Hkkjrh; ;ksxnku dks vk;kfrr crkus dh dps"Vk

kfUr dk tks lw;Zfl)kUrh; lw= ij n'kkZ;k x;k gS]mlh dk iz;ksx fueZy pUnz ykfgM+h th djrs Fks izek.k gsrq Advance Ephemeris, page 79 ns[ksaAij lw;Zfl)kUr dks vkmV&vWo &MsV dgus okys bu egkuqHkkoksa dks ;g Lohdkj djus esa Hk; yxrk Fkk fd lw;Zfl)kUrh; lw=ksa dk vk/kqfud foKku esa mi;ksx djus ls igys lw;Zfl)kUr dks bu lw=ksa d vkfo"dkj djus dk Js; fn;k tkuk pkfg;sAHk; dk dkj.k Fkk ikkR; Hkkjrfonksadh ;g ftn fd Hkkjrh;ksa dk leLr Kku ;wuku ls pqjk;k gqvk gS ftld fy;s izkphu Hkkjrh;ksa us ;wukfu;ksa dks Js; Hkh ugha fn;kA19oha 'krh d rFkkdfFkr Hkkjrfonksa ls vf/kd iwokZxzgh vkt d dbZ fo}ku gSa tks mijks >wBs fopkjksa d izpkj esa yxs jgrs gSaA ,sls fopkjksa d fy;s czkmu fofo|ky; d MsfoM fiUxzh izfl) gSaA vesfjdk d yksfjMk LVsV fofo|ky; d Msful Mwd fy[krs gSa % under the Pingree van der Waerden Hypothesis, the Indian texts summarize centuries old traditions inherited from the Greeks. (D. Pingree, History of Mathematical astronomy in India, Dictionary of Scientific Biography, 15 (1978), 533-633; rFkk D. Pingree, Concentric with Equant, Archives Internationales dHistoire des Sciences, 24 (1974) 26-28.)] ysfdu Msful Mwd us lk{;ksa dh tkWap dh rks ik;k fd Hkkjrh; [kxksyh; ekWMy d ksr Hkkjrh; gSa ;k vKkr xzhd&jkseu ijEijk;sa] bld lk{; miyC/k ugha %Without further information we cannot say whether the model was developed in India or in some earlier, and unknown to us, Greco-Roman tradition.( - The Second Lunar Anomaly in Ancient Indian Astronomy, Dennis W. Duke, Florida State University, USA.)A fVuh tSls Hkkjr fojks/kh ys[kdksa d fo#) lw;Z& fl)kUr d Hkk";dkj ctsZl us ;gkWa rd fy[k fn;k fd xzhl dks Hkkjrh; fo|kvksa dk ksr crykus okys Hkwyrs gSa fd [kxksyfoKku esa xzhl dk ;ksxnku cgqr ckn dk gS]vkSj mld vf/kdka'k ekSfyd fopkj Hkkjr ls m/kkj fy;s gq;s gSa % I must think the Hindus original in regard to most of the elementary facts and principles of astronomy,... and that the Greeks borrowed from them.ifjf'k"V] lw;Zfl)kUr

ij ,oustj ctsZl dk Hkk";Aftu fopkjksa dk izkphu ife esa dksbZ

izek.k ugha]mud fy;s Hkh fiUxzh tSls fo'ks"kKksa dk ;gh ekuuk gS fd Hkkjrh;ksa us lc dN xzhl ls pqjk;kA vkSj ftu fopkjksa dk izkphu ife ls fdlh izdkj dk lEcU/k LFkkfir djuk lEHko ugha] mUgsa diksj dYiuk dgk tkrk gSA ,slh gh ,d diksj dYiuk gS es# ioZr dh] ftld fo"k; esa osnO;kl th tSls egf"kZ;ksa us rFkkdfFkr :i ls xIisa gkWadhA egf"kZ;ksa dh bu ^diksj dYiukvksa*dk fu"i{k vkSj foLrr` xf.krh; fos"k.k djus dk vodk'k fdlh d ikl ughaA lw;Zfl)kUrh; yXuku;u lw= dh xf.krh; tkWap lkSj yXulw= esa lw;ZkfUr dh vko';drk iM+rh gSA pWwafd gekjk vHkh"V T;ksfr"k gS] vr% Xxf.kr d fookn esa u iM+dj lw;Zfl)kUrh; yXuku;ulw= dh tkWap djrs gSaA igys fofHkk kfUro`rh; jkf'k;ksa d yksn;ekuksa dh x.kuk dh tkrh gS]vkSj fQj muesa b"VLFkkuh; pj& laLdkj djd fofHkk kfUror`h; jkf'k;ksa d b"V LFkkuh; mn;eku Kkr fd;s tkrs gSaAkfUro`rh; jkf'k;ksa d fo"kqorh; mn;ekuksa dks yksn;eku dgk tkrk gS] ftldh xf.krh; vkSj T;kferh; O;k[;k izLrqr ys[k esa gSA lw;Zfl)kUr d rhljs v/;k; ^f=izkf/kdkj* esa mn;eku Kkr djus dk tks lw= fn;k x;k gS mls fuEuks ljy rjhd ls fy[kk tk ldrk gS % yksn;T;k HkqtT;k ijdksT;k dksT;kij HkqtT;k

bl lw= esa ^ij* ls rkRi;Z gS ^ije& lw;ZkfUr*ftldk lkSji{kh; eku gS 24AHkqtT;k dk vFkZ gS Hkqt dh T;k] vkSj Hkqt dk vFkZ gS es"kkjEHk ls fofHkk jkf'k;ksa dk dks.kh; eku] ftls fp lfgr 90 va'k d Hkhrj ifjofrZr fd;k tk; rks Hkqt dgrs gSaA izkphu fof/k esa Hkqt dh vko';drk iM+rh Fkh] fdUrq lkbf.VfQd dydysVj dk iz;ksx djus ij Hkqt cukus dh vko';drk ugha iM+rh] 360 va'k rd fdlh Hkh dks.k dks lh/ks lw= esa Mkydj Qy Kkr dj ldrs gSa] ftls HkqtT;k d cnys jkf'kT;k fy[kk tk ldrk gSA bls fuEuks lw= esa A n'kkZ;k x;k gS lw= dh miifk ys[k d vUr esa gS%

yksn; 10 fuEuks lw= d Qy dk pkiHkqtT;k dksT;k24 dksT;k24 HkqtT;k vFkok

[(sin A cos 24 ) cos(24 sin A)]bl lw= esa A dk eku 30j[ksa rks Qy

278-3826496 iy feyrk gSA ;g izFke jkf'k dk iykRed yksn;eku gSAiqu% lw= esa A 60 j[ksa vkSj izkIr Qy 578-0342604 iy esa ls izFke jkf'k d mijks mn;eku dks U;wu djsa rks f}rh; jkf'k dk yksn;eku 299-6516108 iy feysxkA iqu% lw= esa A dk eku 90 j[ksa vkSj izkIr Qy 900 iy esa ls izFke rFkk f}rh; jkf'k;ksa d lfEefyr mn;ekuksa578-0342604 iydks U;wu djsa rks rr`h; jkf'k dk yksn;eku 321-9657396 iy feysxkA bu rhuksa jkf'k;ksa d 'kq) iykRed eku fuEuks gSa %

jkf'k&1 278-3826496112616645391jkf'k&2 299-6516108009967262328jkf'k&3 321-9657395877416092281

LFkwy xf.krKksa us n'keyo ij /;ku ugha fn;k vkSj igyh nksa jkf'k;ksa dk yksn;eku e'k% 278 rFkk 299 fy;k] ftUgsa 900 esa U;wu djus ij rhljh jkf'k dk yksn;eku mUgsa 323 iy feykA nh?kZdky ls bUgha LFkwy yksn;ekuksa dk iz;ksx gks jgk gSA ftu T;ksfrf"k;ksa dh "k"Va'k tSls mPp oxksZa esa #fp ugha] mud fy;s bruh =qfV ux.; gSA fdUrq ;fn mijks xf.kr esa jkh Hkj Hkh =qfV u dh tk; rks dN vn~Hkqr fu"d"kZ feysaxs] ftuij /;ku ugha fn;k tkrkAm rhuksa jkf'k;ksa dk lfEefyr yksn;eku vgksjk= dk prqFkkZa'k ;k 900 iy gSA igyh jkf'k 300 iy ls vR;f/kd U;wu gS]rhljh jkf'k 300 iy ls vR;f/kd vf/kd gSA e/; jkf'k dk eku 300 iy gksuk pkfg;s] ij 'kq) x.kuk djus ij^&0-3483892*iy dk vYi vUrj izkIr gksrk gSA lw;Zfl)kUr dks xEHkhjrk ls ugha ysus okys rFkkdfFkr^fo'ks"kKksa* dk /;ku ,sls vYikUrjksa dh vksj ugha tkrk] os lw;Zfl)kUrh; lw=ksa dks v'kq) ekudj tkWap gh ugha djrsA ;fn lw;Zfl)kUr HkwdfUnzd gksrk rks e/; jkf'k dk yksn; eku Bhd&Bhd 300 iy gksrkA fdUrq okLro esa 300 iyksa ls &0-348389199 iy

dk vYikUrj gS tks e/;jkf'k d e/;e yksn; eku 300 iy dk 861-1059150464 okWa Hkkx gSA ;g HkwdUnz ls jfod{kkdUnz d vUrj dk |ksrd gS] ftldk ;kstukRed eku fuEuks fof/k }kjk Kkr fd;k tk ldrk gSA lw;Zfl)kUr d vuqlkj jfod{kk dk eku 43]31]500 ;kstu gSA ;|fi jfod{kk vR;Ur tfVy nh?kZo`rh; vfHkpfdk (elliptical epicycloid) gS]bls yxHkx nh?kZor`h; eku ysa rks ifjf/k ,oa O;klk/kZ d vuqikr2pi 2 3-14159265ls foHk djus ij lS)kfUrd lw;Z ls d{kkdUnz dh vkSlr nwjh izkIr dj ldrs gSaA;g nwjh eq[;O;klk/kZ ,oa xkS.k O;klk/kZ dk vkSlr gSAlw;Zfl)kUrh; ijeeUnQyk/kZ 2%10% 32 dk vk/kk dh T;k jfod{kk dh mRdUnzrk dk eku nsrh gS 0-018984163 tks d{kk d T;kferh; dUnz ls eq[;ukfHk es# dh nwjh dk eq[; O;klk/kZ ls vuqikr gS] rFkk ijeeUnQyk/kZ dh dksT;k jfod{kk d xkS.k O;klk/kZ ,oa eq[; O;klk/kZ dk ijLij vuqikr gSA xkS.kO;klk/kZ 0-9998197845,oa eq[;O;klk/kZ 1d ijLij vUrj d vk/ks 0-0000901077333 dks eq[;O;klk/kZ rFkk xkS.kO;klk/kZ d vkSlr 1-9998197845 2 4331500 ;kstu 2pi esa tksM+s rks lw;Zfl)kUrh; jfod{kk d eq[;O;klk/kZ dk ;kstukRed eku Kkr fd;k tk ldrk gSA x.kuk bl izdkj gS % jfod{kk vkSlr O;klk/kZ 4331500 2pi 689379-636 ;kstu A bls eq[;O;klk/kZ 1 rFkk vkSlr O;klk/kZ 1-9998197845 2d ijLij vuqikr ls xqf.kr djsa rks nh?kZo`rh; lw;Zfl)kUrh; jfod{kk d eq[;O;kl dk ;kstukRed eku 689441-7600366 ;kstu izkIr gksrk gSA bls 861-105915 ls foHk djus ij HkwdUnz ls jfod{kkdUnz dh nwjh dk LFkwy eku fu%l`r gksrk gS %

689441-7600366 861-1059150464 800-64687512 ;kstu

;g HkwdUnz ls jfod{kkdUnz dh nwjh gSA lw;Zfl)kUrkuqlkj fo"kqorh; HkwO;klk/kZ 800 ;kstu gS] tks vk/kqfud eku esa 6378-197 fdyksehVj gS]vr% 0-646875 ;kstu dk eku 5157-37 ehVj gksuk pkfg;sA bldk vFkZ ;g gS fd HkwdUnz ls

jfod{kkdUnz dh nwjh fo"kqorh; HkwO;klk/kZ ls 5157 ehVj vf/kd gksuk pkfg;s] vFkkZr~ fo"kqor ij Hkwry ls 5157 ehVj Wapk dksbZ ioZr f'k[kj jfod{kk dk dUnz gksuk pkfg;s] D;ksafd yksn; fo"kqor ij jk';ksn; gksrk gSA fo"kqor ij yxHkx brus gh Waps nks f'k[kj gSa],d vhdk d dU;k ns'k esa rFkk nwljk nf{k.k vesfjdk esaA pwWafd lS)kfUrd jfod{kk ^nh?kZo`rh; vfHkpfdkdkj* gS] u fd 'kq) nh?kZo`kkdkj tSlk ekudj mijks LFkwy x.kuk dh xbZ gS] vr% &41-63 ehVj dh =qfV feyh gSA vhdk d dU;k ns'k esa 5199 ehVj Wapk ioZr gS ftldh rygVh esa ogkWa dh LFkkuh; vkfnoklh Hkk"kk esa es# uke dk uxj] es# uke dh tkfr vkSj es# uke dh Hkk"kk vkt Hkh fo|eku gSA bl tkfr dk gky esa bZlkbZ /keZ esa /kekZUrj.k djk;k x;k gS] ftld ikr vc mUgsa iknfj;ksa }kjk f'k{kk nh tk jgh gS fd es# tkfr bkby ls dU;k xbZ Fkh] ;|fi oSKkfud lk{; crykrs gSa fd dUnzh; vhdk d mlh iwohZ Hkkx esa gh yxHkx 40 yk[k o"kZ igys ekuo tkfr dk izknqHkkZo gqvk FkkA fdUrq blh oSKkfud rF; dk tc iqjk.kksa ,oa T;ksfr"k&fl)kUr d xzUFkksa esa o.kZu feyrk gS fd vkt ls 3893]111 lkSj o"kZ igys izy; d ikr orZeku egk;qx vkjEHk gqvk Fkk vkSj czk th ckjEckj es# ioZr ls gh ltZuk djrs gSa rks iqjk.kksa vkSj fl)kUrksa dks feF;k dgk tkrk gSA

yksn;lk/ku d mijks lw;Zfl)kUrh; lw= esa ijekfUr dk eku 'kwU; j[kus ij gh e/;jkf'k dk yksn;eku 300 iy gks ldrk gS] fdUrq ijekfUr dk eku 'kwU; lEHko ugha gSA mijks lw;Zfl)kUrh; lw= dks v'kq) dgus okys bl iz'u dk mkj ugha ns ldrs fd bl lw= }kjk HkwdUnz d cnys fo"kqorh; es# ij d{kkdUnz dh flf) gksrh gS ftldk ikSjkf.kd ,oa lS)kfUrd xzUFkksa esa fn;s x;s fooj.kksa ls rknkRE; gS] ftls la;ksx dgdj Vkyuk vuqfpr gS D;ksafd es# ioZr dh WapkbZ d ikWap iF`kd lS)kfUrd lw= bl ys[kd dks Kkr gSa ftuesa ls nks izLrqr ys[k esa fn;s x;s gSaA

es# dh HkkSxksfyd fLFkfr % lkfgfR;d izek.knsof"kZ ukjn us T;ksfr"k'kk dk Kku

lh/ks czk th ls izkIr fd;kA ukjn iqjk.k esa os es# ioZr d ckjs esa fy[krs gSaiwoZHkkx]v/;k; 3] ksd 41Hkwrys e/;xks es#% loZnsolekJ;%A vFkkZr~ es# Hkwryd e/; esa gSAJhen~ Hkkxor iqjk.k ,oa vU; iqjk.kksa esa Hkh ,slk gh o.kZu gSA ujifrt;p;kZ d ys[kd us fy[kk fd Hkwe/; esa es# d fLFkr gksus dh ckr os lqurs rks gSa fdUrq Hkwe/; esa mUgsa es# fn[kk ugha';rs u rqA ujifrt;p;kZ d HkkSxksfyd o.kZu ls Li"V gS fd Hkkjr ls ckgj dk Kku ujifr dfo dks ugha Fkk] vr% mUgsa es# ugha feykA fdUrq es# d Hkwe/; esa gksus dh ckr os Lohdkjrs gSaA lw;Zfl)kUr esa fuEuks ksd gS %

vusdjRufup;ks tkEcwune;ks fxfj%AHkwxksye/;xks es##Hk;= fofuxZr%34

ia- jkepUnz ik.Ms; us bldh lgh O;k[;k nh %vusd jRuksa d lewg ls ifjiw.kZ tkEcwun Lo.kZunh ls ;q Hkwxksy d e/; esa x;k gqvk rFkk iF`oh d nksuksa Hkkxmkj&nf{k.kesa fudyk gqvk es# ioZr gSA ctsZl us Hkh ,slk gh vFkZ fn;kA eq[; es# ioZr Hkwxksye/;js[kk ij fLFkr tEcw}hi d tkEcwun izns'k esa gS] tks HkwdUnz gksrs gq;s mkj rFkk nf{k.k /kzqoksa dh vksj Hkh fudyk gqvk gSlqes# rFkk des#A vkt Hkh ekm.V dU;k d izns'k esa tkEcwunh tkEcsth unh gS] tEcw}hi d ml dUnzh; izns'k esa tkfEc;k] eq&tkfEcd ^eq* vjch milxZ gS] ftEckcos] tkEcks ls dkaxks vkSj tkEcwu ls xScksu vkfn ns'k ml izns'k esa feyrs gSaA es# uke d vusd ioZrkfn rUtkfu;k] dU;k] bZFkh;ksfi;k vkSj lwMku esa gSa] ftuesa lcls egRoiw.kZ gS fo"kqor ij fLFkr dU;k ioZr dh rygVh esa fLFkr es# uxj] tks fl) djrk gS fd dU;k ioZr gh izkphu es# gS] vkSj nwljk egRoiw.kZ LFky gS izkxSfrgkfld dkWaL;;qxhu es# uxj tks nf{k.k lwMku esa fLFkr ,d ,slh fodflr vhdh lH;rk dh jkt/kkuh Fkk ftldh fyfi ius dh Hkwy dbZ yksx djrs gSaA fdUrq mkj /kzqo ij leqnz gS] ioZr ughaA vhdk esa fLFkr fo"kqorh; es# ioZr dks T;ksfr"kh; mkj /kzqo ekudj mlh izdkj ls v{kka'k&js[kka'k cuk;sa tk; tSls fd HkkSxksfyd /kzqoksa ls cukrs gSa vkSj ,sls ekufp= ij lalkj dh

d.Myh u{k=izos'k dkyksa esa cukbZ tk; rks iwjs lalkj dk lgh Qykns'k izkIr gksrk gSA ujifr& t;p;kZ us ,sls p dks ip dh laKk nh] tks deZp dk lcls cM+k Lo:i gS vkSj bls gh es#dfUnzr iF`ohp Hkh dgk tkuk pkfg;sA

es# jfod{kkdUnz gh ugha] lf`"VdUnz Hkh gSvHkhrd izLrqr ys[k esa jfod{kk&dUnz

d :i esa es# d xf.krh; ,oa ikSjkf.kd lk{;ksa dh ppkZ dh xbZ gSAiqjk.kksa esa es# dks lEiw.kZ l`f"V vkSj leLr yksdksa dk dUnz ekuk x;k gS] ftld f'k[kj ij cSBdj czk th l`f"V dh jpuk djrs gSaA czk.Miqjk.k d mijks vuq"k esa gh nsoxzgkuqdhrZu uked 22osa v/;k; esa egf"kZ osnO;kl th dk fuEuks opu gS %mkkuikniq=kslkS es

fl)kUrf'kjksef.k esa ugha gS bl fo"k; ij izLrqr ys[kd }kjk ,d iF`kd ys[k gS % Ayanamsha versus Precession, website www.jyotirvidya.wetpaint.comA fl)kUrf'kjksef.k esa tks gS] og Hkh fyf[kr lk{;ksa d vk/kkj ij izkphu dky esa lEikr&iqjLlj.k p dk lokZf/kd 'kq) eku gSA fdUrq ,d Hkh Hkkjrh; ok ikkR; ys[kd bldh ppkZ ugha djrk( lHkh ys[kd U;wVu ls igys kfUro`r rFkk UkkMh o`rksa d ijLij lEikr fcUnq d iqjLlj.k&p ij doy fgIikdl dks m)r` djrs gSa ftldk lEikrp 36000 o"kksZa dk gksus d dkj.k vR;Ur v'kq) FkkA;gkWa bl izl dh ppkZ doy ;g n'kkZus d fy;s dh xbZ gS fd ikSjkf.kd dky esa Hkh /kzqo d ?kw.kZu dk Kku _f"k;ksa dks FkkA vk/kqfud fodklokfn;ksa dks ;g fl) djus esa etk vkrk gS fd mud iwoZt Kku d {ks= esa vfodflr vkSj vlH; Fks] vr% izkphu xzUFkksa esa tks Kku gS mlij mudh f"V ugha tkrhAlw;Zfl)kUr dk yXulw= nh?kZdky ls T;ksfrf"k;ksa }kjk yksn;eku Kkr djus d fy;s iz;q gks jgk gS] fdUrq bl lw= esa l`f"V d es#dfUnzr gksus dk jgL; vkSj xf.krh; izek.k Nqik gS blij dksbZ /;ku ugha nsrk] D;ksafd lw{e x.kuk dh lS)kfUrd ifjikVh T;ksfrf"k;ksa us nh?kZdky ls R;kx j[kh gS vkSj vk/kqfud xf.krKksa dh lw;Zfl)kUr d fo"k; esa iwokZxzg mUgsa lw;Zfl)kUrh; lw{exf.kr le>us ugha nsrkA

es# dh WapkbZ dk nwljk lkSjlw= rhu izkjfEHkd jkf'k;ksa d tks yksn;eku lw;Zfl)kUrh; lw= }kjk ij fu%l`r fd;s x;s gSa]vc mudh tkWap ,d vU; fof/k }kjk djsaA yksn;eku dk lw;Zfl)kUrh; lw= HkwdfUnzd u gksdj es#dfUnzd gS]D;ksafd e/;jkf'k dk yksn; eku HkwdUnz ls fo"kqorh; HkwO;klk/kZ vkSj yxHkx 5157 ehVj nwj ij dUnz dh fLFkfr n'kkZrk gSAij es# ioZr ekm.V dU;k dh okLrfod WapkbZ 5199 ehVj gS]ftldk lw;Zfl)kUrh; eku 0-65209651 ;kstu gSA vr% HkwdUnz ls es# f'k[kj dh nwjh 800-65209651 ;kstu gSA jfod{kk d eq[; O;klk/kZ dk ;g 861-10029942073473 okWa Hkkx gS] ftls 300 iy d vkSlr eku esa Hkkx

nsus ij tks vYikUrj feyrk gS mls 300 iy esa U;wu djsa rks 299-65160852899272 iy feysxkA fo"kqor vFkok yk ij ;g kfUror` d fdl Hkkx dk mn;eku gS] vc ;g iz'u mBrk gSA iwjh jkf'k dk yksn;eku lgh vkdyu djus esa lgk;rk ugha djrk] D;ksafd jkf'k d vkjfEHkd vkSj vfUre Hkkxksa d mn;ekuksa esa cgqr vUrj jgrk gSA vr% 30 dh jkf'k d LFkku ij 0-001 dk yksn;eku Kkr djd 30000 ls xqf.kr djsa rks kfUro`r d fo'ks"k fcUnq ij yksn; dk 'kq) eku Kkr gks ldrk gSA 30000 ls xqf.kr djus dk dkj.k gS jkf'k d mn;eku ls rqY;rk esa lqfo/kkA e/;jkf'k d e/; esa] vFkkZr~ 45 d vklikl vHkh"V eku gksuk pkfg;s] fdUrq mlls dN vf/kd cqdk fn;k tk; rks nh?kZo`r curk gS]ftld eq[; rFkk xkS.k O;klksa dk vuqikr >qdko d dks.k dh dksT;k gksrh gSA0-078721 dh dksT;k jfod{kk esa bl >qdko d dkj.k cus nh?kZo`r d eq[; rFkk xkS.k O;klksa dk vuqikr nsrh gS]ftud ijLij vuqikr dks jfod{kkO;klk/kZ ls xqf.kr djus ij eq[; rFkk xkS.k O;klksa dk vUrj 5-188 fdyksehVj feyrk gS] tks es# ioZr dh WapkbZ ls doy 11 ehVj U;wu gS;g =qfV 16 vksa rd x.kuk dh lhek d dkj.k gSA bl izdkj ge ns[krs gSa fd lEiw.kZ jkf'k d LFkku ij NksVs [k.Mksa dh tkWap djus ij lw;Zfl)kUrh; yksn;lw= }kjk es# ioZr dh okLrfod WapkbZ fey tkrh gSA bl izksxzke dk fotqvy csfld VB6 dksM uhps fn;k tk jgk gSA ,d QkWeZ cukdj mlij dek.M cVu j[ksa] ftld dksM esa fuEuks Hkj nsa %DefDbl DPrivate Sub Command1_Click() dBhuj = 45.078 Q = CDec("57.295779513082320876798154814105") dM = 0.001Repeat:dLankod = Sin(dBhuj / Q) * Cos(24# / Q) / Cos((24# * Sin(dBhuj /

Q)) / Q)dLankoday =10#*Q*Atn(dLankod / Sqr(-dLankod * dLankod + 1#))dLankod2 = Sin((dBhuj + dM)/Q) * Cos(24#/Q) / Cos((24# * Sin((dBhuj + dM)/Q)) / Q)dLankoday2 = 10#*Q*Atn(dLankod2/ Sqr (-dLankod2*dLankod2+1#))Diff = (dLankoday2 - dLankoday) * 30# / dMDifference=CDec("299.65160852899271887423655116163")- Diff If Difference < 0.0000000001 Then GoTo Skip dBhuj = dBhuj + 0.000000001 dK = dK + 1 GoTo RepeatSkip: dHtMeru = 5496744.207 * (1# - Cos((dBhuj - 45#) / Q)) Debug.Print Diff; dBhuj; dHtMeru; dK; Difference; dMEnd Sub

m dksM esa ;fn dM dk eku 0-001 ls vf/kd djsa rks Qy esa LFkwyrktfur nks"k vk tk;xk] vkSj ;fn U;wu djsa rks 16 vksa dh x.ku&{kerk ls vf/kd l{ke dEI;wVj izksxzke dh vko';drk iM+sxh( Qy dh 'kq)rk fdruh gS bldh tkWap bl izksxzke esa Difference ls dh tk ldrh gSA bl izksxzke esa 220741 ckj dK x.kuk djus ij lgh Qy dh izkfIr gqbZA;g xf.kr fcuk dE;wVj d izkphudky esa ekuo gsrq lEHko ugha FkkA es#dfUnzr xf.kr ij vk/kkfjr ikSjkf.kd&lS)kfUrd xf.kr ftUgksaus fufeZr fd;k] os fuLlUnsg gh lk/kkj.k ekuo ugha gks ldrsA

jfod{kkO;klk/kZ dk lw;Zfl)kUrh; eku ysus ij gh lw= lgh dk;Z djrk gS] tks Di{kh; jfod{kkO;klk/kZ ls 27-2 xq.kk U;wu gSA bldk dkj.k ;g gS fd lw;Zfl)kUrh; jfod{kk vkSj Di{kh; jfod{kk ijLij fHkk gSa] ftldk izek.k gS lw;Zfl)kUrh; xf.kr dk ikyu djus ij T;ksfr"kh; Qykns'k dh lR;rkA Di{kh; lw;Z Hkwyksd d HkkSfrd fi.M gSa] rFkk lw;Zfl)kUrh; lw;Z Hkqoyksd d fnO; fcEc gSa tks T;ksfr"k dk Qy nsrs gSaA okLrfod lw;Znso rks Loyksd esa gSaA lkSjiqjk.k esa lw;Z dks f=ekxhZ dgk x;k gS % rhu yksdksa esa rhu ekxksZa ij pyus okys rhu lw;Z] tks ,d gh lw;Znso d fofHkk :i gSa! fu"d"kZ ;g gS fd lw;Zfl)kUrh; yksn; lw= es#dfUnzd gSAes#ioZr dh WapkbZ vkSj fo"kqorh; HkwO;klk/kZ dks gVkus ij lw= v'kq) gks tkrk gSAlgksa o"kksZa ls iwjs fo us bl vn~Hkqr es#dfUnzd lw= dk iz;ksx yXuku;u esa fd;k vkSj vkt Hkh dj jgs gSa] fdUrq bl lw= esa Nqis es# d xw

^ijekfUr HkqtT;k* dh dksT;k ;k |qT;kA bls yksn;lw= esa ^dksT;kij HkqtT;k* fy[kk x;k gSAvr% iwjs lw= dks bl izdkj fy[ksa %yksn;T;kHkqtT;k ijdksT;kdksT;kij HkqtT;kHkqtT;k dksT;k 24 dksT;k24 HkqtT;k

Hkqt dk eku 30 j[kus ij izFke jkf'k es"k dk yksn;eku izkIr gksxkAHkqt dk eku 60 izFke ,oa f}rh; jkf'k;ksa dk lfEefyr yksn; eku nsxk]ftlesa ls es"k dk mn;eku U;wu djus ij o`"k dk yksn;eku izkIr gksxkA Hkqt dk eku 90 gks rks izkIr Qy 90 vFkok 900 iy gksxk] ftlesa ls es"k rFkk o`"k d yksn;ekuksa dks U;wu djus ij feFkqu dk yksn;eku feysxkA o`r d vU; rhu iknksa d yksn;eku izFke ikn d rqY; gh gksaxsA jkf'k;ksa d ijEijkxr iykRed LFkwy ekuksa d vuqlkj fuEuks fp= ckjg jkf'k;ksa d yksn;eku Li"V djrk gS %

'kq) lw= d }kjk u doy jkf'k;ksa d 'kq) yksn;eku izkIr gksrs gSa]cfYd pjlk/ku djd b"VLFkkuh; 'kq) mn;eku Hkh feyrs gSaA bruk gh ugha]yXuku;u dh izf;k esa vkjfEHkd ,oa vfUre v'kq)vFkkZr~ viw.kZjkf'k[k.Mksa d [k.M &mn;eku Hkh 'kq)rk lfgr Kkr fd;s tk ldrs gSaAmnkgj.kkFkZ];fn v'kq) jkf'k esa vkjfEHkd 12 dk mn;eku Kkr djuk gS rks mijks lw= esa Hkqt d LFkku ij 12 j[kusij 'kq)eku feysxk] tcfd iwjh jkf'k d vkSlr }kjk x.kuk djus ij v'kq) eku feysxk] D;ksafd ;g vkSlr eku jkf'ke/; gsrq gh lgh gSAn'kelk/ku esa Hkh 'kq) izf;k dk iz;ksx fd;k tkuk pkfg;sA,slk djus ij "k"Va'k oxZ rd leLr oxZ lgh cusaxsA

mijks fp= esa lHkh ckjg jkf'k;kWa leku 30 dh gSa]fdUrq mud LFkwy yksn;eku e'k% 278] 299 rFkk 323 iyksa d gSaA bls cnydj

fuEu izdkj ls Hkh iznf'kZr fd;k tk ldrk gS %

bl nwljs fp= esa lHkh ckjg Hkkx leku dks.k d ugha gSa] fdUrq mud yksn;eku leku gSa % 300 iyksa dA leku dkyeku d foHkkxksa esa fo'ks"krk ;g gS fd mud }kjk cuk;s x;s {ks=Qy ,dleku gSa]tks diyj }kjk [kksts x;s fu;eksa d v gSa % leku dky esa leku {ks=A fp= ns[kus ls Hkh Li"V gS fd dks.k U;wu gks rks yEckbZ c

dfBu gS] vuUr lekdyksa dk Hkh iqu% lekdy djuk iM+sxk vkSj bld fy;s tfVy dEI;wVj izksxzkeksa dh vko';drk iM+sxhA fdUrq ets dh ckr gS fd lw;Zfl)kUr esa yksn;ekuksa ,oa b"VLFkkuh; mn;ekuksa d lw= brus ljy gSa fd fcuk ;U=ksa dh lgk;rk d Hkh vko';d 'kq)rk d lkFk x.kuk lEHko gSA bruk gh ugha] ;fn lax.kd dh lgk;rk yh tk; rks lw;Zfl)kUrh; lw= dh tkWap }kjk es#dfUnzd ikSjkf.kd& lS)kfUrd l`f"VfoKku dh lPpkbZ d lk{; Hkh lqLi"V gks tkrs gSa] tks bu ljy lw=ksa dh lPpkbZ d lk{; gSaA ;fn ;s ljy lw= LFkwy gksrs rks budh lgk;rk ls es# dh WapkbZ dh x.kuk lEHko ugha gks ikrhA ljyrk d lkFk&lkFk iw.kZ 'kq)rk lw;Zfl)kUrh; lw=ksa d fnO; gksus dk izek.k gSA izkphu _f"k;ksa us ckjEckj blij cy fn;k fd es# gh xzgd{kkvksa ,oa l`f"V dk dUnz gS]fdUrq dfy;qxh uDdkj[kkuksa esa mudh vkokt rwrh cudj jg xbZA fdlh izkphu ok vk/kqfud fo}ku us lw=ksa dh tkWap dk iz;kl ugha fd;kA vc ;g ns[ksa fd yksn;eku dks T;kferh; :i ls dls ifjHkkf"kr djsaA fuEuks fp= esa /kzqo Z ls vkus okyh v{kka'kjs[kk kfUro`r ,oa fo"kqor o`r dks e'k% H rFkk fcUnqvksa ij dkVrh gSA kfUro`r ,oa fo"kqoro`r dk fuj;u lEikr fcUnq E gSA kfUro`r dk EH [k.M izFke jkf'k es"k gS] ftldk yksn;eku E pki d mn;

dk eku gS] tks fo"kqor o`r dk Hkkx gSAVkWyseh us bldh Li"V O;k[;k vyektsLV ;g ckn dk 'kCn gS tks xzhd izdfr esa vjch milxZ

yxkdj cuk;k x;k] xzUFk dk ewy uke Fkk , eFkefrd lqarf{kl~ Mathematical Syntaxisd cqd&1 d vfUre v/;k; esa nh gS ftlls vk/kqfud oSKkfud Hkh lger gSa % ns[ksa A History of Ancient Mathematical Astronomy by Otto Neugebauer, VI-B1,4. Spherical Coordinates, p.1080 : At sphaera recta the north pole N lies in the horizon and the equator is perpendicular

to the horizon. Since the meridian is also at sphaera obliqua perpendicular to the equator the meridian at sphaera obliqua plays the role of horizon at sphaera recta.AHkkjrh; Vhdkvksa dh O;k[;k;sa Hkh ,slh gh gSaA yksn; d ckjs esa VkWyseh d v/;k; dk 'kh"kZd gS pi* vFkkZr~ On rising-times (ascensions) at sphaera rectafo"kqor ij mn;eku] ftlesa yksn; dh ifjHkk"kk lgh gS fdUrq xf.kr lw;Zfl)kUrh; ugha gSA lw;Zfl)kUr esa lw;Z dh ijekfUr dk eku 24iw.kkZ gS] tcfd VkWyseh dk eku gS 23%51%20Ablls Hkh vf/kd vUrj gS jkf'k;ksa d mn;eku Kkr djus dh fof/k esa]ftl dkj.k Qy dkQh vUrj j[krs gSa % VkWyseh d rhuksa yksn;eku gSa e'k% 27%50(29%54(rFkk 32%16] ftUgsa n'kxqf.kr djus ij iykRed eku izkIr gksaxs %278%50] 299]rFkk 322%40 iyA lw;Z& fl)kUrh; eku gSa e'k% 278-38] 299-65] rFkk 321-96574 iyAlw;Zfl)kUrh; e/;jkf'k o`"k dk yksn;eku 300 iy ls yxHkx 0-35 iy dh U;wurk d dkj.k jfod{kkdUnz HkwdUnz ls 800-65 ;kstu dh nwjh ij fl) gqvk Fkk] fdUrq VkWyseh d xf.kr esa ;g U;wurk 0-35 iy dh ctk; 1 iy dh gS300 iy ls 1 iy U;wu]vr% jfod{kk dk ;kstukRed eku leku eku ysa rks VkWyseh dk jfod{kkdUnz HkwdUnz ls 800-35 ;kstu dh vis{kk1 0-3484 2-87 xq.kk vf/kd nwjh ij fLFkr gksxk] vFkkZr~ HkwdUnz ls 2298-14 ;kstu dh nwjh ij! ;g Hkh "VO; gS fd xzgd{kkvksa dk lkis{k ;k fujis{k vkdkj;kstukRed ekuVkWyseh dks fcYdy Hkh Kkr ugha FkkAikkR; ^fo}kuksa* dh ftn gS fd dWkilfudl ls igys bldk Kku fdlh dks ugha Fkk]tcfd lw;Zfl)kUr esa xzgd{kkvksa dk ;kstukRed eku fn;k x;k gS vkSj ij fn[kk;k x;k gS fd jfod{kk d lw;Zfl)kUrh; eku d vk/kkj ij es# dh WapkbZ izkIr dh tk ldrh gSA ;gkWa leL;k ;g gS fd lw;Zfl)kUrh; jfod{kk d O;klk/kZ dk eku 55 yk[k fdyksehVj ls Hkh de gS]tcfd HkkSfrd lw;Zd{kk dk O;klk/kZ 1496 yk[k fdyksehVj gSAvr% lw;Zfl)kUrh; d{kk HkkSfrd d{kk ls dbZ xq.kk NksVh gSAlHkh xzgksa esa ;g vUrj

fuEuks gS % cq/k dh lkSji{kh; d{kk Di{kh; d{kk ls 43-747 xq.kh NksVh gS] 'kq dh 32-002 xq.kh]lw;Z 27-218]ey 22-050]cg`Lifr 11-939 ] ,oa 'kfu dh 8-811 xq.khs NksVh gS!T;ksa &T;ksa ge nwjLFk xzgksa dh vksj c

VkWyseh d vuqlkj ,jkrksLFkhuht vkSj fgIikdl Hkh brus eku dk gh iz;ksx djrs FksA fu"d"kZ d :i esa VkWyseh us 360 d 1183 Hkkx dks lw;Z dh ijekfUr dk nksxquk ekuk vkSj vius xzUFk esa loZ= iz;q fd;kA ,jkrksLFkhuht vkSj fgIikdl ijekfUr dk dkSu lk eku iz;q djrs Fks bldk ,dek= izek.k VkWyseh gSA VkWyseh us vusd LFkyksa ij ,d lPps oSKkfud dh rjg Lo;a i;Zos{k.k djd fu"d"kZ fudkyus dh Mhsa gkWadh gS]ysfdu fgIikdl dh rkjklwph dks pqjkdj VkWyseh us futh i;Zos{k.k dk urhtk ?kksf"kr dj fn;k Fkk] ftlij nks lgkfCn;ksa rd ifeh txr fokl djrk jgk] fdUrq chaloh 'krh esa ;g fl) gks x;k fd m lwph esa rkjkvksa dh tks fLFkfr;kWa nh xbZ gSa os VkWyseh ls rhu 'krh iwoZ fgIikdl d dky d gSa vkSj fgIikdl dh [kkstksa dks VkWyseh us vius uke ij izpkfjr fd;k ,slk vc lkjs oSKkfud ekurs gSaA vr% ijekfUr d ekeys esa Hkh VkWyseh }kjk futh i;Zos{k.k djus d nkos dh tkWap gksuh pkfg;sA VkWyseh us lw;Z dh ijekfUr dk eku 23%51%20 crk;k] fdUrq vk/kqfud HkkSfrdfoKku d lw=ksa }kjk ;g eku bZlkiwoZ 1381 dk fl) gksrk gS!ftUgsa ljy lk{; pkfg;s os www.cybersky.com osclkbV ls eqr dk 'ks;jos;j MkmuyksM djd bl ckr dh tkWap dj ldrs gSa & LFkku vysDtsf.M;k pqusa vkSj twu d vUr esa e/;k dk le; ysa] ml fnu lw;Z dk MkVk [kksyus ij kfUr Declination dk mijks eku gh vk;xkA vk'p;Z dh ckr gS fd bZlkiwoZ 1381 dk vkWadM+k VkWyseh us bZlk d 150 o"kZ mijkUr ^futh i;Zos{k.k* }kjk izkIr fd;k] tc ijekfUr dk eku 652 fodyk ?kVdj 23%40%28 jg x;k Fkk! VkWyseh dk nkok Fkk fd mld }kjk i;Zos{k.k ls izkIr eku 23%50%20 ,oa 23%52%30 d chp gh Fks] ftl dkj.k mlus vkSlreku 23%51%20 23%51%25 vkSlr Fkk Lohdr fd;k] ftlesa mld 'kCnksa esa 150 ls vf/kd dh =qfV lEHko ugha FkhA fdUrq mlus ijekfUr dk tks eku fn;k mlesa =qfV 652 dh Fkh] vr% lEHkkouk blh ckr dh gS fd Mh ekjus dh chekjh d dkj.k mlus izkphu feJ]

eslksiksVkfe;k ;k Hkkjr d fdlh ksr ls ijekfUr dk eku pqjk;kA bl lUnHkZ esa ;g "VO; gS fd tks yksx lw;Zfl)kUr dks i;Zos{k.k ij vk/kkfjr Di{kh; xzUFk ekurs gSa vkSj vHkkSfrd xzgnsoksa d lkSji{kh; xf.kr dh lEHkkouk dks ugha Lohdkjrs mUgsa ugha Hkwyuk pkfg;s fd lw;Zfl)kUr dh ijekfUr bZlkiwoZ 2760 dh Di{kh; ijekfUr d rqY; Fkh! VkWyseh us u rks i;Zos{k.k }kjk ijekfUr dk eku izkIr fd;k]vkSj u gh iwoZdky d fdlh i;Zos{kd us ;g eku [kkstk FkkA;g lw;Zfl)kUrh; ijekfUr dk gh fodr :i Fkk ftldk izek.k VkWyseh d gh xzUFk vyektsLV esa gSAVkWyseh us ijekfUr dk tks eku iz;q fd;k og mud rFkkdfFkr^i;Zos{k.k*dk vkSlr eku 23%51%25 u gksdj 23%51%20 Fkk] ftldk dkj.k os Lo;a dgrs gSa %dd vkSj edj d chp lw;Z d v{kka'k esa tks vUrj gksrk gS og ijekfUr dk nksxquk gksrk gS tks mud 'kCnksa esa 360dk 1183okWa Hkkx FkkAx.kuk djus ij ;g 23%51%19-52 fudyrk gS]ftls VkWyseh us 23%51%20fy[kkAvr% VkWyseh }kjk iz;q eku 'kfr;ksa iwoZ ls pys vk jgs iw.kkZksa d vuqikr dh x.kuiz.kkyh in vk/kkfjr Fkk ftls ^js'kuy uEcj* dgk tkrk gSA ijekfUr dk nksxquk] vFkkZr~ dd vkSj edj d chp lw;Z d v{kka'k dk vUrj Fkk 360 11 83 ( lw;Z& fl)kUrh; ijekfUr dks bl i)fr esa fy[kk tk; rks 360 11 82-5 fy[kuk iM+sxk tks n'keyo d dkj.k ;ouksa dks jkl ugha vkrkA vr% fo"kqor ls lw;Z fdruk mkj vkSj nf{k.k

foLFkkiu djrs gSa bls ;fn v{kka'ko`r d vuqikr esa n'kkZ;k tk; rks lw;Zfl)kUrh; ijekfUr dks LFkwy :i ls 1183 gh

fy[kuk iM+sxkA VkWyseh us ijekfUr dk eku 23%51%20 crk;k]mlh dks vk/kkj cukdj yksn; eku Kkr djus dh VkWyseh dh fof/k dh tkWap djsaA Vwej us VkWyseh dk fuEuks 'kCnksa esa vuqokn fn;k

gS] ftls lqLi"V djus d fy;s bVSfyDl esa miifk izLrqr ys[kd us tksM+h gSAT;kfi.M 2ZB : T;kfi.M 2BA= (T;kfi.M 2ZH : T;kfi.M 2H) (T;kfi.M 2E : T;kfi.M 2EA)fdUrq 2ZB = 132%17%20 180& 2BA( mkj /kzqo ls fo"kqor 90 gS rFkk mlesa ijekfUr BA U;wu djsa rks ZB feyrk gSvr% bldk T;kfi.M 109%44%53132%17%20 d vk/ks dh T;k dks nksxquk djd Qy dks 60 xq.kk djd dykRed cuk;kA pwWafd 2BA f}xqf.kr ijekfUr 47%42%40] vr% bldk T;kfi.M 48%31%55 ijekfUrT;k dk nksxquk djd Qy dks 60 xq.kk djd dykRed cuk;kA2ZH = 156%40%01 180& 2H( 30 ij kfUr dk eku gS H ftls Kkr djus dk lw= gS % ^30 dh T;k ijekfUrT;k* d xq.kuQy dk pkiA Chord dks Crdfy[ksa %Crd.2ZH 117%31%15 156%40%01 d vk/ks dh T;k d nksxqus dks 60 xq.kk djd dykRed cuk;kA2H=30 ij kfUr dk nksxquk 23%19%59Crd.2H 24%15%57 23%19%59d vk/ks dh T;k d nksxqus dks 60 xq.kk djd dykRed cuk;kAvc mijks ewy iz'u dks ,sls fy[ksa %T;kfi.M 2E T;kfi.M 2EA = (T;kfi.M 2ZB T;kfi.M 2BA )(T;kfi.M 2ZH T;kfi.M 2H)109%44%53 48%31%55117%31%15 24%15%57 54%52%26 117%31%15vfUre gy ^T;kfi.M 2E T;kfi.M 2EA = 54%52%26 117%31%15* dks fuEujhfr ls fy[ksa % T;kfi.M 2E T;kfi.M 2EA = 56%01%53 120pwWafd 2EA180]vr% T;kfi.M 2EA120 90 dh T;k 1 gS ftldk dykRed eku 60 gS] vr% 180 dk T;kfi.M bldk nksxquk 120 gksxkAQyLo:i ^T;kfi.M 2E* 56%01%5356%01%53 d vk/ks dk pki ^2E* dk eku gS 27%50%06 VkWyseh 27%50 crykrs gSaAvc lw;Zfl)kUrh;

lw= esa VkWyseh dh ijekfUr Mkydj x.kuk djsa % [(Sin 30 Cos 23:51:20) Cos(23:51:20 Sin 30)]mijks dk pki ysus ij Qy 27%51%50-56 va'kkRed yksn;eku izkIr gksrk gS ftls n'k xqf.kr djus ij izFke jkf'k dk iykRed yksn; eku izkIr gksrk gS]tks VkWyseh d 27%50%06 ls 104vf/kd gSAxksy&xf.kr d vuqlkj VkWyseh dh fof/k yxHkx lgh gSA rc D;k lw;Zfl)kUrh; lw= xyr gS tks fHkk Qy crk jgk gS\m rFkkdfFkr =qfV dks jfod{kk&O;klk/kZ d vuqikr esa cnydj ns[ksa % nksuksa va'kkRed yksn; ekuksa dh T;k dk vuqikr 1$1041-76 feyrk gSAvFkkZr~ T;k esa rFkkdfFkr =qfV dh ek=k jfo& d{kkO;klk/kZ dk 1042 okWa Hkkx gSA ij ge ns[k pqd gSa fd HkwO;klk/kZ ,oa es# dh WapkbZ dk ;ksx djsa rks jfod{kkO;klk/kZ dk 861 okWa Hkkx gksrk gSA izk;% mruk gh eku bl ckj Hkh ikrs gSa %;fn ekusa fd VkWyseh dk jfod{kkO;klk/kZ lw;Zfl)kUrh; eku d rqY; Fkk rks m rFkkdfFkr =qfV jfo& d{kkdUnz dks HkwdUnz ls jfod{kkO;klk/kZ 1042 dh nwjh ij foLFkkfir djsxhA lw;Zfl)kUrh; jfod{kk dk O;klk/kZ 689441-7600366 ;kstu dks 1041-763157 ls foHk djsa rks ;g foLFkkiu 661-8 ;kstu dk fudyrk gSA ;g es# lfgr HkwO;klk/kZ d cjkcj800-65 ;kstu rks ugha] fdUrq LFkwy :i ls rqY; gSAvUrj dk dkj.k ;g gS fd geus doy izFke jkf'k d yksn;eku d vk/kkj ij m x.kuk dhAe/;jkf'k dk yksn; eku VkWyseh 299 iy crykrs gSa] ftls HkwdfUnzd ekusa rks lw;Zfl)kUrh; jfod{kkdUnz HkwdUnz ls jfod{kkO;klk/kZ d 505-782 okWa Hkkx rqY; nwjh ij foLFkkfir gksuk pkfg;sArr`h; jkf'k dk yksn;eku VkWyseh d vuqlkj 322-666667 iy gS] ftldk lw;Zfl)kUrh; eku ls rqyuk djsa rks jfod{kkdUnz dk HkwdUnz ls foLFkkiu jfod{kkO;klk/kZ dk 514-89okWa Hkkx feyrk gSA1041-76]505-78 ,oa 514-89 dk vkSlr gS 687-48] tks lw;Zfl)kUrh; vuqikr 861-1 d vf/kd fudV gSA rhuksa jkf'k;ksa d yksn;ekuksa esa rhu rjg d vuqikr feyrs gSa] ftlls Li"V gS fd VkWyseh dh fof/k LFkwy gS vkSj HkwdfUnzd ugha gS] vU;Fkk izR;sd ekeys esa i`Fkd ifj.kke ugha feyrsAbldk dkj.k ;g gS fd

VkWyseh us iF`oh dks 'kq) xksy ekuk]tks xyr gSA vr% m xf.kr esa ZH, H, ZB ,AB v{kka'kh; pkiksa dh yEckbZ kfUro`rh; pki EH, BH rFkk fo"kqorh; pki E, A ls U;wu gksuk pkfg;sA

fdUrq bl x.kuk ls bruk Li"V gks tkrk gS fd VkWyseh dk xf.kr yxHkx dkepykm rks Fkk fdUrq es#dfUnzr u gksdj LFkwy :i ls HkwdfUnzr Fkk] tSlk fd vyektsLV esa Lohdkjk Hkh x;k gSA vr% VkWyseh dks lw;Zfl)kUrh; xf.kr dk ksr crykuk ljklj xyr gSArF; foijhr gS %jkf'k;ksa d mn;ekuksa d lw= fl) djrs gSa fd VkWyseh jfod{kkdUnz HkwdUnz dks gh ekurs Fks]ij izR;sd xzg dh d{kk os i`Fkd&iF`kd nsrs gSa]ftudh Hkw& dUnz ls nwjh mRdUnzrk eUnQyk/kZT;k dh vuqikrh gksrh gSA blh dkj.k VkWyseh xzgd{kkvksa d lkis{k ok fujis{k eku ij dN Hkh dgus ls drjk x;sA dksbZ fl)kUr vius ikWao ij [kM+k gksrk gS rks mlesa ,slh xEHkhj folfr;kWa ugha gksrhAdgha dk bZaV dgha dk jksM+k ysdj csesy cSlkf[k;ksa d cyij tks fl)kUr [kM+k fd;k tkrk gS og xzgksa dk dkepyk xf.kr Hkys gh ns ns] xzgpkj dh lS)kfUrd O;k[;k djus esa loZFkk vleFkZ jgrk gSA VkWyseh HkkSfrdoknh Fks] T;ksfr"k

esa Di{k dks ekurs Fks] fdUrq HkkSfrd fl)kUr ugha ns ik;s ftld fy;s ife dks U;wVu dh ckV tksguh iM+hA T;ksfr"k esa HkkSfrdokn dks izJ; nsus dk nq"ifj.kke ;g gqvk fd HkkSfrdh dk fodkl gksus ij T;ksfr"k dks R;kx fn;k x;kA bld foijhr vHkkSfrd osn&foKku d vHkkSfrd v ^T;ksfr"k* dk fl)kUr gkssus d dkj.k lw;Zfl)kUr lnk ls T;ksfr"k dk lS)kfUrd vk/kkj jgk gSA HkkSfrdfoKku d vk/kkj ij lw;Z fl)kUr dks rkSyus dh ps"Vk gh leL;kvksa dh tM+ gSA izLrqr ys[k esa tks izek.k fn;s x;s gSa os bruk fl) djus d fy;s i;kZIr gSa fd es#dfUnzd [kxksyfoKku iqjk.kdkjksa dh cdokl ugha Fkk]bld ihNs _f"k;ksa dk fnO; xf.kr Fkk ftldk iqufuekZ.k ,d pqukSrh gSAlw;Zfl)kUr ij vk/kqfud HkkSfrd& oknh foKku Fkksiu s dh ps"Vk djus okyksa dks igys lw;Zfl)kUr dk xwus dk iz;kl djuk pkfg;s] tks lw;Zfl)kUr d vfUre ksd d vuqlkj vR;n~Hkqrre~ yksd jgL;e~ cz& lfEere~ gSA tks lw;Zfl)kUr dk xzgxf.kr ugha tkurs os bls v'kq) ;k ^vkmV&vWo&MsV* dgus esa yTtk dk Hkh vuqHko ugha djrs!