Sterrekunde

Hoe wissel die voorkoms van die analemma met die breedtegraad

Hoe wissel die voorkoms van die analemma met die breedtegraad


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Hoe wissel die voorkoms van 'n analemma met die breedtegraad?

Dit is wat ek beskou as 'n definisie van 'n analemma: as die son se posisie elke dag om die middaguur (sê UTC) uitgestippel of gefotografeer word vanaf 'n regs suidelike rigting (in die noordelike halfrond), vorm dit 'n figuur van agt vorm soos in die prentjie.

Foto's wys dit gewoonlik met die lang as skuins. My vraag is, as ons aanneem dat die hoek verband hou met die breedtegraad van die kamera, hoe wissel hierdie hoek namate die kamera van die ewenaar na die paal beweeg word, en waarom?


Analemma is 'n diagram wat die afwyking van die son van sy gemiddelde beweging in die lug toon, gesien vanaf 'n vaste plek op die aarde. Let daarop dat dit niks oor tyd sê nie; dit kan enige vaste tyd wees. Analemmas wat op verskillende tye van die dag geskep word, het effens verskillende vorms. Kyk byvoorbeeld na die sonanalemmas wat op verskillende tye op dieselfde plek geneem word.

Son-analemma om 07:00 UTC deur Anthony Ayiomamitis, van solar-center.stanford.edu

Sonanalemma om 1400 UTC deur Anthony Ayiomamitis, van solar-center.stanford.edu

Die beste manier om die effek van die breedtegraad op die vorm van die analemma te verstaan, is om die effek van die aksiale kanteling van die aarde op die vorm van die analemma te oorweeg.

As die baan van die aarde ellipties was, maar die as nie gekantel was nie, sou die analemmakurwe ovaalvormig wees. By die ewenaar sou hierdie lyn 'n reguit lyn wees wat strek van links na regs of van Wes na Oost.

Die 23,5 grade aksiale kanteling van die aarde beïnvloed die oënskynlike posisie van die son in die lug - soos die jaar vorder en die aarde op 'n skuins as draai om die son, draai dit asof die son op en af ​​beweeg (Noord-Suid) ) in die lug. Dit het tot gevolg dat die twee lusse van figuur 8 gegenereer word.

Dit is reg dat die kanteling van die analemma met die breedtegraad wissel. Waarnemers in die Noordelike Halfrond sal 'n analemmakurwe kry met die breër lus aan die onderkant. Dit keer om vir waarnemers in die Suidelike Halfrond, waar die breër lus bo-aan die kromme is. By ewenaar lê die anlaemma aan sy kant. By die noordpool sou slegs die bokant van die analemma sigbaar wees, terwyl dit die teenoorgestelde is aan die suidpool.


Ek dink dat die antwoord is dat die analemma altyd vertikaal sal wees, reghoekig met die ewenaar, as dit teen die middag gefotografeer word. Die skynbare helling van foto's is te wyte aan perspektief en word op 'n ander tyd van die dag geneem, nie teen die middaguur nie.

By die ewenaar sal die analemma direk bo-oor die equinoxes wees, en hiervan af deur die hoek van die ekliptika op die sonstilstand.

Aan die pole sal die analemma op die horison gesentreer wees; die boonste helfte gee die lang tydperk sonder nag in die somer, en die verduisterde helfte van die lang winters sonder daglig.


Dit is 'n effek wat veroorsaak word deur die neiging van die presisie-as. Dit neem ongeveer 23 000 jaar om hierdie as te voltooi. As ons so lank kon lewe, sou ons die anemale in die lug sien draai


29 Desember 2006

Die laaste paar jaar woon ek aan die oostekant van 'n eiland met 'n bergagtige binneland, en mis ek een van die belangrikste gebeurtenisse ter wêreld. Ongeveer 6:30 op 'n oggend, nie lank gelede nie, het ek die Son bo die horison dopgehou om die kruin van Mauna Kea te verlig, gevolg deur 'n sagte sneeustorting teen die hange af en in die volle daglig. Toe ons omstreeks 05:45 die aand begin, na 'n rit van twee uur en 'n reünie met familielede, ontspan ons almal op 'n marmer-lanai-uitkrag oor getypoele terwyl die son sy tog voltooi en vervaag. Lank nadat die boonste ledemaat van die Son verdwyn het, het die wolke hul ware, fyn skakerings ontmasker, gewoonlik oorweldig deur die direkte glans van die son.

Om sonsopkoms en sonsondergang op dieselfde dag te sien, is miskien nie so 'n groot saak nie, behalwe dat dit een van die klassieke voorbeelde van gebeure is wat ons as vanselfsprekend beskou. In werklikheid word sonsopkoms so vanselfsprekend aanvaar dat sonsopkoms 'n dikwels genoemde definisie van die Bayesiese afleiding is. Net daar, met die fases van die maan, gaan die toenemende veranderinge in die daaglikse beweging van die son voort met hul dans, en wag dat ons 'n dag sal sien.

Gister was een daarvan - die wintersonstilstand.

Die gewone beskrywing as die kortste dag en langste nag van die jaar is so ver as wat dit geld, maar kom nie aan die moere en boute daarvan nie. Dit vertoon ook 'n sekere chauvanisme van die halfrond, want ons winterstilstand is die somer (en die langste dag van die jaar) vir diegene in die suide. Hoe dit ook al sy, die aarde is in Desember naby sy naaste plek aan die son op sy baan. Die werklike naaste punt (perihelion) kom in Januarie, dus die koue weer en kort dae het 'n ander oorsaak as afstand van die vuur.

Alhoewel ons die oorsaak van hierdie verskynsel hieronder kan ondersoek, is die voorkoms waarskynlik die beste plek om te begin. Die sonstilstand in Desember is die kortste dag van die jaar vir waarnemers op die noordelike halfrond, maar dit is nie die vroegste sonsopkoms of die jongste sonsondergang nie. Dit kom voor op twee verskillende datums wat wissel volgens u breedtegraad, maar dikwels in November en Januarie. Wat wel op die wintersonstilstand gebeur, is dat die son op sy verste noordpunt op die horison opkom, maak nie saak waar jy is nie. Terwyl die son wel in die Ooste opkom en in die Weste sak, val dit nie altyd presies op daardie hoofrigtings nie.

Noukeurige waarneming van die opkoms en ondergang van die son, gemeet aan vaste punte soos heuwels of klippe, sorg vir uiters akkurate kalenders, en sulke plekke word gereeld in pare in heel Europa aangetref. E.C. Krupp het onder andere uitstekende foto's en vertellings oor megalitiese waarnemings in sy boeke. Sodra u 'n goeie aantal waarnemings het, kan u relatiewe gemak bouplekke soos Stonehenge, Newgrange en baie Suid- en Sentraal-Amerikaanse terreine bereik om ooreen te kom met die veranderinge van hierdie stygings en instellings. Nadat u die peiling (rigting op die horison, wat nie noodwendig met 'n kompas verband hou nie) bepaal het vir hierdie seisoenale sonsopkoms en sonsondergange, is u redelik gereed vir 'n gegewe plek, aangesien dit elke jaar weer sal voorkom.

Met satellietfoto's van ons 'Blue Marble' is ons deesdae gewoond aan hemelse gebeure so esoteries dat dit amper abstrak is, eerder as waarnemend. Die meting van die son se posisie ten opsigte van die sterre is die manier om die 'dag' van die sonstilstand te bepaal, alhoewel dit soos die volmaan is - iets wat ons toeskryf aan 'n hele dag wat net 'n oomblik aanhou. In hierdie geval is die oomblik wanneer die son die verste noordvlek in die lug bereik, wat nie alle waarnemers sal kan sien nie (dit kan byvoorbeeld vir sommige gedurende die nag wees). Net om dit lastiger te maak, is dit redelik moeilik om albei gelyktydig te sien as u die son se posisie aan die sterre meet, en gebruik dan die laers om op te staan ​​of te sak.

Die geleidelik gekantelde as en die herhalende jaarlikse rewolusie van die Aarde bring die Son op verskillende tye van die jaar direk oorhoofs na verskillende kolle op die aarde, en dan verander die daaglikse rotasie van die Aarde daardie plekke in breedteringe. Die breedtegraad waar die son bo-op die sonstilstand in Desember staan, word die Steenbokskeerkring genoem, en die eweknie van Junie is die Kreefskeerkring. Verdeel die verskil tussen die twee en dan kry u die ewenaar, wat in die ekwinoxe speel, in 'n latere berig bespreek.

Die oorsaak van al hierdie seisoenale variasies is die kanteling van die Aarde se as wat alomteenwoordig is 23 en grade van die loodregte af verander, gemeet vanaf die plat vlak van sy baan. As die Aarde se as op die Noordpool die stok van 'n karamelappel is, wys die stok op dieselfde plek in die ruimte, ongeag waar die aarde rondom die son is. As die son dus 'n naeltjie-lemoen (vir ons vakansie-geur) is en hy sowel as die karamelappel op die tafel sit, wys die karamel-appelstokkie in Desember skuins weg van die lemoen af. Op die Junie-sonstilstand wys die stokkie skuins na die lemoen, regoor die bokant daarvan.

En natuurlik vier die viering van hierdie tyd van die jaar enige historiese verslae en enige hedendaagse godsdienste, waarvan die meeste die viering in hul kalenders ondergeskryf het. Sien Guy Ottewell se Astronomical Companion vir meer daaroor. Gelukkige wintersonstilstand-ek gaan strand toe.


Die langste nag.

Te veel vrye tyd en Sky Safari lei my na hierdie drie sinne:

Die vroegste sonsondergang op my breedtegraad van 44º 25 '07 "vind op 9 Desember plaas.

Die jongste sonsopkoms vind eers 2 Januarie plaas.

Die langste nag kom ongeveer halfpad tussen die datums voor, wat op 21 Desember die sonstilstand is.

Ek vermoed dat die datums van vroegste sonsondergang en jongste sonsopkoms op laer breedtegrade nader aan mekaar kom, maar die langste nag bly die 21ste Desember. dus, by die ewenaar (?) is die drie datums dieselfde. maar haal my nie aan nie. dit kan ingewikkelder wees as dit.

# 2 sg6

Dit is die afwyking van datums vir sonsondergang en sonsopkoms wat my laat dink dat Stonehenge hier gebou is vir die jongste sonsopkomsdatum. Soos daarna is dit die begin van die langer dae, en ek sou dus verwag het dat hulle die een of ander uiterste sou meet.

Om die kortste dae te meet, beteken dat u son- en sonsopkoms tye afsonderlik meet en die verskil bepaal, en omdat hulle nie so goed weet nie, het ek kwarts of selfs meganiese horlosies van die vereiste akkuraatheid op die oomblik dat dit lyk asof hulle die Solstice self nie sou kon spesifiseer nie. . Maar die verste beweging van die son sou 'n moontlikheid gewees het.

Ek sou ook gesê het dat dit vir die winter nie soveel somer was nie. Mid Winter en Mid Summers dae verwag ek.

En dit is duisende jare voor Druïde gebou, wat blykbaar dit op een of ander manier aangeneem het.

# 3 Dave Mitsky

Die vroegste einde van die aandskemer van die jaar met 40 grade noord vind op 4 Desember plaas en die vroegste sonsondergang vind op 7 Desember plaas. Die jongste sonsopkoms van die jaar op breedtegraad 40 grade noord vind op 5 Januarie plaas en die laaste aanvang van oggendskemer op 40 breedtegraad noord vind op 8 Januarie plaas.

# 4 vroeë opkoms

Ek dink dit het meer te make met die variasies in die lengte van die sterre dag as gevolg van die baan van die aarde ellipties as enigiets anders.

# 5 Dave Mitsky

Ek dink dit het meer te make met die variasies in die lengte van die sterre dag as gevolg van die baan van die aarde ellipties as enigiets anders.

Die Desember-sonstilstand bring altyd die kortste dag na die Noordelike Halfrond en die langste dag na die Suidelike Halfrond. Maar dit is duidelik dat die jongste sonsopkoms nie saamval met die dag van die minste dag nie, en die jongste sonsondergang gebeur nie op die dag van die grootste daglig nie. Hoekom nie?

Die hoofrede is dat die Aarde se rotasie-as 23,5 grade uit vertikaal gekantel is tot op die vlak van ons wentelbaan om die son. 'N Sekondêre rede is dat die baan van die aarde nie 'n perfekte sirkel is nie. As gevolg van ons eksentrieke wentelbaan (dit is 'n baan wat gevorm is soos 'n platgetrekte sirkel, met die son effens van middel), beweeg die aarde die vinnigste in Januarie en die stadigste in Julie.

# 6 Dave Mitsky

Die datums en tye wissel sterk met die breedtegraad op aarde. Met hoër breedtegrade word die verskil tussen die somer- en wintertye groter, maar die datums wanneer die uiterstes bereik word, kom nader aan die datums van die sonstilstand. Byvoorbeeld, op 60 ° noord, verskil die tye twee of drie uur van 06:00 tot 18:00, maar die datums waarop hierdie uiterstes bereik word, is slegs tussen 2 en 6 dae weg van die sonstilstanddatums. By laer breedtegrade word die verskil tussen die somer- en wintertye kleiner, maar die datums wanneer hierdie effense uiterstes bereik word, word verder van die sonstilstanddatums af. Op die ewenaar is die tye van sonop en sonsondergang net 'n paar minute van 06:00 tot 18:00 af, maar die datums waarop hierdie effense uiterstes bereik word, is 10 en 12 Februarie (jongste sonsopkoms en sonsondergang) en 2 en 4 November (vroegste sonsopkoms en sonsondergang).

# 7 Dave Mitsky

Die datums vir die vroegste sonsondergang en die laaste sonsopkoms vir 'n plek hang ook af van die breedtegraad daarvan. Plekke nader aan die ewenaar het hul vroegste sonsondergang iewers in November. Lokasies op hoër breedtegrade, daarenteen, het hul vroegste sonsondergang later, nader aan die werklike datum van die wintersonstilstand.

Die tydsvergelyking is gelyk aan 0 (gemiddelde sontyd is gelyk aan die skynbare sontyd) op 25 Desember.

# 8 Tony Flanders

Ek dink dit hou meer verband met die variasies in die lengte van die dag van die aarde as gevolg van die baan van die aarde ellipties as enigiets anders.

Nee, daar is twee verskillende effekte wat bydra tot die vergelyking van die tyd, wat ongeveer beskryf kan word as die verskil tussen gemiddelde plaaslike sonmiddag en ware sonmiddag. Hoe belangriker is die feit dat die aarde se as gekantel is ten opsigte van die ekliptika. Die feit dat die baan van die aarde ellipties is, dra aansienlik by, maar dit is minder belangrik as die skuins van die as.

Ongelukkig het ek nog nie 'n baie kernagtige en verstaanbare manier gevind om te verduidelik waarom die skuins van die Aarde die daglengte laat wissel nie. Dit is voor die hand liggend genoeg as u dit eers verstaan, maar dit verg 'n bietjie driedimensionele meetkunde, wat vir die meeste van ons moeilik is om te visualiseer.

# 9 brentwood

Dit het my nog altyd gefassineer, en ek vind dit altyd irriterend as jy die weerpersoon op die nuus hoor sê dat dit in die aande ná vandag, met die sonstilstand, ligter gaan word! Ek het probeer om 'n paar van hulle tevergeefs te kontak.

Ek het dit ook op webwerwe soos Quora genoem en baie mense het gesê dat ek heeltemal verkeerd was en dat "almal weet dat 21/22 Desember die vroegste sonsondergang en die jongste sonsopkoms is"!

Wat ek wel verwarrend vind, is dat daar verskillende datums is oor wanneer dit voorkom. Vir ons eie ligging, 48 *, kan die vroegste sonsondergang wissel van 11 Desember tot 16 Desember. Webwerwe soos Weatherspark sal die datum eintlik aanhaal, ander sal 'n tabel met sonsondergang tot die tweede toon, terwyl sommige net tot die minuut waarin u moet aanneem dat die vroegste datum die middelpunt van dieselfde tye sal wees.

Soos ander vind ek dit baie moeilik, indien nie onmoontlik om te verduidelik nie. Ou aardbole het vroeër die analemma in die middel van die Stille Oseaan gehad wat die vergelyking van tyd aangedui het. Regop op en af ​​staan, toon die analemma om middag, maar as u dit aan die westelike horison visualiseer, as dit regs, noord leun, kan u sien dat die jongste sonsondergang NIE by die sonstilstand is nie, en dat hierdie verskil die nader aan die ewenaar wat jy kry!

Stel u voor dat u dit probeer verduidelik terwyl u met 'n pint in die hand by die kroeg staan!

# 10 KB Hornblower

Dit het my nog altyd gefassineer, en ek vind dit altyd irriterend as jy die weerpersoon op die nuus hoor sê dat dit saans na vandag, met die sonstilstand, ligter gaan word! Ek het probeer om 'n paar van hulle tevergeefs te kontak.

Ek het dit ook op webwerwe soos Quora genoem en baie mense het gesê dat ek heeltemal verkeerd was en dat "almal weet dat 21/22 Desember die vroegste sonsondergang en die jongste sonsopkoms is"!

Wat ek wel verwarrend vind, is dat daar verskillende datums is oor wanneer dit plaasvind. Vir ons eie ligging, 48 *, die vroegste sonsondergang kan wissel van 11 Desember tot 16 Desember. Webwerwe soos Weatherspark sal die datum eintlik aangehaal, ander sal 'n tabel met sonsondergang tot die tweede toon, terwyl sommige net tot die minuut waarin u moet aanneem dat die vroegste datum die middelpunt van dieselfde tye sal wees.

Soos ander vind ek dit baie moeilik, indien nie onmoontlik om te verduidelik nie. Ou aardbole het vroeër die analemma in die middel van die Stille Oseaan gehad wat die vergelyking van tyd aangedui het. Regop op en af ​​staan, toon die analemma middag, maar as u dit aan die westelike horison voorstel, as dit regs, noord leun, kan u sien dat die jongste sonsondergang NIE by die sonstilstand is nie, en dat hierdie verskil die nader aan die ewenaar wat jy kry!

Stel jou voor dat jy dit probeer verduidelik terwyl jy met 'n pint in die hand by die kroeg staan!

My vet. Hierdie variasie kan 'n illusie wees om die gepubliseerde sonsondergang tot die naaste minuut af te rond. Aan 'n paar dae aan weerskante van die betrokke datum verander die sononder slegs enkele sekondes.

# 11 kersfees

Te veel vrye tyd en Sky Safari lei my na hierdie drie sinne:

Die vroegste sonsondergang op my breedtegraad van 44º 25 '07 "vind op 9 Desember plaas.

Die jongste sonsopkoms vind eers 2 Januarie plaas.

Die langste nag kom ongeveer halfpad tussen die datums voor, wat op 21 Desember die sonstilstand is.

Ek vermoed dat die datums van vroegste sonsondergang en jongste sonsopkoms op laer breedtegrade nader aan mekaar kom, maar die langste nag bly die 21ste Desember. dus, by die ewenaar (?) is die drie datums dieselfde. maar haal my nie aan nie. dit kan ingewikkelder wees as dit.

Dave

# 12 Starman1

Dit is die afwyking van datums vir sonsondergang en sonsopkoms wat my laat dink dat Stonehenge hier gebou is vir die jongste sonsopkomsdatum. Soos daarna is dit die begin van die langer dae, en ek sou dus verwag het dat hulle die een of ander uiterste sou meet.

Om die kortste dae te meet, beteken dat u son- en sonsopkoms tye afsonderlik meet en die verskil bepaal, en omdat hulle nie so goed weet nie, het ek kwarts of selfs meganiese horlosies van die vereiste akkuraatheid op die oomblik dat dit lyk asof hulle die Solstice self nie sou kon spesifiseer nie. . Maar die verste beweging van die son sou 'n moontlikheid gewees het.

Ek sou ook gesê het dat dit vir die winter nie soveel somer was nie. Mid Winter en Mid Summers dae verwag ek.

En dit is duisende jare voor Druïde gebou, wat blykbaar dit op een of ander manier aangeneem het.

Konsensus van argeologiese datering sê dat alhoewel die eerste klippe op die terrein ongeveer 3000 v.C. opgerig is, dat die belangrikste klippe wat ons vandag Stonehenge noem

is omstreeks 2500 v.C.

Die vroegste bekende rekord van 'n 'Druïde' was ongeveer 300 v.C., dus u het basies gelyk - 'n paar duisend jaar tevore.

dit wil voorkom asof die middel- en die winterdag ook belangrik sou gewees het.

Vir 'n agrariese samelewing is ek verbaas dat die eweninge nie hoër sou wees nie - die een vir die plant, die ander vir die oes.


Hoe wissel die voorkoms van die analemma met die breedtegraad - Sterrekunde

Vir baie astronomiestudente is die son nie net die helderste astronomiese voorwerp wat hulle kan waarneem nie, maar ook die interessantste, want dit het 'n onmiddellike uitwerking op hul daaglikse lewe. Studente hou daarvan om hul eie waarnemings te ontleed met behulp van 'n Sunspotter of beelde uit argiewe soos die RBSE CD-ROM (1999, 2000, T. Rector), of huidige beelde wat op die internet gevind word. Hulle kan elke sonvlek se breedtegraad, lengte- en benaderde oppervlak meet deur deursigtige Stonyhurst-roosters en fyn grafiekpapier, of NIH Image- of Scion Image-gereedskap. Die breedtegraad teenoor die tyd toon die nabye konstantheid. Lengtegraad neem lineêr toe met tyd en laat die son se rotasietydperk meet. Area teenoor tyd neem toe vir sommige kollegroepe, neem af vir ander en vervaag, maar herleef vir ander. Hierdie gedrag ontlok baie vrae, hipoteses en planne vir meer waarnemings. Die variasie van die sonrotasieperiode met die breedtegraad kan getoets word. Verander die son se rotasietydperk ook met maand en jaar? Een van die oudste kalendermerke is die sonhoogte om die middaguur. Dit kan maklik gemeet word met 'n papierskaal wat aan die wieg van 'n Sunspotter geheg is. As u die burgerlike tyd om die middaguur opmerk, kan u die analemma verstaan. Waarmee korreleer sonvlekke? Studente het die korrelasie van sonvlekgetalle of -areas met radiobarstings, sigbare lig of röntgenstrale, sonwindsnelheid, digtheid of magneetveld, aurorae, geomagnetiese storms, die aarde se osoonlaag, vliegtuigvliegveiligheid, ultravioletlig, wêreldwye ondersoek. gemiddelde temperatuur, plaaslike daaglikse temperatuurvariasies, stroomonderbrekings, onderbrekings van die aarde wat satelliete of interplanetêre ruimtetuie wentel, aardbewings, orkane, tornado's of ander natuurrampe,


12/02/2014 & # 8211 Ephemeris & # 8211 Die ongelyke datums van jongste sonsopkoms en vroegste sonsondergang

Ephemeris vir Dinsdag 2 Desember. Die son sal om 8:00 opkom. Dit sal 9 uur en 3 minute aanhou en om 05:03 instel. Die maan, drie dae na die eerste kwartaal, sal moreoggend om 04:41 sak.

Hierdie sonsondergang is net 'n minuut van die vroegste sonsondergang van die jaar af. Die vroegste sonsondergang sal eintlik op die 9de wees. Die jongste sonsopkoms sal egter nie tot 2 Januarie plaasvind nie. Die rede kombineer die gevolge van die kanteling van die aarde se as en die feit dat die aarde slegs 'n maand van die perihelium af is, dit is die naaste aan die son. Albei hierdie effekte laat blyk dat die son vinniger ooswaarts beweeg as die gemiddelde, dus moet die aarde elke dag 'n bietjie verder draai om die son in te haal. Dit maak die sonsopkoms en ondergaande gebeure later as wat 'n mens sou verwag, en dit kom dus nie saam op die kortste dag van die jaar, die 21ste vanjaar, voor nie. Ons sonsopkoms vanoggend is nog 19 minute vroeër as die jongste sonsopkoms op 2 Januarie 2015.

Die tye is vir die Traverse City / Interlochen-gebied in Michigan. Dit kan verskil vir u ligging.

Addendum

Hierdie figuur 8 word 'n analemma genoem. Mens kan dit op ou aardbole in die Stille Oseaan vind. Verduideliking hieronder. Geskep met behulp van my LookingUp-program vir Traverse City, MI naby + 45 ° breedtegraad.

Die analemma is 'n grafiese voorstelling van 'n daaglikse waarde wat die vergelyking van tyd genoem word. Die bekendste gebruik is om die sonwysertyd reg te stel. Die vertikale as is die deklinasie van die son of die noord-suid-posisie. Dit is die hoogste by die somerstilstand en die laagste by die winterstilstand. Dit is die resultaat van twee effekte: die kanteling van die Aarde se as na die vlak van die Aarde se wentelbaan om die Son, en die verandering in die Aarde se snelheid rondom die Son as die Aarde van die perihelium af beweeg, die naaste aan die son vroeg in Januarie tot aphelion, die mees afgeleë in Julie.

As die aarde se wentelbaan sirkelvormig was, en dit met dieselfde snelheid om die son wentel. Die analemma sou skraal wees en die noord- en suidlobbe sou ewe groot wees. Aangesien ons in die winter nader aan die son is, beweeg ons vinniger as gemiddeld rondom die son, dus dit lyk asof dit vinniger ooswaarts beweeg. Dit kombineer met die vinniger verskyning van die son wat die nouer uurlyne kruis by hoër en laer afname. Let op dat die vertikale uurlyne aan die onderkant en boonste effens nader aan mekaar is, sodat die son, wat elke dag ooswaarts beweeg, dit vinniger kruis. Naby die wintersonstilstand werk die twee effekte saam, sodat sonsopkoms en sonsondergang later as normaal sal wees. Vir die somer-sonstilstand is die son se oostelike spoed stadiger as normaal, want ons is verder van die son af. Dit werk teen die effek van die aarde se kanteling, maar kan dit nie heeltemal ontken nie, wat die bokant van die lus kleiner maak as die onderkant. Die pyle wys die snelheid en rigting van die son by die sonstilstand.

Om werklike analemmas te sien, soek na analemmabeelde op die internet. Dit neem 'n jaar om een ​​te neem.


Hoe om die sonanalemma in u blaaier te visualiseer (skakel in kommentaar)

Wat presies wys dit? Die ligging van die son deur die jaar?

Die & quotpad & quot wat die son sou neem as u elke dag op dieselfde tyd en posisie die son neem. 'N Beter beskrywing is in die skakel OP wat verskaf word

Gemaak met CesiumJS, live demo en bronkode + instruksies hier: https://omarshehata.me/notebook/visualizing_the_solar_analemma

Normaalweg kan u hierdie soort foto's neem deur elke dag 'n foto van die son te neem. Ek het dit gedoen, maar in 'n sagteware-simulasie, sodat u die klok kan bespoedig of dit in verskillende stede kan probeer, of kan uitvind wat 'n goeie tyd en plek is om dit te doen, sodat u nie deur berge of geboue verduister word nie.

Ek wil ook graag weet. Ek het 'n paar jaar gelede van hierdie vorm geleer en kon nie my kop rondkrap waarom die son nie net in een as beweeg nie (maar 'n reglynige analemma agterlaat), maar in twee beweeg (skep 'n figuur 8).

Regtig cool. Dit sal interessant wees om een ​​te sien wat uit 'n stad op die ewenaar geneem is.

Groot visualisering! Ek woon in Alaska en ons is nou aan die onderkant. So donker heeltyd!

Ek het dit gesien in Castaway waar Tom Hanks dit gebruik om die maand van die jaar te bepaal (hy het dit die skaduwee op 'n rots aangedui). Het altyd daaroor gewonder. Dankie

Dit is die eerste ding waaraan ek ook gedink het!

Waarom die groot verskil tussen San Francisco en Nepal?

Omdat ek albei oor die ewenaar was, het ek dieselfde kant van die helling verwag (met 'n soortgelyke hoek sowel as ongeveer dieselfde breedte).

Kan iemand asseblief verduidelik? Dankie

Goeie vraag! Ek dink dat dit net 'n faktor is dat ek een sonsopkoms en een teen sononder gedoen het? Wat ek gedoen het net om die son in die posisie te kry wat ek agter die berg wou hê.

Ons moet dit kan verifieer deur dit in die live demo te herskep met die instruksies hier en om te sien of dit ooreenstem as u albei op dieselfde plaaslike tyd bestuur: http://omarshehata.me/notebook/visualizing_the_solar_analemma

Hierheen gekom om 'n AME-vraag te stel, hulle is albei naby dieselfde breedtegraad en moet dieselfde lyk.

Waar in Alaska is die plek? Denali?

Yup, dit & # x27s Denali! Presiese koördinate is, lat / lon:

Verklaar dit waarom ek die son elke dag (vroeg in Desember) verder suid ondergaan, alhoewel ons nog nie by die sonstilstand gekom het nie?

Verander die geslinger van die aarde nie al hierdie perspektiewe om nooit dieselfde te wees nie?

Bedoel jy as jy hierdie jaar dieselfde foto's geneem het en volgende jaar nie meer so goed sou wees nie?

Ek dink dit is waar, maar (1) ek weet nie hoe groot 'n verskil dit jaar tot jaar is nie en (2) ek weet nie of dit in hierdie sagteware in ag geneem word nie. Dit kan wees. Dit sal regtig interessant wees om dit in 2020 te bestuur en dan in ongeveer 1010 (of honderdduisend jaar later?) En sien.


Gemiddelde sontyd

Dit maak ware sontyd onvoldoende as 'n tydstandaard. Sondae het nie almal dieselfde lengte nie (ten opsigte van verskynsels wat meer vertrou word soos uniform soos die ossillasies van 'n slinger of siërêre tyd) en 'n & kwotsolêre tweede & quot gebaseer op 'n onderverdeling van die sondag sal afhang van die seisoene strek of krimp.

Vandaar die idee van 'n gemene son, 'n fiktiewe voorwerp wat verband hou met die werklike son, maar wat eenvormig langs die hemelse ewenaar beweeg (eerder as die ekliptika), wat as verwysingsobjek vir 'n astronomiese tydskaal gebruik kan word, met die voordele van sontyd bo die tyd, maar sonder die nadele.

Die idee van gemiddelde son was al bekend vir die antieke Griekse sterrekundiges (Hipparchos, Ptolemeus). Dit word nou streng soos volg omskryf (Meeus [2, p. 183], Smart [3, pp. 139 & ndash140]) in twee stappe.

  • 'N Eerste fiktiewe voorwerp wat ons kan noem eenvormige son by gebrek aan 'n standaardterm, beweeg dit met die konstante hoeksnelheid langs die ekliptika en val dit saam met die ware son by die perigee en apogee.
  • 'N Tweede fiktiewe voorwerp, die gemene son, beweeg langs die ewenaar met konstante hoeksnelheid en val saam met die eenvormige son op die ekinoktiale punte.

Die gemiddelde son is die verwysingsvoorwerp wat gebruik word om te definieer gemiddelde sontyd. Dan plaaslike gemiddelde (son) tyd (LMT) op een of ander plek op aarde is die uurhoek op die gemiddelde son. Deur 'n verwysingsmeridiaan te kies, kan 'n wêreldwye tydskaal vasgestel word, soos Greenwich gemiddelde (son) tyd (GMT).

Universele tyd (UT) en burgerlike tydskale is aanvanklik gebaseer op GMT, met die dag wat om middernag begin eerder as (gemiddelde) middag. In die 1960's het die ontdekking van die onvoorspelbare vertraagde rotasie van die aarde gelei tot die instelling van addisionele tydskale wat as meer eenvormig beskou word. Die hele verhaal word in ESAA [1, pp. 9 & ndash14 en Hoofstuk 3] vertel.


Die Naghemel

In die Sky.org-gidse vir die naghemel Wil u meer van die naghemel leer? Kyk na hierdie webwerf! 'N Groot versameling kaarte, artikels, interaktiewe kaarte en meer van Dominic Ford.

Leksikon en woordelys van sterrekunde Vanuit Caltech - die tuiste van NASA JPL. 'N Baie lang, volledige samestelling van sterrekunde-terme met uitstekende, gedetailleerde beskrywings.

Woordelys van woordeskat vir sterrekunde Gebruik hierdie webwerf (of ander) om die definisies van die toegekende terme vir lugwaarnemer te vind. Bespaar ruimte vir sketse.

Kyk na hierdie tydsverloop film uit 'n Italiaanse omgewing.

Roterende Sky Explorer Op watter maniere verander die lug gedurende 'n enkele nag?

  • 3. Hoe hou die skynbare bewegingssterre verband met die hemelse sfeer?
  • 4. Is sommige konstellasies altyd sigbaar in die naghemel?
  • 5. Maak u ligging op aarde (breedtegraad en lengtegraad) saak?

Gebruik hierdie interaktiewe antwoorde op hierdie vrae.

Precession of Earth & # 39s Axis Wys die Noordpool altyd op die North Star? Beantwoord hierdie vraag nadat u hierdie video's gekyk het. Precession of Earth (en die equinoxes)

Die Night Sky-woordeskat Besoek hierdie webwerf om diagramme te sien wat die terme waarneem wat ons in die klas gebruik het, insluitend: hemelsfeer, meridiaan en hoogtepunt (bladsy 7), gaan dan voort deur bladsye 7, 8, 9 en 10 vir konstellasies, sterretjies,

  • Hoe kan u die beweging van die Son deur die konstellasies beskryf soos die weke verbygaan?

Speel bietjie met hierdie animasie - kyk na die verband tussen die sonposisie en die sterrebeeldkonstellasies.

Big Dipper Clock Toon hoe sterre mettertyd om die North Star draai (daaglikse en seisoenale bewegings word getoon).

Die draaiende lug (van die Universiteit van Nebraska-Lincoln Astronomy Education-program)

Werk deur die toeligting aan Die waarnemer en Twee stelsels - hemelse, horison, thePaths of Stars. Al die konsepte wat op hierdie bladsye behandel word, word in die Rotating Sky Explorer gebruik en daar sal meer volledig ondersoek word.

Azimuth / Hoogte-betoger Demonstreer die horisonkoördinaatstelsel, waar hoogte en azimut 'n voorwerp se posisie in die lug definieer.

Waarom verskyn verskillende sterre met seisoene? Lees dit aandagtig deur die antwoord op hierdie vraag wat aan 'n sterrekundige aan die Cornell Universiteit gestel is. Kan u sin maak uit die diagram? Kan u 'n soortgelyke diagram maak en aan iemand anders verduidelik hoe dit werk?

  • Kan u die aanvanklike vraag self beantwoord?Wat is die antwoord op die aanvanklike vraag?

Sun Motions Oorsig Toon die paaie van die son op die hemelse sfeer. Eksperimenteer hiermee 'n bietjie - waarheen sou u kop om middernag in Junie wys? Hoe gaan dit met Desember? Sien ons verskillende konstellasies gedurende verskillende seisoene? Hoe help hierdie model u om hierdie vraag te verstaan?

Sun Motions Demonstrator Modelleer die bewegings van die son in die lug met behulp van 'n horisondiagram en toon daaglikse en seisoenale veranderinge in die son se posisie aan.

Sidereal en Solar Time Help om die verskil tussen son- en sontyd te demonstreer.

Aarde & # 39; s wentel om die son: nie so eenvoudig soos dit lyk nie Sideriese jaar, tropiese jaar, analemma, presessie. soveel dinge gaan aan!

Resensie: Basiese moties van die lug: 'N Reeks & quotclicker-vrae & quot van die Universiteit van Nebraska & quotClass Action 2 & quot vraestel. These are the same questions used in class. This is a great way to check your understanding before the unit evaluation!

Astrological vs. Astronomical Birth Signs Why is a person's "Sun sign" (listed on a horoscope web site) usually different from a person's astronomies sun sign? Compare your astrological and astronomical birth signs on this chart. Follow the links on the page to learn why there is a difference between the two.

Precession of Earth's Axis Why is your astrological birth sign different from your astronomies birth sign? Why have birth signs changed since they were originally set up? Watch this short computer animation to see how the precession of Earth's axis has caused the celestial poles to move and the equinoxes to change. How long does it take for one complete cycle of precession?

Astronomy vs Astrology: What's the Difference? A very short article from Sky and Telescope Magazine. Be prepared! Be able to describe how astronomy and astrology are different!

Astrology vs. Astronomy Read this short article to get a sense of the common origin of astronomy and astrology--and to understand their differences. Read this article as well Sidereal and tropical Astrology to learn about why your "astrological" birth sign is probably different from your "astronomical" birth sign.

Cosmos 3: Harmony of the Worlds Complete the video questions as you view this classic movie from Carl Sagan.

Kepler's Laws of Planetary Motion. Find "Kepler's Second Law Interactive" en "Kepler's Third Law Interactive" on this website McGraw Hill Interactives


Figure-Eight in the Sky

To see a world in a grain of sand, / And a heaven in a wild flower, / Hold infinity in the palm of your hand, / And eternity in an hour.

—William Blake, Auguries of Innocence

O NE OF my favorite things to look at when I was a kid was my dad's globe. This was a National Geographic affair it was not mounted, but instead sat freely in a clear plastic stand. It was also a quality item, and my dad made it clear to me that I was only to look and touch gently, not throw about like a ball.

I formed all sorts of weird ideas about the globe. It was one of my first exposures to the idea that we were not on top of the world. (I grew up in the Bay Area in California.) Instead, we were at a latitude of 40 degrees, and it occurred to me that we therefore did not stand up straight, when we thought we were standing up straight. Instead, we stood at an angle, of 50 degrees to the vertical. If we had really wanted to stand up straight, we should have leaned over by an angle of 50 degrees, toward the north. As I said, I formed all sorts of weird ideas about the globe.

The clear plastic stand, incidentally, had a number of fascinating symbols and etchings on it. There was a grid of squares, each covering 100 square miles on the globe. There were latitude and longitude markings, so one could see at an instant how far two different cities were displaced in those coordinates.

The thing that fascinated me most about the globe, however, was an unexplained, elongated figure-8 that was unceremoniously placed in the sparse expanse of the southeast Pacific. What was it, I wondered? It had the names of the months marked at various points around the curve, so it clearly had something to do with the year, but what was the significance? Why was it in the shape of a figure-8? What was it doing down there in the south Pacific? And couldn't people remember the months of the year without being reminded by a strange marking on a globe?

I'm sure you're dying to know the answers to those questions (well, maybe not the last one), so I'll give them to you, but let me start the usual way—with something that seems unrelated at first blush.

In sy Republic, Plato (427–347 B.C.) describes—among a whole host of other things—his curriculum for the ideal schooling in the Republic. One of the subjects to be studied, as a science, is that of astronomy.

We must keep in mind, however, that Plato's conception of astronomy was not what we moderns are used to. The image that most people today have of astronomers is that of a solitary observer, dwarfed by a tremendous telescope, staring up at the sky in search of goodness only knows what. (As a matter of fact, most professional astronomers today rarely if ever look through the telescopes they use to do their research, but that's a development of the last century or so.) The job of the astronomer is to make observations of the heavens, and from those observations, enhance our knowledge of the cosmos.

That was most certainly not Plato's ideal. His curriculum was designed in order to form rigorous thinkers, and to that end, the "real" astronomy was not what was up in the sky. The stars and the planets showed inconsistencies that were a result of being sensible objects in the physical world. It would be no more appropriate to study the "real" astronomy by looking up at the sky than it would be to study geometry by looking at the imperfect straight lines and round circles that humans could draw out in the sand. Astronomy was a set of abstract concepts that could only be approached by logical thought. (He would surely have been distressed by Hipparchus's attempt to keep track of the changing heavens by mapping the stars.)

Accordingly, when Plato and his followers sought solutions to astronomical conundrums, the first criterion by which the solutions were measured was not how well they matched observations (although it was something of a consideration of Plato's), but by how elegant those solutions were. For example, Plato and his contemporaries felt that the most perfect shape was the circle. It is as perfectly symmetrical as any shape can be it is, in a sense, the figure that all regular polygons aspire vainly to be. So, they concluded, the ideal astronomical theory for any problem must consist of circles or combinations of circles.

One such problem was the motions of the planets in the sky. The planets do not stay in place as the stars do, but instead move through the constellations. Mostly, they move slowly from west to east ("prograde" or "direct" motion) as the months pass, but occasionally, they move east to west ("retrograde" motion). Even such an idealist as Plato could not ignore that blatant a variation in motion. After all, the Sun and the Moon don't exhibit retrograde motion, so there was a clear basis for comparison. But Plato was no mathematician—he was an idea man, not an analytical genius. So he was forced to pose this question to others: What theory, consisting of circles, either in isolation or in combination, could explain the apparent motion of the planets?

Eventually, a workable solution was arrived at, centuries after Plato's death, by the Greek astronomer Ptolemy (c. 85–165), in his geocentric theory of the solar system. But long before Ptolemy, other Greeks tried their hand at solving Plato's poser. One such person was Eudoxus of Cnidus (c. 400–347 B.C.), a Greek mathematician and a contemporary of Plato.

Eudoxus's idea can be imagined as follows. Suppose that you have, resting on a tabletop, a globe that spins on a tilted axis (unlike my dad's free-standing globe). Imagine that there's an ant walking along the equator. Obviously, the ant retraces its path periodically, and we might call each time around the path one orbit.

Because the globe is tilted, the ant does not stay at the same height above the table throughout each orbit, but rather rises and falls. If at one point during its travels, the ant is at its lowest point, then half an orbit later (and half an orbit earlier as well), it is at its highest point. Midway between these extremes, the ant is at its average height.

Now, suppose that instead of putting the globe on a table, you put it on a turntable, and you set the turntable spinning at exactly the same rate as the ant's walking, but in the opposite direction. For example, if we assume that the ant is walking west to east along the equator—that is, counterclockwise, as seen from above the north pole—then the turntable is spinning clockwise. Then, because the two motions roughly cancel each other out, the ant appears to remain more or less in place (relative to an outside observer).

But not presies in place. The ant would stay exactly in place if the globe weren't tilted, for then both the ant and the turntable would be moving horizontally, and their equal but opposite rotations would cancel each other out completely. But because the globe is tilted, the rotations don't cancel out perfectly, and the ant must at least be sometimes high, sometimes low. After all, without the turntable, the ant's height goes up and down, and the turntable can't affect the ant's height it can only move the ant side to side.

Is that all? Does the ant enigste move up and down, or does it trace out a more complex figure? Now, to make that more precise, suppose you start the globe with the ant on the equator exactly at its average height, and you shine a laser pointer on the ant. (It's a weak pointer that doesn't hurt the ant.) As the turntable rotates clockwise, both the ant and the laser dot move west to east across the globe, but whereas the ant stays at the same latitude (0 degrees, on the equator), the laser dot appears to change latitude throughout its orbit. In fact, since the globe is tilted by 23.4 degrees—the tilt of the Earth's axis—the laser dot's latitude fluctuates between 23.4 degrees north and 23.4 degrees south. Now, the crucial question: Relative to the laser dot, what is the motion of the ant—or just as significantly, from the point of view of the ant, what is the motion of the laser dot?

Eudoxus had sufficient genius for visualization that he arrived at the surprising but right answer. Here's how he might have reasoned. If the Earth were flat, you could walk forever in a straight line without retracing any part of your path. But the Earth is not flat instead, as Eudoxus probably suspected, it's a sphere. And since the sphere is curved, you can't walk a literally straight line. The curvature of the Earth forces your path to be curved one way or another. The straightest path you can walk is to go around the Earth in as wide a circle as possible. One such path is the equator you can easily see that by walking along the equator, you are neither turning north nor south. Another way to walk as straight as possible is to start at the north pole, walk due south along some particular line of longitude until you get to the south pole, and then return to the north pole along the "opposite" line of longitude.

Each of these straightest paths is called a great circle. There are an infinite number of them on the Earth, or on the globe, or indeed on any sphere. Each of them has the same diameter as the sphere, and the center of any great circle is the same as the center of the sphere. The ant on the globe traces out a great circle—namely, the equator. The laser dot traces out another great circle, but one that is horizontal and therefore nie the equator. Since the globe is tilted by 23.4 degrees, the laser dot's great circle is tilted to the equator by 23.4 degrees as well. These two circles intersect at two opposite points, which must obviously be along the equator, 180 degrees apart. This is the key to Eudoxus's idea.

Suppose we start with the ant and the laser dot at the same spot again. The ant proceeds directly eastward along the equator. The laser dot follows a great circle that is inclined to the equator, by 23.4 degrees, either to the northeast, or the southeast. For the sake of discussion, let's suppose that the laser dot is moving to the northeast of the original starting point.

At first, the ant and the laser dot are still close together, and we can for all practical purposes ignore the spherical shape of the globe, just as, in real life, we can ignore the spherical shape of the Earth when navigating inside our home. Since the ant and the laser dot are moving at the same speed, they appear to be carried along at the edge of an ever-expanding compass dial, as in Figure 1.

Initially, the laser dot seems to be moving mostly northward, relative to the ant. But because the ant puts all of its motion into the eastward direction, and the laser dot only puts most of it there, the laser dot must also appear to be moving slightly westward, from the standpoint of the ant. (See Figure 2.)

If the globe were actually flat, the ant and laser dot would spread out forever, with the dot always moving to the north-northwest of the ant. But the globe isn't flat, and if the ant and laser dot continue far enough, the globe's curvature will come into play.

For example, after a quarter of an orbit, the ant is 90 degrees (1/4 of 360) away from its starting point, along the equator. The laser dot, travelling at the same rate, is also 90 degrees from its starting point, but north of the ant. You might expect that it would also be somewhat to the west of the ant, as before, but it's not. Instead, it's exactly due north of the ant. (See Figure 3.)

What has happened? The new factor is that the laser dot's path is taking it to higher latitudes on the globe, where the lines of longitude are closer together. As they both approach the 1/4-orbit point in their travels, therefore, the laser dot is gaining on the ant in longitude. This makes up perfectly for the start of their voyages, where the ant moved out ahead of the dot in longitude, so by the time that they have gone through a quarter orbit, both the laser dot and the ant have moved through exactly 90 degrees of longitude.

If we follow their motion further, into the second quarter of the orbits, the laser dot now races ahead of the ant in longitude. But we know that they must meet again after both have travelled through a half orbit at that time, they must both be on the opposite side of the globe from their original starting point. As seen in Figure 4, from the point of view of the ant, the laser dot must have travelled in a wide looping path, starting toward the north-northwest, then curving eastward, then returning from the north-northeast.

In the second half of their orbits, the exact same thing happens, except inverted. Again, the laser dot, with some of its motion toward the south, falls behind the ant in longitude, and it appears to the ant to be moving to the south-southwest. Then, as it moves to more southern latitudes, where the lines of longitude are closer together, it catches up with and overtakes the ant in longitude. Finally, as its path takes it back toward the equator, the ant and the laser dot meet once more at the starting point, one orbit later for each. (See Figure 5.)

This figure-8 shape is the path that the laser dot appears to take from the perspective of the ant. The amazing thing is that Eudoxus was able to figure this all out without the benefit of actual globes or laser pointers. To him, incidentally, the looping path, retracing itself over and over again, resembled the loops placed around a horse's feet to fetter it, so he called the path a "horsefetter." Naturally, he spoke Greek, so the word he used was seekoei, pronounced "hip-POP-puh-dee," from the Greek words for "horse" and "feet."

Eudoxus thought that by superimposing this figure-8 loop on a third, underlying west-to-east motion, he could simulate the retrograde motion of the planets. Half the time, the hippopede would also be moving west to east, so the combined motion would be west to east as well—this would be prograde, or direct, motion. Even much of the rest of the time, the hippopede would not be moving enough in the opposite direction to counteract the general west-to-east translation. Only when the hippopede was moving nearly as fast as possible, east to west, would there be a resulting backward slide, and this backward slide Eudoxus identified as retrograde motion.

It was a clever bit of explanation, but there were a number of problems with it. First of all, if it were correct, then all of the retrograde loops should have been symmetrical, and that wasn't so. Secondly, and more seriously, all the planets should remain at the same brightness throughout their orbits, and they certainly did not. Mars, in particular, is dozens of times brighter at some times than at others. For these reasons, Eudoxus's hippopede was eventually replaced, first by Ptolemy's theory of deferents and epicycles, equants and eccentrics, and 1,400 years thereafter by Copernicus and the heliocentric theory.

The hippopede re-entered science, though, in a completely unexpected way—a way that was only opened up by the advent of accurate timekeeping.

For millennia, humans kept track of time by noting the general location of the Sun. One might speak of leaving for town at sunrise, or of returning when the Sun was a hand's breadth above the horizon, and so forth. The Sun's motion was sufficiently constant to provide a convenient basis for telling time.

At some point, it became expedient to divide both the day and the night into portions, and the Babylonians chose to divide them both into 12 equal parts called "hours," from an ancient Greek word meaning "time of day." Twelve was a useful number, in that a quarter, or a third, or a half of a day or night all came out to a whole number of hours. These hours could be labelled on a sundial, so the moving shadow of a stylus, or gnomon, would mark out the advancing hours—at least, during the daytime.

Unfortunately, all of the daytime hours were equal to each other, and all of the nighttime hours were also equal, but the daytime hours were not the same length as the nighttime hours. Instead, they were longer in summer (naturally) and shorter in winter. The explanation for this was in the changing height of the Sun. It rose higher in the sky in summer, and more of its circular path was then above the horizon, so naturally the 12 daytime hours took longer to pass. In the winter, exactly the opposite was true: the Sun did not get very high at all in the sky, even at its peak. Less of its circular path was above the horizon, so the 12 daytime hours took less time to pass.

Eventually, other devices for telling time were developed that did not depend on the slightly variable nature of the Sun's path: for instance, hourglasses, or burning candles. With the introduction of these timekeepers, the variations in the daytime and nighttime hours became quite troublesome. It was tedious to have to change candles or hourglasses with each month. How much easier it would be to replace the inconstant hours with 24 equal ones. The only inconvenience was that sunrise and sunset would take place at slightly different hours throughout the year, but that could easily be accounted for.

Then, in 1656, the Dutch astronomer and physicist Christiaan Huygens (1629–1695) developed the first pendulum clock. Galileo had had the idea previously, while watching a chandelier sway back and forth in a cathedral, but had never followed through on a design. Huygens was the first to overcome the physical obstacles to building a clock based on the principle of the pendulum, and he ushered in the era of precision timekeeping.

Huygens's clock was also the first to be accurate to minutes a day, and the clock face gained another hand. Later clocks were even accurate to seconds, and now was discovered an interesting discrepancy. The moment that the Sun crosses the meridian—an imaginary north-south line in the sky—is called local noon, after an old word meaning the ninth (daytime) hour of the day. (This was midafternoon, but later was moved back earlier, to midday.) By all rights, the time between local noon on two successive days should be exactly 24 hours. But as measured by these accurate clocks, the interval between two consecutive local noons was sometimes a few seconds long at others, a few seconds short. If we set a clock exactly to noon when the Sun was at local noon on one day, then the next day, the Sun would reach local noon, not at 12:00 exactly, but perhaps at 11:59:58, or at 12:00:10. These discrepancies added up, so that at various times of the year, the Sun was as much as a quarter of an hour "early" or "late." The errors repeated in a cycle of length one year, year after year.

Either the clocks were wrong, or the Sun's apparent motion across the sky was not as constant as previously thought (or both). We now know that it's the latter, and this repeating cycle is called "the equation of time" by astronomers. The Sun does not go at the same rate in right ascension (the astronomical version of longitude) all year long, but instead moves through lines of right ascension faster at some times, slower at others. At no point does it actually go the "wrong" way—it doesn't exhibit retrograde motion, in other words—but this variation is what causes the Sun to cross the meridian early or late. And if we plot the "location" of the Sun, with its northern and southern advances drawn along the vertical axis, and its earliness or lateness drawn along the horizontal axis, we get the figure drawn on my dad's globe, which is called an "analemma." (See Figure 6.)

The word "analemma" is Greek for the pedestal of a sundial, and itself comes from the Greek verb analambanein, meaning "to take up, to resume, to repair," so that the pedestal is something that supports the sundial upon it. Early on, "analemma" seems to have been extended to refer to a particular kind of sundial, in which only the height of the Sun was indicated, by measuring the size of the shadow cast by the sundial. Later, it was used for a number of meanings related to the height of the Sun its latest meaning, and that with which we are interested here, is some kind of representation of the Sun's gradually changing path in the sky at the same time (noon by the clocks) each day.

It surely hasn't escaped your attention that the analemma and Eudoxus's hippopede share a certain resemblance, a resemblance that, as it turns out, is more than accidental. The hippopede results from the conjunction of two circular motions, and so does the analemma.

The apparent motion of the Sun is really due to two motions of the Earth. One is the Earth's orbit around the Sun. The Earth completes one revolution about the Sun in one year, and if that were the only motion that the Earth had, then we on the Earth would see the Sun appear to go around the Earth just once a year.

However, the Earth has a second motion: its rotation on its axis. It does so approximately once a day, and it is for that reason, mostly, that the Sun appears to revolve around the Earth once each day. Since these two motions have periods in approximately the ratio 365.25:1 (the number of days in a year), while the hippopede results from two motions with equal periods, you might think that the hippopede doesn't have much relevance to the analemma.

But you'd be wrong. As I mentioned, the Earth rotates on its axis only approximately once a day, and the Sun's apparent motion across the sky is only mostly due to this rotation. A tiny component is due to the first motion of the Earth, its orbital revolution. Since this revolution takes 365.25 times longer than the rotation, it contributes 1/365.25 as much to the Sun's apparent motion across the sky as does the Earth's rotation. Now, the Earth's rotation makes the Sun seem to move east to west, from dawn to dusk, but its orbital revolution appears to add a second component, from west to east. This second component very slightly counteracts the first, so that the 24-hour day is longer than you might expect based solely on rotation. In fact, the Earth actually rotates on its axis, with respect to the stars, every 23 hours, 56 minutes, and 3.5 seconds. This slightly shorter day is called the "sidereal day," after a Latin word meaning "star," since this is the time it takes for the Earth to rotate once relative to the stars. The extra four minutes each day is due to the Earth's orbit around the Sun, and is 1/365.25 of the 24-hour day.

In other words, if the Earth didn't revolve around the Sun, but only rotated in place, in defiance of the law of gravity, the Sun would appear to go once around the Earth in 23 hours, 56 minutes, and 3.5 seconds, instead of the customary 24 hours. And if we were to take a snapshot of the Sun every day at the same time by the clock, it would be 3 minutes and 56.5 seconds further along each day. After two days, it would be ahead (that is, further west) by 7 minutes and 53 seconds after three days, by 11 minutes and 49.5 seconds after four days, by 15 minutes and 46 seconds, and so forth.

How long would it take for this margin to extend to 24 hours, so that the Sun would once again be "on time," on the meridian at noon? Why, as many times as 3 minutes and 56.5 seconds goes into 24 hours—and as we noted above, this interval is 1/365.25 of 24 hours, so it would take 365.25 days for the Sun to "lap" the 24-hour clock. A year, in other words. In short, if the Earth only rotated, and didn't revolve around the Sun, the Sun would appear to revolve around us every 23 hours, 56 minutes, and 3.5 seconds, but by taking snapshots of the Sun every 24 hours, which is just about four minutes longer, this motion would appear to be slowed down to just one revolution per year.

In case that sounds confusing, it's like watching a car drive by you on the road. In reality, the car's wheels may be rotating very rapidly—let's say, 25 times a second. (That'd be one fast car, by the way—probably around 150 to 200 kilometers an hour!) But if you watch a film of the car, where the camera takes 24 frames per second, each frame catches the wheel when it has gone through 1-1/24 of a rotation. Since the eye can't tell the difference between 1-1/24 of a rotation and just 1/24 of a rotation, it appears as though the wheel is actually rotating at only 1/24 rotation per frame. That works out to one rotation every 24 frames—or once a second.

In much the same way, when we take our figurative snapshots of the Sun every 24 hours, the Earth's rotation, alone, makes the Sun appear to revolve around the Earth, once a year, from east to west, along a path called the hemelse ewenaar. Meanwhile, as described above, the Earth's orbital revolution, alone, makes the Sun appear to revolve around the Earth, once a year in the opposite direction, from west to east, along another path called the ekliptika. Both the celestial equator and the ecliptic are great circles. What's more, these two great circles are not the same, but because of the Earth's axial tilt, are instead inclined to one another by an angle of 23.4 degrees.

We therefore have an exact analogue of Eudoxus's hippopede, but this time applied to the apparent motion of the Sun throughout the year. These two motions combine to create the figure-8 shape of the analemma. Eudoxus could not possibly have known about this application of his theory, which was originally designed to account for the retrograde motion of the planets. As an explanation of daardie behavior, the hippopede was basically dead on arrival. Too bad that accurate clocks were not available in his day otherwise, he might have found the right use for his geometric intuition.

But one last objection remains: The analemma on the globe is not a symmetric figure-8 at all! Rather, it's smaller on the northern end, and larger on the southern end. Why is that?

That asymmetry is due to one further property of the Earth's orbit around the Sun: its eccentricity. The Earth's orbit is nearly circular, but not precisely so. It is actually an ellipse, and the Earth moves along that ellipse in accordance to Kepler's laws of planetary motion. (See "Music of the Ellipses.") As such, the Earth moves faster when it is closer to the Sun, and slower when it is further from the Sun, and this translates to a corresponding variation in the Sun's apparent west-to-east motion due to the Earth's revolution. Just hoe elliptical the orbit is, and the angle between the long axis of the orbit and the axis of the Earth, determine the contour of the analemma.

Incidentally, I'm not certain just why the analemma is specifically in the southern Pacific—perhaps because that's the least crowded part of the planet, cartographically speaking—or why it's needed on a globe at all. It does have some significance to sundial builders, since it can be used to correct for the equation of time, if the months of the year are marked out (as they are on my dad's globe) and one rotates the dial of the sundial according to the analemma. But it doesn't seem to need to be on a globe, and indeed, more modern globes now eschew the analemma in favor of a more extensive legend.


24 August 2009

Generally speaking, it is unusual for ‘economic stimulus jobs’ and ‘underwater robots’ to appear in the same sentence. For a month this summer, though, those two concepts went hand-in-claw at a camp organized by Linn-Benton Community College staff and students. As a part of the Oregon Underwater Volcanic Exploration Team, high school students from all over the state received training in job skills like electrical circuit design, budget-keeping, and geographic information systems as they built and operated research submersibles called ROVs. The high schoolers were nominated by teachers and counselors in their home towns, and spent six days camping on Paulina Lake inside Newberry National Volcanic Monument east of LaPine. Each student designed and built their own ROV, which they got to take home at the end of the week. Money for the project came from a grant by The Oregon Consortium and the Oregon Workforce Alliance, by way of legislative money for job training in Oregon, where high-tech job growth requires constant workforce training.


Starship Asterisk*

Analemma Over the Porch of the "Maidens" (2008 Dec 21)

Post by JohnD » Sun Dec 21, 2008 12:28 pm

OK, picky, picky, but this is more strictly termed the "Caryatid Porch" (21st December 2008).

"Caryatids" were devotees of Artemis the Huntress, rather than Athena Polias - "City (of Athens) Protector)" - to whom, with Poseidon, the Erechtheum was dedicated but the term has become used for any supporting pillar carved in a female shape. To call the structure the "Porch of the Maidens" implies some significance to their inviolate status, as if the cult of Hestia had similar civic functions to the Roman Vesta cult, which it didn't.
They may portray Athena Parthenos, but that implies her virgin birth , not her chastity.

And nice analemma, but haven't a lot of APODs been so?
John

Cary & Anna: the little Lemma sisters

Post by neufer » Sun Dec 21, 2008 3:36 pm

JohnD wrote: OK, picky, picky, but this is more strictly termed the "Caryatid Porch" (21st December 2008).

"Caryatids" were devotees of Artemis the Huntress, rather than Athena Polias - "City (of Athens) Protector)" - to whom, with Poseidon, the Erechtheum was dedicated but the term has become used for any supporting pillar carved in a female shape. To call the structure the "Porch of the Maidens" implies some significance to their inviolate status, as if the cult of Hestia had similar civic functions to the Roman Vesta cult, which it didn't.

They may portray Athena Parthenos, but that implies her virgin birth , not her chastity.

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Cary & Anna: the little Lemma sisters
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Analemma , n. [Gr. ανάλημμα, any supporting pedestal of a sundial, fr. to take up + to take.]

A caryatid (Greek: Καρυάτις, plural: Καρυάτιδες) is a sculpted female figure serving as an architectural support taking the place of a column or a pillar supporting an entablature on her head. The Greek term karyatides literally means "maidens of Karyae", an ancient town of Peloponnese. Karyai had a famous temple dedicated to the goddess Artemis in her aspect of Artemis Karyatis: "As Karyatis she rejoiced in the dances of the nut-tree village of Karyai, those Karyatides, who in their ecstatic round-dance carried on their heads baskets of live reeds, as if they were dancing plants"

P.S., OK, picky, picky, but where is the Daylight Saving time glitch?
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<<Explanation: If you took a picture of the Sun at the same time each day, would it remain in the same position? The answer is no, and the shape traced out by the Sun over the course of a year is called an analemma.>>

<<Greece is in the Eastern European Time Zone. Eastern European Standard Time (EET) is 2 hours ahead of Greenwich Mean Time (GMT+2). Like most states in Europe, Summer (Daylight-Saving) Time is observed in Greece, where the time is shifted forward by 1 hour 3 hours ahead of Greenwich Mean Time (GMT+3). After the Summer months the time in Greece is shifted back by 1 hour to Eastern European Time (EET) or (GMT+2)