Astronomi

Hvordan har vi målt jordens radius (gammel og ny)?

Hvordan har vi målt jordens radius (gammel og ny)?


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Jeg kan forestille mig, at gamle metoder er sjove øvelser i geometri. hvordan har målingen udviklet sig over tid?

Den første metode krediteres Eratosthenes. Han vidste, at i sommersolhverv i Syenne var Solens vinkel ved middagstid $ 0 ^ circ $. Efter dette foretog han den samme måling i Alexandria og målte vinklen på Solens overhead ved hjælp af skygger og beregnede den til $ ca. 7 ^ circ $, hvilket er cirka $ 1/50 $ af en cirkel. Derfor er både omkredsen og radius let beregnet og ret nøjagtig for sådanne råmetoder.


Dette er et ret bredt spørgsmål, så jeg begrænser mig til at beskrive en forekomst af, hvordan jordens radius måles. Specifikt vil jeg tale om, hvordan det måles i dag med den nuværende teknologi.

Efterhånden som teknologien er skredet frem, er vores evne til at måle jordens facetter nøjagtigt forbedret. På dette tidspunkt kan vi måle den nøjagtige form og størrelse på jorden med en sådan præcision, at det ikke længere er meningsfuld at spørge om "Jordens radius". Primært fordi vi kender jordens form til en sådan præcision, at vi ved, at den ikke er en perfekt sfære med en fast radius.

Den nuværende standard, der bruges til at beskrive den nøjagtige form på jorden, er verdensgeodetiske system, hvis seneste udgave omtales som WGS84. I virkeligheden er dette et koordinatsystem centreret på Jorden, der præcist beskriver jordens form. Dette gøres ved at bruge følsomme satellitmålinger til at tilpasse de sfæriske harmoniske til jordens geoid. Den nuværende, mest opdaterede version af WGS84 har mere end 4,6 millioner harmoniske udtryk med en nøjagtighed i "radius" på et givet punkt på 10 km. Det vil sige, du kan vælge en hvilken som helst præcis placering på Jorden og bruge WGS84 til at beregne jordens radius på det nøjagtige punkt til en nøjagtighed på 10 km. Denne radius ville naturligvis variere, når du bevæger dig rundt på jorden.

Hvis du virkelig vil opdele dette til et simpelt tal, betragter WGS-modellen på det groveste niveau Jorden som et afblændet sfæroid med en ækvatorial radius på $ R_ {eq} = 6 : 378 : 137 : mathrm {m} $ og en polar radius på $ R_ {p} = 6 : 356 : 752.3 : mathrm {m} $.


Hvordan har vi målt jordens radius (gammel og ny)? - Astronomi

Måling af jordens radius

Vi kan måle jordens radius for os selv, bruger intet andet end et ur!

Ved solnedgang måles det tidsrum, mellem hvilket solen ser ud til at sætte sig fra jordoverfladen og fra højden på dit hoved (h). Når du står op, kan du "se lidt længere rundt om hjørnet", og solen tager lidt længere tid at sætte sig. Dette billede viser Jorden og solen, der ser ned på solsystemet fra toppen af ​​Nordpolen. Jorden roterer mod uret, så solen går først ned på jorden og derefter senere i hovedhøjden. Jordens radius identificeres som en afstand R, og er den vinkel, jorden roterer igennem i dette tidsinterval T.

Mål ved solopgang, hvor lang tid solen ser ud til at stige op fra hovedet på dit hoved (h) og fra jordoverfladen. Når du står op, kan du "se lidt længere rundt om hjørnet", og solen stiger lidt hurtigere. Dette billede viser Jorden og solen, der ser ned på solsystemet fra toppen af ​​Nordpolen. Jorden roterer mod uret, så Solen stiger først i hovedhøjde og derefter senere på jorden. Jordens radius identificeres som en afstand R, og er den vinkel, jorden roterer igennem i dette tidsinterval T.

Her er forholdet mellem din højde h, tidsintervallet Tog Jordens radius R, hvor R og h måles i centimeter, T måles i sekunder, og T/ 240 er i enheder i grader.

Her er resultaterne for forskellige frygtløse medlemmer af en tidligere klasse, der udførte eksperimentet.

T (sekunder) h (cm) R (10 8 cm)
451800.3
271630.8
141522.9
111474.7
12178 4.8
81609.4

Folk har målt Jordens radius på detaljerede måder og fundet den til at være 6,4 & # 215 10 8 centimeter. Vi klarede os ret godt!


Hvordan har vi målt jordens radius (gammel og ny)? - Astronomi

Der er et par forskellige definitioner af krumning og flere måder at beregne den på. Se krumning på Wikipedia.
Du kan downloade lommeregneren på mit andet indlæg her
Jeg forklarer også matematikken for afstand til horisont og synsfelt her.

Jeg har fundet et par forskellige metoder, der er ret nøjagtige op til omkring 100 miles. Så er der en mere kompleks metode, der er nøjagtig op til 3.963 miles, som er jordens radius. Så støv din gamle geometri og trig-bøger af, og lad os begynde!

Zetetisk astronomi

Så den første metode, jeg skal nævne, er fra Samuel Birley Rowbotham. Han nævnes ofte af Flat Earth Society, og hans matematik bruges i mange flat earth-videoer. Han troede, at Jorden var flad og udgav en bog, der optagede sine eksperimenter Zetetic Astronomy, Earth Not a Globe. Du kan tjekke det ud her.

Rowbotham siger, at hvis jorden er 25.000 miles i omkreds, ville krumningen være 8 inches per mil.

For at bruge hans beregning kvadrerer du bare kilometertal og ganger med 8. Så hvis du bruger 3 miles, er det 3 i kvadrat (9) og ganget med 8 (72), hvilket er 6 fod. Derfor falder jorden 6 fod på 3 miles.

Pythagoras sætning

Den næste metode bruger Pythagoras sætning, der siger, at summen af ​​firkanten af ​​tilstødende og modsatte sider er lig med kvadratet af hypotenusen i en højre trekant. a & # 178 + b & # 178 = c & # 178.

Hvis radius er 3.963 miles og afstanden er 1 mile, kan vi løse ligningen. & # 8730 (3963 & # 178 + 1 & # 178) - 3963 = drop.

At sætte det i en lommeregner får du drop = .000126 mi. Der er 5280 fod i en kilometer og 12 inches i en fod. Så .000126 * 5280 * 12 = 7,98336 in.

Trigonometri

Jeg bliver muligvis nødt til at undskylde min matematiklærer for at have fortalt hende, at jeg aldrig ville bruge disse oplysninger. Den næste metode er den sværeste, så jeg vil gøre mit bedste for at forklare. Den næste metode bruger SIN COS og TAN. Hvis du har brug for en bedre måde at forklare det på, skal du gå her.

Så hvis du ikke kan huske det, bruger vi SOH CAH TOA for at løse dette.

Sin = modsat / hypotenus
Cosine = tilstødende / hypotenus
Tangent = Modsat / tilstødende

12 kommentarer:

Krumningsformlen præsenteret af de flade ørere KAN IKKE være korrekt.

BREDDEN har NUL virkning på, hvor buet eller ikke buet jorden er over en given afstand.

Hvis du ikke tror mig tjekke det ud selv ved hjælp af en appelsin eller en kugle og et målebånd, øges ikke krumningens størrelse, når du måler en længere afstand!

De anvender firkanten til det forkerte element i formlen, afstanden!

Hvordan giver det mening? Med andre ord ville krumningen på 1 mile være 1 mile x 1 mile x 8 inches = 8 inches, mens en 2 mile krumning = 2 miles x 2 miles x 8 inches = 32 inches ?! Det er klart, at det ikke er rigtigt, det kan ikke være begge dele!

Det SKAL anvendes på observatørens HØJDE for at bestemme jordens krumning ved hjælp af Pythagoras sætning, men da det er gjort, ved vi, at krumningen på jorden er 8 tommer pr. Mil.

Få din lommeregner på din telefon ud, og du kan se, hvor meningsløs denne formel bliver, hvis du øger antallet

du kan se, at det ikke engang følger en logisk progression - den bliver større med lidt mere, hver gang du prøver at finde ud af, hvad krumningen er, afhængigt af hvilken afstand du bruger (?! wtf), resultatet er, at jorden & # 39's krumning ændrer sig konstant ?!

eller med andre ord, krumningen eller faldet fra jorden over en mil er 8 inches, men over 6 miles er det 24 fod (36 gange større end ved en mile !?)? Det er klart, at disse begge ikke kan være sande.

Så her har jeg vist ved hjælp af simpel matematik, at krumningsformlen, der præsenteres af de flade ører, IKKE kan være korrekt.

De 8 tommer pr. Kilometer kvadratisk er faktisk korrekt i op til omkring 100 miles. Hvis du tegner en stor cirkel og en lige kant, der strækker sig lige ud fra toppen af ​​cirklen, vil du se, at hver inkrementel måleenhed langs den lige kant korrelerer med et længere fald end den forrige enhed.

Det er fordi du beskriver en bold med matematik. Denne beregning har eksisteret meget lang tid. Det går tilbage til Pythagoras, tror jeg. Dette er geometri. Jeg er ingen matematiker, men jeg kan fortælle, det er du heller ikke.

Først og fremmest forvirrer du dråbe med krumning, for det andet er alt, hvad du skal gøre, at bruge dine øjne. Når du ser på et bjergkæde, der ligger 50 miles væk, og det stadig er vinkelret på det fly, du er på, viser det sig, at der ikke er DROP! På en kuglejord, hvis disse bjerge var synlige, ville de IKKE være vinkelrette, de ville læne sig, og du kunne IKKE se deres toppe!

den kvadratiske formel på 8 tommer per mil er ikke korrekt til at få jordens kurve. Denne formel er til beregning af en parabel, ikke kurvens kurve.


Afstand til centrum af jorden

[/ billedtekst]
Den gennemsnitlige afstand til centrum af jorden er 6.371 km eller 3.959 miles. Med andre ord, hvis du kunne grave et hul 6.371 km, ville du nå midten af ​​jorden. På dette tidspunkt ville du være i jordens kerne af flydende metal.

Jeg sagde, at dette tal er et gennemsnit. Det er fordi Jorden ikke er en perfekt kugle, det er faktisk en afblåst sfæroid og en klemt kugle. Jorden roterer på sin akse og drejer rundt en gang om dagen. Punkter på ækvator bevæger sig i en cirkel mere end 1.600 km / time. Dette skaber en centrifugalkraft, der trækker områder af ækvator udad og flader polerne.

Afstanden til centrum af jorden fra ækvator er 6.378 km eller 3.963 miles. Og afstanden til centrum af jorden fra polerne er kun 6.356 km eller 3.949 miles. Det er en forskel på 22 km. Med andre ord, hvis du står på ækvator, er du 22 km længere væk fra jordens centrum end nogen, der står på Nordpolen.

Så hvis du ville grave hullet ned i Jorden, ville den korteste afstand være fra Nord- eller Sydpolen. Held og lykke!

Vi har skrevet flere artikler om Jordens centrum. Her er en artikel om Jordens radius, og her er en artikel om Jordens lag.

Hvis du gerne vil have mere information om det indre af jorden, skal du tjekke denne artikel fra University of Nevada, Reno.

Vi har optaget en hel episode af Astronomy Cast om Jorden. Lyt her, afsnit 51: Jorden.


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Mest nøjagtige måling nogensinde af en planetens radius uden for vores solsystem

Ved hjælp af data fra NASAs Kepler og Spitzer rumteleskoper har forskere foretaget den mest præcise måling nogensinde af størrelsen af ​​en verden uden for vores solsystem, som illustreret i denne kunstners opfattelse. Billedkredit: NASA / JPL-Caltech

Forskere har foretaget den mest præcise måling nogensinde af en planetes radius uden for vores solsystem, hvilket bekræfter Kepler-93b som en & # 8220super-Earth & # 8221, der er omkring en og en halv gange størrelsen af ​​vores planet.

Takket være NASAs Kepler- og Spitzer-rumteleskoper har forskere foretaget den mest præcise måling nogensinde af radius på en planet uden for vores solsystem. Størrelsen på exoplaneten, kaldet Kepler-93b, er nu kendt med en usikkerhed på kun 119 km (119 kilometer) på hver side af planetkroppen.

Resultaterne bekræfter Kepler-93b som en & # 8220super-Earth & # 8221, der er omkring en og en halv gange størrelsen på vores planet. Selvom superjord er almindelige i galaksen, findes der ingen i vores solsystem. Eksoplaneter som Kepler-93b er derfor vores eneste laboratorier, der studerer denne store klasse af planeten.

Med gode grænser for størrelser og masser af superjord, kan forskere endelig begynde at teoretisere om, hvad der udgør disse underlige verdener. Tidligere målinger fra Keck Observatory på Hawaii havde sat Kepler-93b & # 8217 s masse til ca. 3,8 gange den for Jorden. Tætheden af ​​Kepler-93b, afledt af dens masse og nyopnåede radius, indikerer, at planeten faktisk meget sandsynligt er lavet af jern og sten, ligesom Jorden.

& # 8220Med Kepler og Spitzer har vi fanget den hidtil mest nøjagtige måling af en fremmed planet, som er kritisk for at forstå disse fjerntliggende verdener, sagde Sarah Ballard, en NASA Carl Sagan-stipendiat ved University of Washington i Seattle og hovedforfatter af et papir om resultaterne offentliggjort i Astrophysical Journal.

& # 8220Målingen er så præcis, at det bogstaveligt talt er som at være i stand til at måle højden på en seks fod høj person inden for tre fjerdedele af en tomme & # 8212, hvis personen stod på Jupiter, & # 8221 sagde Ballard.

Kepler-93b kredser om en stjerne, der ligger omkring 300 lysår væk med cirka 90 procent af solens masse og radius. Eksoplanetens orbitale afstand & # 8212 kun omkring en sjettedel af Mercury & # 8217s fra solen & # 8212 indebærer en brændende overfladetemperatur omkring 1.400 grader Fahrenheit (760 grader Celsius). På trods af de nyfundne ligheder i sammensætningen med Jorden er Kepler-93b alt for varm til livet.

For at foretage nøglemåling om denne toastiske exoplanetradius så Kepler- og Spitzer-teleskoperne hver Kepler-93b krydse eller transit, stjernens ansigt, og formørkede en lille del af stjernelyset. Keplers blændende blik spores også samtidig dæmpningen af ​​stjernen forårsaget af seismiske bølger, der bevæger sig inden i dens indre. Disse aflæsninger koder for præcise oplysninger om stjernens interiør. Holdet udnyttede dem til snævert at måle stjernens radius, hvilket er afgørende for måling af planetens radius.

Spitzer bekræftede i mellemtiden, at exoplanetens transit så det samme ud i infrarødt lys som i Keplers observationer med synligt lys. Disse bekræftende data fra Spitzer & # 8212, hvoraf nogle blev samlet i en ny, præcis observationsfunktion & # 8212, udelukkede muligheden for, at Keplers påvisning af exoplaneten var falsk eller en såkaldt falsk positiv.

Samlet set kan dataene prale af en fejlbjælke på kun en procent af Kepler-93b's radius. Målingerne betyder, at planeten, anslået til ca. 18.700 kilometer (18.800 kilometer) i diameter, kunne være større eller mindre med ca. 240 kilometer (240 kilometer), den omtrentlige afstand mellem Washington, D.C. og Philadelphia.

Spitzer samlede i alt syv gennemgange af Kepler-93b mellem 2010 og 2011. Tre af transitene blev snappet ved hjælp af en & # 8220peak-up & # 8221 observationsteknik. I 2011 genindrettede Spitzer-ingeniører rumfartøjet 's top-up kamera, der oprindeligt blev brugt til at pege teleskopet præcist for at kontrollere, hvor lyset lander på individuelle pixels i Spitzers infrarøde kamera.

Resultatet af denne afbrydelse: Ballard og hendes kolleger var i stand til at skære halvdelen af ​​usikkerhedsområdet for Spitzer-målingerne af exoplanetradiusen og forbedre aftalen mellem Spitzer- og Kepler-målingerne.

& # 8220Ballard og hendes team har gjort et stort videnskabeligt fremskridt, mens de demonstrerer kraften i Spitzer's nye tilgang til observationer af exoplanet, "sagde Michael Werner, projektforsker for Spitzer-rumteleskopet ved NASAs Jet Propulsion Laboratory, Pasadena, Californien.

JPL administrerer Spitzer Space Telescope-missionen for NASAs videnskabelige missionsdirektorat, Washington. Videnskabsoperationer udføres på Spitzer Science Center ved California Institute of Technology i Pasadena. Rumfartøjsoperationer er baseret på Lockheed Martin Space Systems Company, Littleton, Colorado. Data arkiveres på Infrarød Videnskabsarkiv, der ligger i Infrarød Processing and Analysis Center i Caltech. Caltech administrerer JPL til NASA.

NASAs Ames Research Center i Moffett Field, Californien, er ansvarlig for Keplers jordsystemudvikling, missionsoperationer og videnskabelig dataanalyse. JPL styrede Kepler-missionens udvikling. Ball Aerospace & amp Technologies Corp. i Boulder, Colorado, udviklede Kepler-flyvesystemet og understøtter missionsoperationer med laboratoriet for atmosfærisk og rumfysik ved University of Colorado i Boulder. Space Telescope Science Institute i Baltimore arkiverer, er vært og distribuerer Kepler-videnskabsdata. Kepler er NASAs 10. opdagelsesmission og blev finansieret af agenturets direktorat for videnskabsmission.

Offentliggørelse: Sarah Ballard, et al., & # 8220Kepler-93b: En jordbaseret verden målt inden for 120 km og en testkasse til en ny Spitzer Observing Mode, & # 8221 2014, ApJ, 790, 12 doi: 10.1088 / 0004- 637X / 790 / 1/12


Hvordan har vi målt jordens radius (gammel og ny)? - Astronomi

Al-Biruni var så langt forud for sin tid, at hans mest geniale opdagelser syntes uforståelige for de fleste lærde i hans tid.


Figur (a). Artikelbanner

1. Introduktion


Figur (b). Et USSR-frimærke fra 1973, der skildrer Al-Biruni (Kilde)

George Sarton, grundlæggeren af ​​disciplinen History of Science, definerede al-Biruni som "en af ​​de allerførste videnskabsmænd i islam, og alle betragtet som en af ​​de største gennem alle tider" [1,2]. Et universelt geni, der boede i Centralasien for tusind år siden, al-Biruni “var så langt forud for sin tid, at hans mest geniale opdagelser syntes uforståelige for de fleste lærde i hans tid”, skrev Bobojan Gafurov i sin artikel på Unesco Courier [3].

Abū al-Rayhān Muhammad ibn Ahmad al-Bīrūnī (973–1048) blev født i Kath, Khwarezm [4]. Khwarezm, også kendt som Chorasmia, er en stor oase-region i det vestlige Centralasien, omgivet af Aralhavet og ørkener. Det var landet for den Khwarezmiske civilisation og for flere kongeriger. I dag er den fraktioneret og tilhører Usbekistan, Kasakhstan og Turkmenistan. Efter at have forladt sit hjemland vandrede al-Biruni i Persien og Usbekistan. Derefter, efter at Mahmud fra Ghazni erobrede emiratet Bukhara, flyttede Al-Biruni til Ghazni. Denne by, der ligger i det moderne Afghanistan, var på det tidspunkt hovedstaden i Ghaznavid-dynastiet [4-6]. I 1017 rejste al-Biruni til det indiske subkontinent, studerede den indiske videnskab og formidlede den til den islamiske verden [4,5].

Αl-Biruni var astronom, matematiker og filosof og studerede også fysik og naturvidenskab. Han var den første i stand til at opnå en simpel formel til måling af jordens radius. Desuden mente han, at det var muligt, at Jorden drejede sig om solen og udviklede ideen om, at geologiske epoker efterfølger hinanden [3]. Faktisk henvender han sig i næsten alle videnskaberne i hans videnskabelige arbejde [4,7]. Han havde fremragende kendskab til antikgræsk og studerede adskillige værker af antikke græske forskere i deres oprindelige former blandt dem. Der var Aristotelesets fysik, metafysik, De Caelo og meteorologi, værkerne af Euklid og Arkimedes, Almagest for matematikeren og astronomen Ptolemaios [7,8]. ”Da religiøs fanatisme fejede middelalderens Europa ... var al-Biruni som en forløber for renæssancen langt forud for den videnskabelige tanke, som dengang opnåede i Europa” [7,8]. Efter en kort diskussion om hans liv, lad os gennemgå nogle eksperimentelle metoder og instrumenter, denne fremragende mand foreslog og brugte.


Figur (c). En illustration fra Al-Birunis astronomiske værker forklarer de forskellige faser på månen (Kilde)

2. Liv og værker

Som tidligere fortalt blev al-Biruni født i Kath, et distrikt i Khwarezm. Faktisk betyder ordet "Biruni" på persisk "fra et ydre distrikt", og derfor blev han kendt som "den biruniske" med det latiniserede navn "Alberonius" [4,9]. I sin tidlige ungdom bragte formue al-Biruni kontakt med en uddannet græker, der var hans første lærer [3]. Hans fosterfar, Mansur, var medlem af den kongelige familie og en fremtrædende matematiker og astronom. Han introducerede al-Biruni til euklidisk geometri og ptolemæisk astronomi [3]. Derefter tilbragte al-Biruni sine første 25 år i Khwarezm, hvor han studerede kroppen af ​​islamisk lov, teologi, grammatik, matematik, astronomi og andre videnskaber. På det tidspunkt havde Khwarezm længe været berømt for sin fremrykningskultur. Dens byer havde storslåede paladser og religiøse gymnasier, og videnskaben blev værdsat og højt udviklet [3].


Figur (d). Den 4. september 2012 fejrede Google Al-Birunis fødselsdag med denne & # 8216doodle & # 8217 (Kilde)


Figur (e). Et 18. århundredes diagram over en astrolabe fra Al-Biruni & # 8217s Kitab al-Tafhim (Kilde)

Efter at have forladt sit hjemland vandrede al-Biruni i en kort periode. Han var interesseret i at fortsætte sine studier i astronomi, men dette ville kun være muligt i en stor by. Derefter bosatte al-Biruni sig på Ravy, som lå i nærheden af ​​nutidens Teheran [10]. Desværre var al-Biruni i 996 endnu ikke kendt uden for Kath, og da kunne han ikke finde en protektor i Ravy, han var fattig, men forblev selvsikker og fortsatte med at studere [10]. Det skete, at al-Khujandi (9401000), en respekteret astronom, registrerede i 994 solens transit nær solsticerne og målte Ravys breddegrad. Al-Biruni fandt, at al-Khujands resultater var unøjagtige. I sin ”Bestemmelse af koordinering af placeringer og korrekt afklaring af afstande mellem steder” forklarede al-Biruni, at problemet var i sekstanten, der blev brugt til målinger. På grund af denne iagttagelse begyndte han at blive accepteret af andre forskere og forskere [10]. I 998 gik al-Biruni til retten for Amir i Tabaristan [4]. Der skrev han et vigtigt værk, kendt som "Kronologien fra de gamle nationer". Al-Biruni forklarede, at formålet med hans arbejde var at fastlægge så nøjagtigt som muligt tidsrummet for forskellige epoker [3]. Bogen diskuterer også forskellige kalendersystemer såsom arabisk, græsk og persisk og flere andre [3]. Da Mahmud fra Ghazni erobrede emiratet Bukhara (1017), tog han alle de lærde til sin hovedstad Ghazni. Al-Biruni tilbragte derefter sit liv i at tjene Mahmud og senere hans søn Mas & # 8217ud. Han var domstolastronom og fulgte Mahmud under invasionen af ​​det nordvestlige Indien og boede der i et par år [4]. I løbet af denne tid skrev han ”Indiens historie” og sluttede den omkring 1030. Lad os bemærke, at de fleste af værkerne fra Al-Biruni er på arabisk, skønt han skrev et af sine mesterværker, Kitab al-Tafhim, begge på persisk. og arabisk [4].


Figur (f). Portræt af Rhazes (al-Razi), Wellcome Images (Kilde)

Al-Biruni katalogiserede både sine egne værker og al-Razis værker. I 1035-36, eller lidt derefter, skrev al-Biruni på opfordring fra en ven en "brev om en liste over bøgerne om Mohammad ibn Zakarīyā 'al-Rāzī" [11]. Dette brev består af to dele, den første afsat til al-Razi og hans værker, den anden til al-Biruni selv med en oversigt. Denne form for bibliografisk behandling er modelleret efter dem, der blev produceret af Galen i antikken [11]. Al-Birunis katalog over sin egen litterære produktion lister 103 titler opdelt i 12 kategorier: astronomi, matematisk geografi, matematik, astrologiske aspekter og transitter, astronomiske instrumenter, kronologi, kometer, en titelløs kategori, astrologi, anekdoter, religion og bøger, hvoraf han har ikke længere kopier [4,11]. Hans eksisterende værker inkluderer “Indica, a Compendium of Indian Religion and Philosophy”, “Book of Instruction in the Elements of the Art of Astrology” og ovennævnte “Chronology of Ancient Nations”. Vi finder også "The Mas & # 8217udi Canon", et encyklopædisk arbejde om astronomi, geografi og teknik, dedikeret til Mas & # 8217ud, søn af Mahmud fra Ghazni, "Forståelse af astrologi", som er en bog, der indeholder spørgsmål og svar om matematik og astronomi , "Apoteket", om medicin og medicin, "Gems" en bog om geologi, mineraler og ædelstene, dedikeret til søn af Mas & # 8217ud, "Astrolabe", "Historien om Mahmud fra Ghazni og hans far" og “Historie af Khwarezm” [4].

3. Jord, himmel og astronomi

Al-Biruni behandlede Jorden i mange af hans værker [12]. Han foreslog en metode til at måle dens radius ved hjælp af trigonometriske beregninger. Lad os se, hvordan han gjorde det. Først og fremmest målte han højden på en bakke ved at måle de vinkler, der blev nedlagt af bakken, på to punkter en kendt afstand fra hinanden. Så klatrede han op ad bakken og målte vinklen på horisontens dybhed [13]. I figur 1 er det vist metoden som beskrevet i [13]. Ved hjælp af en arabisk mil svarende til 1.225947 engelske miles var al-Biruni-værdien af ​​radius lig med 3928,77 engelske miles, som sammenlignes gunstigt, idet den var forskellig fra 2%, med den gennemsnitlige krumningsradius for referenceelipsoiden ved målebreddegraden dette den gennemsnitlige radius er 3847,80 miles [14]. Han gjorde dette, da han var i Fort of Nandana i Punjab [15]. Da al-Birunis selvkonstruerede instrument kunne have målevinkler op til 10 'af buen, er nøglen til målingens præcision en præcis sinusværdi, som han synes at have opnået fra forskellige indiske kilder [14].


Figur 1. Al-Birunis metode til at måle jordens radius fra (Kilde: Ref.13)

Som diskuteret i [12] betragtede al-Biruni, at verden, dvs. universet, var kommet til i tid, som muslimer troede, og så var den ikke evig, som Aristoteles fortalte. Det er imidlertid umuligt at bestemme skabelsen af ​​verden i form af menneskelige beregninger. Jorden opstod fra den naturlige tilpasning af de fire elementer med hinanden i centrum af universet, og alle himmellegeme trækkes mod den. Jorden er en klode med en ru overflade på grund af tilstedeværelsen af ​​bjerge og fordybninger, men disse er ubetydelige sammenlignet med klodens størrelse. På grund af denne uregelmæssige overflade dækker vandet ikke helt, da det ville ske for en glat kugle.

”Mens vand, ligesom jorden, har en vis vægt og falder så lavt som muligt i luften, er det ikke desto mindre lettere end jorden, som derfor sætter sig i vand og synker i form af sedimenter i bunden ... Jorden og vandet dannes en kloden, omgivet af alle sider af luften. Da meget af luften er i kontakt med månens kugle, bliver den derefter opvarmet som følge af bevægelse og friktion af de dele, der er i kontakt. Dette der er produceret ild, der omgiver luften, mindre i mængden i nærheden af ​​polerne på grund af slapningen af ​​bevægelsen der ”[12]. Når man diskuterer de geologiske ændringer på Jorden, siger al-Biruni, at "Jordens tyngdepunkt ændrer også sin position i henhold til placeringen af ​​det skiftende stof på dets overflade" [12]. ”Efterhånden som tiden går, bliver havet tørt land og tørt land havet” skrev al-Biruni [3], men “hvis sådanne ændringer fandt sted på jorden før menneskets udseende, er vi ikke opmærksomme på dem” [ 12]. For eksempel fortæller han om den arabiske ørken, som var et hav og derefter blev fyldt med sand. Han rapporterer også om opdagelsen af ​​"sten, der, hvis de blev brudt fra hinanden, skulle indeholde skaller, cowryshells og fiskeører". Ved "fiskøre" skal han have ment fossiler [12].

I Mas & # 8217udi Canon skriver al-Biruni, at Jorden er i centrum af universet, og at den ikke har nogen egen bevægelse, som den er i det ptolemaiske system. Men i denne bog tager han problemer med dette system på flere punkter. ”Han hævder for eksempel, at Solens apogee ikke er fast, og mens han accepterer den geocentriske teori, viser han, at de astronomiske fakta også kan forklares ved at antage, at Jorden drejer sig om Solen” [15]. Derefter fortæller al-Biruni fortsat sin spekulation om Jordens bevægelse, at han hverken kunne bevise eller modbevise den, men kommenterede den positivt [4]. Det ser også ud til, at han skrev i en kommentar til indisk astronomi, at han løste spørgsmålet om jordens bevægelse i et værk om astronomi, der ikke længere eksisterede, hans "nøgle til astronomi".

Lad os opsummere hans synspunkt, der rapporterer, hvad han fortæller os om et astronomisk instrument, "Zuraqi", sandsynligvis en armillarsfære eller en sfærisk astrolabe eller endda en mekanisk astrolabe. Al-Biruni skriver, at Sijzi, en persisk astronom og matematiker fra Sistan, en region, der ligger i det sydvestlige Afghanistan og sydøst for Iran, opfandt en astrolabe, hvis design var baseret på ideen om, at jorden bevæger sig [4 , 16,17]: ”Jeg har set astrolabien kaldet Zuraqi opfundet af Abu Sa & # 8217id Sijzi. Jeg kunne godt lide det meget og priste ham meget, da det er baseret på ideen underholdt af nogle om, at den bevægelse, vi ser, skyldes jordens bevægelse og ikke himmelens. I mit liv er det et problem, der er vanskeligt med løsning og tilbagevisning. … For det er det samme, om du tager det, at Jorden er i bevægelse eller himlen. For i begge tilfælde påvirker det ikke astronomisk videnskab. Det er bare for fysikeren at se, om det er muligt at tilbagevise det ”[4,16].

4. Zijes

Den islamiske guldalder (8.-15. Århundrede) fremmede stærkt astronomien, og flere forskere bidrog til dens udvikling. De islamiske forskere assimilerede og sammensmeltede forskelligt materiale for at skabe deres astronomiske videnskab. Dette materiale omfattede især græske, sassanidiske og indiske værker [18]. Til gengæld havde islamisk astronomi en betydelig indflydelse på astronomien i det middelalderlige Europa. Mange stjerner og astronomiske udtryk som alidade, azimut og almucantar omtales stadig med deres arabiske navne [18]. Fra 700 til 825 har vi assimilering og synkretisering af tidligere hellenistisk, indisk og sassanidisk astronomi. Nogle første astronomiske tekster, oversat til arabisk, havde indisk og persisk oprindelse. Den mest bemærkelsesværdige af disse tekster var "Zij al-Sindhind", et indisk astronomisk værk fra det 8. århundrede, der blev oversat af al-Fazari og Yaqub ibn Tariq efter 770 under tilsyn af en indisk astronom, der besøgte retten til den abbasidiske kalif al -Mansur [18]. I denne periode vedtog araberne sinusfunktionen, nedarvet fra indisk geometri, i stedet for buekorder anvendt i græsk trigonometri [18,19]. Fra 825 til 1025 var der en periode med kraftig efterforskning, hvor det Ptolemaiske astronomisystem blev accepteret, dog under muligheden for observationsforbedringer og matematiske ændringer [18,19]. Et af de største værker var "Zij al-Sindh" skrevet af al-Khwarizmi i 830. I denne periode kom en stor impuls til astronomisk forskning fra de abbasidiske kaliffer. De støttede dette videnskabelige arbejde økonomisk og gav det en formel prestige [18].

Zij er det generiske navn på islamiske astronomiske bøger, der tabellerer parametre, der bruges til astronomiske beregninger vedrørende solens, månens, stjernernes og planets positioner. Navnet stammer fra et persisk udtryk, der betyder ledning. May be, this is a reference to the arrangement of the threads on a loom, like the tabulated data are arranged in rows and columns [20]. Let us remark that the medieval Muslim zijes were more extensive, typically including materials on chronology, and the geographical latitudes and longitudes. Going beyond the traditional contents, some zijes even explain the theory or report the observations from which the tables were computed [20]. Besides the Zij written by al-Khwarizmi, other famous zijes are those of the Egyptian astronomer Ibn Yunus (c. 950-1009). In one of them he described, with precision, forty planetary conjunctions and thirty lunar eclipses [21]. His astronomical tables give data obtained with very large astronomical instruments and the use of trigonometric identities [22].

Probably it was not the entire driving force to this growth of astronomy, but religion contributed to it [21]. In fact, the Islam needed a way to figure out how to orient all sacred structures toward Mecca [21]. And then a precise celestial mapping was necessary to find the right direction, or qibla, toward the Kaaba. By the 9th century, the astronomers were commonly using trigonometry to determine the qibla from geographical coordinates, turning the qibla determination into a problem of spherical astronomy. Al-Biruni for example, in “The Determination of the Coordinate of Locations and for Correctly Ascertaining the Distances between Places”, has the goal to find the qibla at Ghazni.

One of the al-Biruni zijes contains a table giving the coordinates of six hundred places, almost all of them measured by al-Biruni himself. For some places he is reporting data taken from similar tables given by al-Khwarizmi. Al-Biruni seems to have realized that for places given by both alKhwarizmi and Ptolemy, the value obtained by al-Khwarizmi was more accurate [19,21]. Muhammad ibn Mūsā al-Khwārizmī (c. 780 – c. 850) was a Khwarezmian too. In the early 9th century, he produced accurate sine and cosine tables, and the first table of tangents. He was also a pioneer in spherical trigonometry. By the 10th century, Muslim mathematicians were using all six trigonometric functions. Let us note that the term “algorithm” is coming from medieval Latin “algorismus”, a mangled transliteration of Arabic al-Khwarizmi, “native of Khwarezm”. The earlier form of this word in Middle English was “algorism” (early 13th c.) [23].

5. Quadrants, Astrolabes and Clocks

As told in [15], al-Biruni was among those deported in Afghanistan by Mahmud of Ghazni . He was then 44 years old. On 14 October 1018, we find him in a village south of Kabul, where he wanted to measure the height of the sun but had no instrument to hand. So he was obliged to draw a calibrated arc on the back of a reckoning board and used it, with the aid of a plumb line, as a makeshift quadrant. On the basis of the measurements made with this crude device he calculated the latitude of the locality. This quadrant was probably an inclinometer based on quarter-circle panel.


Figur 2. A quadrant.

Along one edge there were two sights forming an alidade. A plumb bob was suspended by a line from the centre of the arc as in the Figure 2. In order to measure the altitude of a star, the observer would view the star through the sights (pinholes in the case of the Sun) and hold the quadrant vertical. The plumb indicates the reading on the graduation. It is better to have a person concentrated on observing the star and holding the instrument and another person to take the reading. The accuracy of such an instrument is limited by its size.

An astrolabe is a more elaborate instrument. It helps in measuring the positions of Sun, Moon, planets, and stars, and it is therefore fundamental to determine the local time at a given latitude and vice-versa. An astrolabe consists of a disk, the “mater”, deep enough to hold one or more flat plates called “tympans” [24]. Each tympan is made for a specific latitude and engraved with a stereographic projection of circles denoting azimuth and altitude, and representing the portion of the celestial sphere above the local horizon (see the Figure 3). Two other sets of curves represent the unequal hours and the houses of the heaven. The rim is typically graduated into hours of time, degrees of arc, or both. Above the mater and tympan, there is the “rete”, a framework bearing a projection of the ecliptic plane and several pointers indicating the positions of the brightest stars [24]. The rete is free to rotate. When it is rotated, the stars and the ecliptic move over the projection of the coordinates on the tympan. One complete rotation corresponds to a day. On the back of the mater, there is often engraved a number of scales, useful in various applications, and a graduation of 360 degrees around the rim. The alidade is attached to the back face. When the astrolabe is held vertically, the alidade can be rotated and the Sun or a star sighted along its length, so that its altitude in degrees can be read from the graduated edge of the astrolabe [24].


Figure 3. Curves of altitude (almucantar) and azimuth on the astrolabe, from the book entitled “Dell’Uso et Fabbrica dell’Astrolabio”, by Egnatio Danti, Giunti, Firenze, 1578 [25].

Al-Biruni, in a treatise on the Astrolabe, describes how to tell the time during the day or night and use it, as it can be used a quadrant, for surveying. In fact, the astrolabe is a complex instrument, and all its features have been added over centuries. Moreover, several other instruments have been used at the time of al-Biruni. Reference 26 contains the critical edition with English translation of an Arabic treatise on the construction of over one hundred various astronomical instruments, composed in Cairo ca. 1330, with citations to the al-Biruni works.

The mechanical astrolabes with gears were invented in the Muslim world. These geared instruments were designed to produce a continual display of the current position of Sun and planets. We find a device with eight gear-wheels (Figure 4, on the right) illustrated by al-Biruni in 996, so that this al-Biruni mechanism can be considered an ancestor of the astrolabes and clocks developed by later Muslim engineers. The same author of [26], François Charette, is considering it a simpler version of the Antikythera mechanism [27], such as previously proposed by Derek J. de Solla Price [28].


Figure 4. On the left, an attempt of reconstruction made by the Rear Admiral Jean Theophanidis [29] of the Antikythera mechanism and, on the right, the al-Biruni mechanism, adapted from Ref.28.

In 1900, a Greek sponge diver discovered the wreck of an ancient ship off the Antikythera island in the Dodecanese. Divers find several bronze and marble statues and other artifacts from the site. In 1902, an archaeologist noticed that a piece of rock recovered from the site had a gear wheel embedded in it. This rock revealed itself as one of the oldest known geared devices, able to display the motions of Sun, Moon and planets. After decades of work on it, de Solla Price, discussed this mechanism in an article entitled “An Ancient Greek Computer” in the Scientific American of June 1959. He saw a direct connection between devices like the Antikythera machine and the Islamic astrolabes. Several years after, a Byzantine device dating from the 6th century, which models the motions of the Sun and Moon, had been discovered: this device can be used as a link between the Antikythera mechanism and the mechanical instrument described by al-Biruni [30]. It is probable that the Antikythera mechanism was not the only one. Cicero, in the 1st century BC, is mentioning an instrument constructed by the philosopher Posidonius, “which at each revolution reproduces the same motions of the sun, the moon and the five wandering stars (the planets) that takes place in heaven day and night” [30].

6. A Balance of Wisdom

Al-Biruni developed experimental methods to determine the density of substance, some based on the theory of balances and weighing and others based on the volume of fluids. He also generalizes the theory of the centre of gravity and applies it to the volumes. As told in [31], “using a whole body of mathematical methods … , Arabic scientists raised statics to a new, higher level. The classical results of Archimedes in the theory of the centre of gravity were generalized and applied to three-dimensional bodies, the theory of ponderable lever was founded and the ‘science of gravity’ was created and later further developed in medieval Europe. The phenomena of statics were studied by using the dynamic approach so that two trends – statics and dynamics – turned out to be interrelated within a single science, mechanics. … Numerous fine experimental methods were developed for determining the specific weight, which were based, in particular, on the theory of balances and weighing. The classical works of al-Biruni and al-Khazini can by right be considered as the beginning of the application of experimental methods in medieval science”.

As told in [32], al-Khāzini (Abu al-Fath Khāzini, who fourished 1115–1130) described an istrument used by al-Biruni in measuring densities. It was a hydrostatic balance. The scales were used to test the purity of metals and to ascertain the composition of alloys. The Arabs used a method based on comparison of the weights of equal volumes: Al-Biruni for example, takes hemispheres of the different metals or rods of equal size and compares their weight [32].


Figur 5. A mizan al-hikma, a balance of wisdom, which is in fact a hydrostatic balance, like that of the “The Book of the Balance of Wisdom” by Al-Khāzini.

In the Figure 5 we can see a drawing of a mizan al-hikma, a balance of wisdom, which is in fact a hydrostatic balance, created after an image from the book of Abu al-Fath Khāzini (flourished 1115– 1130), entitled “The Book of the Balance of Wisdom” [33]. Reference [34] tells that, as early as 1857, the year in which the American Oriental Society published in its journal the contribution

of N. Khanikoff on this book, it was known that as far as the determination of the specific gravity, AlKhazini had drawn much from the work of Al-Biruni.

The hydrostatic balance is an old instrument. The Latin poem “Carmen de Ponderibus et Mensuris” of the 4th or 5th century describes the use of it referring to Archimedes [35,36]. This balance is also linked to a widely known anecdote. A votive crown for a temple had been made for King Hiero II of Syracuse, who supplied the pure gold, and Archimedes was asked to determine whether some silver had been substituted by the goldsmith. Archimedes had to solve the problem without damaging the crown, so he could not melt it down into a regularly shaped body and calculate its density from weight and volume. Concerning the anecdote of the golden crown, Galileo Galilei suggested that Archimedes used the hydrostatic balance.

7. Vitruvius’ and al-Biruni’s methods

However, to evaluate the density or specific weight of materials, al-Biruni refers to another method too. This method is based on the volumes of fluids and on the use of a specific instrument. It was a vessel in which the level of water or oil remained constant, since any excess was drained out of the holes made for this purpose. He was able to measure the displaced water with such exactitude that his findings nearly correspond with modern values [32,34]. The Figure 6 shows this vessel depicted by al-Khāzini, as a cone-shaped vessel. To measure the specific gravities of gemstones, al-Biruni used it.

Before discussing the method, let us read what Vitruvius is writing in his De Architectura, in the chapter entitled “of the Method of Detecting Silver when Mixed with Gold” [37]. “Charged with this commission (to determine whether the crown had silver inside or not), he (Archimedes) by chance went to a bath, and being in the vessel, perceived that, as his body became immersed, the water ran out of the vessel. Whence, catching at the method to be adopted for the solution of the proposition, he immediately followed it up, leapt out of the vessel in joy, and, returning home naked, cried out with a loud voice that he had found that of which he was in search, for he continued exclaiming, in Greek, Eureka, (I have found it out). After this, he is said to have taken two masses, each of a weight equal to that of the crown, one of them of gold and the other of silver. Having prepared them, he filled a large vase with water up to the brim, wherein he placed the mass of silver, which caused as much water to run out as was equal to the bulk thereof. The mass being then taken out, he poured in by measure as much water as was required to fill the vase once more to the brim. By these means he found what quantity of water was equal to a certain weight of silver. He then placed the mass of gold in the vessel, and, on taking it out, found that the water which ran over was lessened, because, as the magnitude of the gold mass was smaller than that containing the same weight of silver. After again filling the vase by measure, he put the crown itself in, and discovered that more water ran over then than with the mass of gold that was equal to it in weight and thus, from the superfluous quantity of water carried over the brim by the immersion of the crown, more than that displaced by the mass, he found, by calculation, the quantity of silver mixed with the gold, and made manifest the fraud of the manufacturer.” What Vitruvius describes is the Archimedean displacing volume method. In Reference [37], I proposed that Archimedes could have used the vessel of a water-clock, that is, of a clepsydra. Moreover, I repeated the experiment to show in detail the method.

Probably al-Biruni read a different report, from a Greek source of this episode. Let us see how al-Biruni could have interpreted it, by describing the method he used to determine the density of a substance. Al-Biruni filled with water the vessel in the Figure 6 until the water began to run out by a pipe at the side then a definite mass, as large as possible, of the substance is weighed (P1) and the pan (P2) of a scale placed under the outlet pipe [32]. Then, the substance is put in the vessel. This body displaces the water so that it flows in the pan. The pan and the water are weighed (P2+P3). The difference ((P3+P2)−P2) is the weight of the displaced water. By the ratio P1/P3 we can have the density of the substance.

Al-Biruni applied the method to determine the density of precious stones. For instance, the sapphire has a specific gravity (the ratio of the density of a substance to the density of a reference substance) of 3.95–4.03, whereas the glass of 2.4–2.8. Using his method, it is possible to distinguish them. For what concerns the accuracy of the method, al-Khāzini remarks that it is difficult to weigh the amount of water displaced, because the water sticks to the sides of the outlet-tubes [34]. And in fact, al-Biruni tells that it is better to use a mass as large as possible in order to increase the accuracy. The determination of specific gravity played a quite important role in the al-Biruni’s researches, and the results he obtained were propagated by various scholars of the Islamic countries. One may ask why this research was so relevant [34]: because al-Biruni acknowledged a social importance for it, that is, an intrinsic worth in metals and jewels. Therefore, certain physical properties had to be found to evaluate them [34]. For instance, al-Biruni objected against the classification of gems on the basis of their colours only, as was the common practice of the time. The colour is a secondary property: specific gravity brilliance and hardness are the relevant properties of materials. The hardness was determined by the use a tip of a sample material and by observing the indentation it is producing [34].

8. Heat and Light

Reference [34] is pointing out that, contrary to his astronomy or astrology works, on which he wrote separate treatises, there does not exist a single book devoted exclusively on physics, but it is necessary to read all the books to evaluate his physical researches. And then in [34], after such a research, we find what al-Biruni thought on heat and light.

Aristotle considered heat to be a fundamental quality of the element fire and inherent in all things. There are two types of heat, by which the bodies can be heated: internal or external. Starting from the Aristotle’s works, Al-Biruni came to the conclusion that “heat is nothing but the rays of the Sun detached from the body of the Sun towards the Earth” [34]. And then, “the heat exists in the rays, it is inherent in them”. As observed in [34], the natural conclusion would be that air is heated by the Sun, but al-Biruni tells that “the warmth of the air is the result of the friction and violent contact between the sphere, moving rapidly, and his body”. This is an Aristotelian manner of thinking. In any case, al-Biruni had the merit of understanding the connection between motion and heat, the same we find in the Kinetic Theory of heat [34].

And heat and rays were the subjects of several letters of a correspondence between al-Biruni and Ibn Sīnā, Avicenna, and there we find that the heat is generated by the motion and cold by the rest, and for this reason, the Earth is hot at the Equator and cold at the Poles. Another important discussion between the two scientist was on the propagation of heat and rays of Sun. Al-Biruni’s opinion was that that light and heat are immaterial, and that the heat exists in the rays and it is inherent in them. How is therefore the propagation of heat? After this al-Biruni’s question, Avicenna answered that the heat was not propagating by itself, but the rays of the Sun are propagating, and the heat is carried by them, like a man in a boat, which is not moving, but his boat is moving [34]. A very interesting discussion between two outstanding persons.

This problem of the propagation of heat leads al-Biruni to study the problem of the nature and propagation of light. He stated that “there is a different opinion regarding the motion of the rays. Some say, this motion is timeless, since the rays are not bodies. Others say, this motion proceeds in very short time: that, however, there is nothing more rapid in existence, by which you might measure the degree of its rapidity, e.g. the motion of the sound in the air is not so fast as the motion of the rays, therefore the former has been compared with the latter and thereby its time (the degree of its rapidity) has been determined” [34]. According to [34], this is the first reference to the problem of measuring the speed of light.

9. Al-Biruni’s Wisdom

Let me conclude this paper with some words written by al-Biruni [39], which illustrate quite well the wisdom of this person and his passion for scientific research. It is the parable of the four pupils, from his “Indica”.

A man is travelling together with his pupils from some business towards the end of the night. There appears something standing erect before them on the road, the nature of which is impossible to recognize because of darkness. The man turns towards his pupils and asks them what it is. The first says “I do not know what it is”, the second “I do not known, and I have no means of learning what it is”, the third “It is useless to examine what it is, for the raising of the day will reveal it”. It is clear that none of them had attained the knowledge: the first because of his ignorance, the second was incapable and had no means of knowledge by learning, and the third because he was indolent and acquiesced on his ignorance. The fourth pupil did not give an answer: he stood still and then he went on in the direction of the object. On coming near, he found that it was pumpkins on which there was something entangled. He considered that no living man, endowed with free will, could stand still in this situation, and therefore it was a lifeless object. To be sure, he went quite close to it and struck again it with his foot till it fell to the ground. Thus, removed all doubt, he returned to his master and gave him the exact account.

10. References

[1] G. Sarton, Introduction to the History of Science, Carnegie Institution of Washington, 1927.

[3] B. Gafurov, Al-Biruni, a Universal Genius Who Lived in the Central Asia a Thousand of Years Ago, The Unesco Courier, June 1974, Pages 4-9.

[5] D.J. Boilet, Al-Biruni, The Encyclopaedia of Islam, Vol. I, H.A.R. Gibb, J.H. Kramers, E. LeviProvencal and J. Schacht Editors, Brill, 1986.

[7] C.K. Skarlakidis, Holy Fire, The Miracle of Holy Saturday at the Tomb of Christ, Forty-five Historical Accounts (9th–16th c.), available at: www.scarlakidis.gr/ENGLISH/09.albiruniENGLISH.html

[8] D. Tsibukidis, Graeco-Hellenistic Philosophical Thought in the Writings of Abu Raikhan Biruni, Graeco-Arabica, 2000, Volume 7–8, Pages 524-533.

[9] C. Edmund Bosworth, Bīrūnī, Abū Rayhān, i. Life, in Encyclopedia Iranica, 2010, Volume IV, Issue 3, Pages 274-276.

[10] B. Scheppler, Al-Biruni: Master Astronomer and Muslim Scholar of the Eleventh Century, The Rosen Publishing Group, August 1, 2005.

[11] D. Pingree, Bīrūnī, Abū Rayhān, ii. Bibliography, in Encyclopedia Iranica, 2010, Volume IV, Issue 3, Pages 276-277.

[12] S. Maqbul Ahaman, Geodesy, Geology, and Mineralogy, Geography and Cartography, in History of Civilizations of Central Asia, Volume 4, Issue 2, Clifford Edmund Bosworth and M.S. Asimov Editors, Motilal Banarsidass Publ., 2003.

[13] B. Lumpkin, Geometry Activities from Many Cultures, Walch Publishing, Jan 1, 1997.

[14] C. K. Raju, Cultural Foundations of Mathematics: The Nature of Mathematical Proof and the Transmission of the Calculus from India to Europe in the 16th C. CE, Pearson Education India, 2007.

[15] J. Boilot, The Long Odyssey, The Unesco Courier, June 1974, Pages 10-13.

[16] S. Hossein Nasr, An Introduction to Islamic Cosmological Doctrines, Pages 135–136, State University of New York Press, 1993.

[17] M. Salim-Atchekzai, A Pioneer of Scientific Observation, The Unesco Courier, June 1974, Pages 16-18.

[19] A. Dallal, Science, Medicine and Technology, in The Oxford History of Islam, J. Esposito Editor, Oxford University Press, 1999.

[21] D. Teresi, Lost Discoveries: The Ancient Roots of Modern Science, Simon and Schuster, May 11, 2010.

[23] D. Harper, Online Etymology Dictionary, 2001-2013.

[25] Egnatio Danti, Dell’Uso et Fabbrica dell’Astrolabio, Giunti, Firenze, 1578.

[26] F. Charette, Mathematical Instrumentation in the Fourteenth-Century in Egypt and Syria, BRILL, 2003.

[27] F. Charette, Archaeology: High tech from Ancient Greece, Nature, 2006, Volume 444, Pages 551-552.

[28] D.J. de Solla Price, Of the Origin of Clockwork, Perpetual Motion Devices and the Compass, in Contributions from the Museum of History and Technology, United States National Museum Bulletin 218, Smithsonian Institution, Washington D.C., 1959.

[29] J. Theophanidis, Praktika tes Akademias Athenon, Athens, 1934, Volume 9, Pages 140-149.

[30] Ö. Wikander, Gadgets and Scientific Instruments, in The Oxford Handbook of Engineering and Technology in the Classical World, John Peter Oleson Editor, Oxford University Press, 2008, Pages 785-820.

[31] M. Rozhanskaya and I.S. Levinova, “Statics”, p. 642, in the Encyclopedia of the History of Arabic Science, Routledge, 1996.

[32] M. Th. Houtsma, E.J. Brill’s First Encyclopaedia of Islam, 1913-1936, Volume 5, BRILL, 1003.

[33] B.A. Danzomo and A.O. Shuriye, The Contribution of Al-Khazini in the Development of Hydrostatic Balance and its Functionality, in Contributions of Early Muslim Scientists to Engineering Sciences and Related Studies, A.O. Shuriye and A.F. Faris Editors, IIUM Press, 2011.

[34] S. M. Razaullah Ansari, On the Physical Researches of Al-Biruni, Vol10. Issue 2, Pages 198217.

[35] F. Costanti, The Golden Crown: a Discussion, in The Genius of Archimedes – 23 Centuries of Influence on Mathematics, Science and Engineering: Proceedings of an International Conference held at Syracuse, Italy, June 8-10, 2010.

[36] M. Berthelot, Sur l’Histoire de la Balance Hydrostatique et de Quelques Autres Appareils et Procédés Scientifiques, Annales de Chimie et de Physique, Série 6, 1891, Volume 23, Pages 475485.

[37] Marcus Vitruvius Pollio, The Architecture, Joseph Gwilt translator, Priestly and Weale, London, 1826.

[38] A.C. Sparavigna, The Vitruvius’ Tale of Archimedes and the Golden Crown, Archaeogate, 1708-2011.

[39] Miniature anthology of al-Biruni, The Unesco Courier, June 1974, Pages 19-26.

* This article had been published in the International Journal of Sciences 12 (2013):52-60. DOI: 10.18483/ijSci.364


How have we measured the radius of the Earth (old and new)? - Astronomi

Ruler means two things, a regulated standard of length and the king who does the regulating, the ruler, so since geometry means earth measure, we can show that the most ancient rulers held power because they could measure and map the earth by astronomy. The greek Eratosthenes of Alexandria circa 300 b.c. is credited to have been the first to have come close to accurately measuring the circumference length of the earth, his estimate of 252,000 stadion. Yet we don’t know what was the length of the greek stadion at his time, so precisely what the circumference length of the earth calculated by him in still unknown.

But what we do know is that the stadion length in more ancient times (during the Ice Age which too actually was the bronze age) was a precise subdivison of the radius length of the earth, hence the origin of the term geometry, earth measure, that archaic original stadion 1/10th of a modern nautical mile, with 600 olympic feet (each of 12.16 modern inches) having composed that most ancient stadion, the math and astronomy of that surprisingly simple ancient method explained here http://genesisveracityfoundation.com/earth-measure-geometry.

So if Eratosthenes had measured the earth by the more ancient method according to the earth’s wobble rate rather than by shadows at Alexandria and Syrene, he would have calculated that the circumference length of the earth is 216,000 original stadions, 21,600 modern nautical miles, that precise knowledge of geometry, earth measure, upon which his ancient predecessors had capitalized to have been rulers, demonstrated with the Maps of the Ancient Sea Kings (Hapgood), those ancient sea kings who sailed and settled all over the world, in line with the Table of Nations in Genesis 10 of the Bible, the science of the future, old school man.


Circumference of the Earth

The circumference of the Earth in kilometers is 40,075 km, and the circumference of the Earth in miles is 24,901. In other words, if you could drive your car around the equator of the Earth (yes, even over the oceans), you’d put on an extra 40,075 km on the odometer. It would take you almost 17 days driving at 100 km/hour, 24 hours a day to complete that journey.

If you like, you can calculate the Earth’s circumference yourself. The formula for calculating the circumference of a sphere is 2 x pi x radius. So, the radius of the Earth is 6371 km. Plug that into the formula, and you get 2 x 3.1415 x 6378.1 = 40,074. It would be more accurate if you use more digits for pi.

You might be interested to know that the circumference of the Earth is different depending on how you measure it. If you measure the circumference around the Earth’s equator, you get the 40,075 km figure I mentioned up to. But if you measure it from pole to pole, you get 40,007 km. This is because the Earth isn’t a perfect sphere it bulges around the equator because it’s rotating on its axis. The Earth is a flattened sphere, and so the distance around the equator is further than the circumference around the poles.

Want some comparison? The circumference of the Moon is 10,921 km, and the circumference of Jupiter is 500,000 km.

Here are a bunch of measurements for you:
Circumference of the Earth in kilometers: 40,075 km
Circumference of the Earth in meters: 40,075,000 meters
Circumference of the Earth in centimeters: 4,007,500,000 centimeters

Circumference of the Earth in miles: 24,901 miles
Circumference of the Earth in feet: 131,477,280 feet
Circumference of the Earth in inches: 1,577,727,360 inches

We have written many articles about Earth for Universe Today. Here are some photos of the Earth and Moon together, and here are the 10 most impressive impact craters on Earth.

We have also recorded an episode of Astronomy Cast about Earth, as part of our tour through the Solar System – Episode 51: Earth.


The Greek Way

I don't know where he got this idea (surely not from the internet), but Eratosthenes estimated the radius of the Earth by looking at two shadows at two different locations on the Earth. This diagram should help.

So, by looking at the length of the shadow at Alexandria and knowing the distance between these two locations, the radius can be calculated. There is one trick. The size of a shadow changes during the day and during the year. How could you overcome these problems before watches, cellphones, accurate maps, and Wikipedia? Simple, you cheat. Instead of measuring the shadow at two different places at the same time, you measure at two different places on the same day (but a year later). So, if you know the day and the time, you can just repeat the experiment. The other trick is to use the local solar noon. This is when the sun is at the highest point in the sky. If you just move north-south, this time is the same for both locations.

In the end, the Greeks obtained a fairly nice value for the radius of the Earth.


StormsHalted (author) from Karachi, Pakistan on November 07, 2019:

fatemeh on November 07, 2019:

I want write a paper about Al-Biruni&aposs.I want use this information.How can addressed your work.

Larry Scott on May 04, 2019:

The trigonometry is quite insightful. And he proof very clear.

The comments are however, bizarre. 500 yrs ago the shape and size of the earth was already well known. The shape has been known for millennia. Heliocentric v geocentric, Copernicus and Galileo, was in debate, not the shape and size pretty accurately given the tech of the times.

However, without accurate values for, or even existence of, refraction the radius would be over stated, by a lot on the order of 15%. And the angle to the horizon is extremely sensitive. An astrolabe, without optics, it’s hard to believe the angle could be measured better than 1/10 of degree.

Still the history shows, the shape and size of the earth was known to spherical, and big, and that is a huge accomplishment.

With a theodolite today, and knowledge of refraction, and the method attributed to Biruni the radius can easily be measured to 0.25%.

Walter Bislin on November 30, 2018:

My hopefully correct error analysis tells, that to get the radius of the earth to 1% accuracy you have to measure the drop angle to the horizon to this amount of accuracy. The error due to standard refraction (k = 0.14) in his configuration (horizon at about 62 km) is about 8%. Did he know about refraction or was it a coincidence to get the radius with such an accuracy?

Anyway: an estimate of R to 10% would not be bad. In no case is the earth flat.

refraction_angle_correction = arcsin( k * distance / diameter_earth ) = 0.04 degrees

Faylasoof on July 11, 2018:

Lacho your comment shows your limited level on knowledge: "Excuse me. didn&apost Biruni lived like a 1200 y. ago ? And didn&apost the globe idea became popular only 500 y. ago ? So, I guess. the question is, who is lying here, because not only that islam claim the Earth is flat, but also. . & quot. Nothing in your statement correct, apart from Birun&aposs name and roughly how long ago he lived! Islam claims the earth is flat! There may be some people who might claim but &aposIslam&apos per se makes no such claim! Besides, during the age we are talking about many mathematical and scientific advances were being made in the Islamic world since orthodoxy, the killer of new ides, had not set in, as yet. The acceptance of new ideas and the effort to better them as paramount in the minds of these people. If in doubt, read the following:

George Saliba Islamic Science And The Making Of The European Renaissance

Arabic mathematics : forgotten brillia

Assessing Arabic contributions to the sciences

Abdul on October 02, 2017:

All guys are from my land UZBEKISTAN though none knows about it much due to USSR. We were the best Scientist of the world but after Russian colonization everything became too unattractive here.

Vinod Kattilapoovam on July 02, 2017:

In the advancement of all aspects of astronomy and geography, stands out the dominating figure of Abu Raihan Muhammad ibn-i-Ahmad Al-Biruni (973-1048AD) who was one of the very greatest scientists of Islam. Once he wrote, I do not scorn to accept truth from whatever source I can find. Having a command over the Sanskrit language he exploited the best sources of Indian sciences including mathematics, astronomy and chronology. He described the earth, its axis and its movements, and threw much light on the Indian contribution to the general geography of India. The teory of the movement of th earth was apparently borrowed by Al-Biruni from Arya Bhatta, who in the fifth century AD suggested that the earth revolved round the Sund and rotated on its axis. His Qanunal-Mas’udi (compiled in 1030 AD) is the most important work on astronomy which is largely based o Indian astronomical ideas. He also utilized the knowledge of Indian geology and minerology. Besides, Al-Biruni translated Surya Siddhanta of Varahamihira. To this period also belonged the celebrated scientist, astronomer and physician Abu Ali Sina (AH 428/1036AD) who advanced the knowledge of physics and astronomy with the help of Indian and Greek sources.

Y𠆚qubi (AH 234/897AD) the famous Arab historian refers to Indian achievements in these words:

The Indians are men of science and thought. They surpass all other people in every science their judgement on astronomical problems is the best. In the science of medicine their ideas are highly advanced. There are a large number of books which deal with their principles. And they have a large number of other books which are too many to be mentioned. (source: India&aposs contribution to world thought and culture. Chapter name: India&aposs contribution to Arab civilization. Page no. 583)

Babak Pakdaman Sardrood on June 22, 2017:

So interesting. I watched a documented film that included an abstracted information on the Great scientist. Then, I did not understand the Scientist&aposs methodology, then I tried to find a way to calculate earth radius. I have studied mathematics till the end of high school and some further during BSc studies. Then, I thought. I have found a simpler method with a simpler formula. The method is different from that used by the Great Iranian Scientist Abu Reyhan Biruni.

Lacho on May 29, 2017:

Undskyld mig. didn&apost Biruni lived like a 1200 y. ago ? And didn&apost the globe idea became popular only 500 y. ago ? So, I guess. the question is, who is lying here, because not only that islam claim the Earth is flat, but also. there was no indication of the Earth as a globe 1200 y. ago ?

Greg on March 09, 2017:

I find this particularly interesting since I&aposve been looking at flat earthers lately, and the number of flat earthers has been growing.

I do have to respond to Alan, though. The Church knew very well that the earth was round. It&aposs a myth that medieval thinkers thought the earth was flat, spread by Enlightenment-era thinkers who wanted to contrast their enlightened and humanistic age with the "dark ages" that came before. We&aposve gotten a lot of notions from them that persist to this day.

But that makes the modern flat earthers even more of a riddle, since it&aposs a form of biblical literalism for them young earth creationism just isn&apost literal enough.

I wonder if the Foshay Tower is tall enough to reasonably reproduce Al-Biruni&aposs measurement. I will try.

Arshad Malik on November 28, 2016:

Al-biruni did first to calculation of the Earth&aposs in Tilla Jogian - The highest peak in the Eastern Salt Range in Province of Punjab Pakistan

Hummingbird5356 on November 11, 2016:

Iran is the modern name for Persia.

jonnycomelately on April 30, 2016:

I am fascinated that even in the 10th Century, people knew the Earth was not flat!

Could it be that we have all been mislead by the Church of Rome?

StormsHalted (author) from Karachi, Pakistan on February 17, 2016:

"Alpha" is the angle of depression of the horizon from the mountain top.

Leo on February 17, 2016:

The equation is useless if you don&apost explain how do you get the ALPHA value?

Hummingbird5356 on November 19, 2015:

Actually, no one has said that Biruni was from Pakistan. He carried out his calculations while in India. This part of the country is in modern day Pakistan.

elektroniska on November 18, 2015:

Interestingly that people from Pakistan are trying to say that Biruni was from Pakistan. He was neither Arab or from Pakistan but he was a Persian scientist. Please read https://en.wikipedia.org/wiki/Al-Biruni

Of course, as we now-a-days publish our work in English, during that era it was common to publish in Arabic. He was from North-East Iran and because Pakistan and Afghanistan were part of the country he had traveled to those places too.

Mohammed shahid on July 07, 2015:

it is a wonderful palace to take information

Ronald E Franklin from Mechanicsburg, PA on June 07, 2015:

Fascinating account. That 10th century scholars even had the confidence to think they could determine the radius of the earth is astounding. One suggestion: your first statement of the law of sines had me befuddled since it uses A and C to represent both angles and points. Other than that, it was a clear and very interesting presentation.

Hummingbird5356 on March 02, 2015:

Pakistan is a country I have visited and like very much and the people too. I have been doing some research into the area and there is a lot to learn. So much has happened in your country over the centuries. It has a rich history and you can be proud of this.

StormsHalted (author) from Karachi, Pakistan on March 02, 2015:

Such a deep insight about the country is rarely found nowadays, even more rare is that it rests with a foreigner!

Hummingbird5356 on March 01, 2015:

Did you know that Al-biruni did this work in what is now Pakistan? He used the mountain at Nandana for his calculations and he studied Sanskrit at the ancient university at Katas Raj. All these places are near the Khewra Salt Mine in the mountains of the salt range.

I have been to the salt mine but did not know the history of the area at the time. As you live in Karachi you could make a trip there.