{"id":387,"date":"2015-12-29T08:00:38","date_gmt":"2015-12-29T07:00:38","guid":{"rendered":"http:\/\/anticopedie.fr\/WordPress\/?p=387"},"modified":"2015-12-10T14:30:49","modified_gmt":"2015-12-10T13:30:49","slug":"grecs-mesuraient-distance-de-terre-a-lune-soleil","status":"publish","type":"post","link":"https:\/\/anticopedie.fr\/WordPress\/?p=387","title":{"rendered":"Comment les Grecs mesuraient la distance de la Terre \u00e0 la Lune et au Soleil"},"content":{"rendered":"

Avant de commencer, posons-nous la question : si l\u2019on vous demandait aujourd\u2019hui de calculer ces distances, ou le diam\u00e8tre de la Lune ou du Soleil, comment vous y prendriez-vous ? C\u2019est l\u00e0 qu\u2019appara\u00eet toute l\u2019inventivit\u00e9 des savants Grecs de l\u2019Antiquit\u00e9, \u00e0 la fois observateurs, astronomes, inventeurs et g\u00e9om\u00e8tres… <\/span><\/p>\n

Le premier pas: conna\u00eetre le diam\u00e8tre de la Lune<\/span><\/strong><\/h3>\n

D\u00e8s le 6e si\u00e8cle av. J.-C., les Grecs (Parm\u00e9nide, Platon, Aristote) admettaient que la Terre \u00e9tait sph\u00e9rique (comment expliquer autrement l\u2019horizon ? Et n\u2019est-ce pas la forme divine id\u00e9ale ?), et que c\u2019\u00e9tait son ombre qui expliquait les \u00e9clipses de Lune. Aristarque de Samos (env. 310-230 av. J.-C.) avait observ\u00e9 combien de temps la Lune dispara\u00eet derri\u00e8re l\u2019ombre de la Terre. Il suffit d’un sablier pour cela.<\/span><\/p>\n

\"CalculerIl en d\u00e9duit que le diam\u00e8tre de la Lune est environ 3 fois plus petit que celui de la Terre. Ce qui est astucieux, mais inexact, car cela suppose que les rayons du Soleil arrivent tous parall\u00e8lement, et donc que la zone d\u2019ombre port\u00e9e par la Terre est cylindrique.
\nC\u2019est Hipparque (env. 190-120 av. J.-C.) qui pr\u00e9cisa ce diam\u00e8tre en d\u00e9couvrant que la projection de l\u2019ombre de la Terre est conique et non cylindrique: il corrigea la valeur ci-dessus \u00e0 4 fois, ce qui est assez proche de la r\u00e9alit\u00e9. Encore fallait-il conna\u00eetre le diam\u00e8tre de la Terre.<\/span><\/p>\n

Calcul de la circonf\u00e9rence de la Terre<\/span><\/strong><\/h3>\n

Aristote, au 4e si\u00e8cle av. J.-C., l\u2019\u00e9valuait \u00e0 60 000 km, mais c\u2019est Eratosth\u00e8ne (276-194 av. J.-C.), conservateur de la biblioth\u00e8que d\u2019Alexandrie, qui l\u2019\u00e9valua avec une extraordinaire pr\u00e9cision.
\nSa m\u00e9thode est souvent cit\u00e9e comme mod\u00e8le de la d\u00e9marche scientifique des Grecs: il avait remarqu\u00e9 qu\u2019au solstice d\u2019\u00e9t\u00e9 (le 21 juin), le Soleil tombait \u00e0 la verticale dans un puits situ\u00e9 \u00e0 Sy\u00e8ne (aujourd\u2019hui Assouan). Ceci n\u2019arrivait pas \u00e0 Alexandrie, o\u00f9 l\u2019ombre d\u2019un ob\u00e9lisque gardait, par rapport \u00e0 la verticale, un angle de 7,2\u00b0. La Terre \u00e9tant sph\u00e9rique et Assouan \u00e9tant au sud d\u2019Alexandrie (pratiquement sur le m\u00eame m\u00e9ridien), il suffisait de conna\u00eetre la distance entre les deux villes pour en d\u00e9duire le diam\u00e8tre de la Terre. Ce que fit Eratosth\u00e8ne en comptant les pas des chameaux, aboutissant (malgr\u00e9 quelques erreurs, qui par chance se compensaient !) \u00e0 une circonf\u00e9rence terrestre de 39 375 km, toute proche de la r\u00e9alit\u00e9.<\/span><\/p>\n

\"Mesurer<\/p>\n

Voici la figure g\u00e9om\u00e9trique qui explique le calcul d\u2019Eratosth\u00e8ne
\n(l\u00e0 aussi, on consid\u00e8re que les rayons du soleil sont parall\u00e8les entre eux).<\/small><\/span><\/strong><\/p>\n

Calcul de la distance Terre-Lune
\n<\/span><\/strong><\/h3>\n

\"LeArchim\u00e8de avait invent\u00e9, d\u00e8s le 3e si\u00e8cle av J.-C. le \u00ab\u00a0dioptre\u00a0\u00bb, un instrument rudimentaire compos\u00e9 d’une r\u00e8gle gradu\u00e9e qui portait \u00e0 son extr\u00e9mit\u00e9 une petite plaque perc\u00e9e d\u2019un trou servant d\u2019oculaire, et \"mesurerun \u00e9l\u00e9ment coulissant d\u2019une largeur bien d\u00e9finie. <\/span>En d\u00e9pla\u00e7ant celui-ci jusqu\u2019\u00e0 ce qu\u2019il cache l\u2019objet vis\u00e9 (la Lune), un petit calcul trigonom\u00e9trique permettait de d\u00e9finir l\u2019angle apparent sous lequel se pr\u00e9sente l\u2019astre. Connaissant le diam\u00e8tre de la Terre, donc celui de la Lune, un autre petit calcul de proportionnalit\u00e9 aboutit \u00e0 la distance Terre-Lune. Notons qu\u2019Aristarque de Samos avait d\u00e9j\u00e0 appliqu\u00e9 cette m\u00e9thode, mais il lui manquait cette donn\u00e9e essentielle: le diam\u00e8tre de la Terre. Il pouvait juste dire que cette distance \u00e9tait d\u2019environ 40 diam\u00e8tres terrestres.<\/span><\/p>\n

Et la distance de la Terre au Soleil ?
\n<\/span><\/strong><\/p>\n

L\u00e0 aussi, il suffit de remarquer comme Aristarque (y auriez-vous pens\u00e9 ?) que, lors d\u2019une parfaite demi-lune, le Soleil l\u2019\u00e9claire \u00ab\u00a0de c\u00f4t\u00e9\u00a0\u00bb, ce qui signifie qu\u2019il forme avec la Terre et la Lune un triangle rectangle.<\/span><\/p>\n

\"Distance\u00a0Connaissant l\u2019angle sous lequel se trouve alors le Soleil et la distance Terre-Lune, on d\u00e9finit la distance de la Terre au Soleil. Et comme on connait aussi le diam\u00e8tre apparent de ce dernier, on peut en d\u00e9duire son diam\u00e8tre… Qui semble bien s\u00fbr \u00e9norme !
\nD\u2019o\u00f9 on d\u00e9duit que l\u2019ombre de la Terre n\u2019est pas un cylindre, mais un c\u00f4ne, etc. etc.
\n<\/span><\/p>\n

Et si la Terre tournait autour du Soleil ?
\n<\/span><\/strong><\/h3>\n

Aristarque (encore lui) avait d\u00e9j\u00e0 subodor\u00e9 la chose: il lui semblait logique que les petits astres tournent autour du plus gros, comme la Lune autour de la Terre, mais sa th\u00e9orie ne s\u2019imposa pas, et Archim\u00e8de lui r\u00e9torqua d\u2019ailleurs que la Terre est solide et donc plus lourde que le feu du Soleil, aussi gros soit-il. Tout le monde peut se tromper, et le mod\u00e8le g\u00e9ocentrique de Claude Ptol\u00e9m\u00e9e (90-168), fort habilement con\u00e7u il est vrai – mais ceci est une autre histoire – s\u2019imposa pendant 13 si\u00e8cles.
\n<\/span><\/p>\n

Les cons\u00e9quences de ces travaux
\n<\/span><\/strong><\/h3>\n

Eh bien, on peut en d\u00e9duire que les Grecs \u00e9taient de grands observateurs et de grands g\u00e9om\u00e8tres, m\u00eame si leurs r\u00e9sultats sont souvent approximatifs… Peu importe car pour eux, la d\u00e9marche compte au moins autant que le r\u00e9sultat.
\nUn r\u00e9sultat qui aurait pu cependant \u00eatre fort utile \u00e0 Chistophe Colomb, mais cela n\u2019a pas int\u00e9ress\u00e9 grand monde pendant des si\u00e8cles : que la Terre fut plate ou immobile, la belle affaire au regard des \u00e9vangiles ! Il faudra attendre Copernic pour en savoir plus…<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Les Grecs de l’Antiquit\u00e9 savaient que la Terre est ronde. Ils ont d\u00e9fini son diam\u00e8tre, celui de la Lune et du Soleil, et ont calcul\u00e9 les distances qui les s\u00e9parent. Ce qu’ignorait Christophe Colomb mille ans plus tard. Voici comment ils s’y sont pris… Continuer la lecture →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[246,50,245,238,239,244,45,51,230,240,242,166,74,243,241],"class_list":["post-387","post","type-post","status-publish","format-standard","hentry","category-articles","tag-alexandrie","tag-antiquite","tag-astronomes","tag-astronomie","tag-calcul","tag-diametre","tag-distance","tag-grece","tag-grecs","tag-instruments","tag-lune","tag-mesure","tag-savants","tag-soleil","tag-terre"],"yoast_head":"\nComment les Grecs mesuraient la distance de la Terre \u00e0 la Lune et au Soleil - AnticoP\u00e9die: le blog<\/title>\n<meta name=\"description\" content=\"Les Grecs de l'Antiquit\u00e9 savaient que la Terre\u00a0est ronde. Ils ont\u00a0calcul\u00e9 son diam\u00e8tre et la distance de la Lune et du Soleil. Voici comment.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/anticopedie.fr\/WordPress\/?p=387\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Comment les Grecs mesuraient la distance de la Terre \u00e0 la Lune et au Soleil - AnticoP\u00e9die: le blog\" \/>\n<meta property=\"og:description\" content=\"Les Grecs de l'Antiquit\u00e9 savaient que la Terre\u00a0est ronde. Ils ont\u00a0calcul\u00e9 son diam\u00e8tre et la distance de la Lune et du Soleil. 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