viernes, noviembre 17, 2006

Eratóstenes y la circunferencia terrestre

Ya en la antigua Grecia, se creía que la Tierra era una esfera perfecta, pero solo por cuestiones filosóficas. Platón y Pitágoras no podían concebir la figura de la misma, que albergaba el pensamiento humano, como algo no perfecto. Y por supuesto, establecieron dicha idea de una esfera perfecta, aunque sin fundamentos. Y es Aristóteles quien aporta evidencias de los dichos de su maestro Platón, al observar que en los eclipses de Luna lunares, la sombra proyectada sobre la Tierra Luna tenia forma circular.

Pero las preguntas continuaban, y llegó el turno del tamaño. ¿Cuán grande era la Tierra?
Eratóstenes, filósofo, astrónomo, matemático, geógrafo, fue uno de los grandes pensadores de la antigüedad, sus contemporáneos lo apodaron Beta, porque afirmaban que era en todo el segundo mejor del mundo. Pero fue el primero en determinar la circunferencia de la Tierra, y debido a que vivió en el siglo III a.C sus herramientas sólo fueron palos, ojos, pies y su cerebro.
Siendo director de la biblioteca de Alejandría, leyó en un papiro que en Siena, actualmente Asuán, Egipto, en el mediodía del 21 de Junio un palo vertical no proyectaba sombra. Pero en Alejandría no sucedía esto, un palo vertical sí proyectaba sombra. Y se preguntó porque. La primera conclusión que determinó fue que definitivamente la Tierra no podía ser plana, porque si así lo fuera, el Sol produciría sombras de igual longitud para ambos palos, sin importar de la distancia que los separaran (el Sol esta tan lejos que sus rayos son paralelos cuando llegan a la Tierra). Comprendió entonces que la única respuesta posible era que la superficie de la Tierra estaba curvada, y cuanto mayor sea la curvatura, mayor iba a ser la diferencia entre las longitudes de la sombra. Y quiso determinar la circunferencia de la Tierra. Sabia que la distancia entre Siena y Alejandría era de aproximadamente unos siete grados a lo largo de la superficie de la Tierra, por la diferencia entre las longitudes de las sombras de los palos; si imaginamos los palos prolongados hasta llegar al centro de la Tierra, formaran un ángulo de siete grados. Este resultado es aproximadamente una cincuentava parte de los trescientos sesenta grados que contiene la circunferencia entera de la Tierra. Pero le faltaba un dato, la distancia entre Siena y Alejandría, por lo que contrató a un hombre para que lo midiera a pasos. El resultado era aproximadamente 5040 estadios egipcios, siendo un estadio egipcio 157,2 metros. Una distancia de 792,29 kilómetros. Entonces, esta distancia entre Siena y Alejandría siendo igual a la cincuentava parte de la circunferencia (como había determinado por las sombras de los palos) da como resultado, multiplicando ambos, 39614,4 kilómetros. Esta debía ser la circunferencia de la Tierra. Solo un error de aproximadamente 1%, ya que la verdadera circunferencia es 40008 kilómetros. Impresionante.

124 comentarios:

Juan dijo...

Realmente es increíble como en la antigüedad podían hacer este tipo de extrapolaciones usando solo la imaginación. quizá la tecnología nos quita mucho de ese poder de abstracción que teníamos originalmente.

Anónimo dijo...

Sin embargo, mucho antes de su tiempo, en el siglo octavo a. de la E.C., el profeta hebreo Isaías había indicado que la Tierra era esférica. Escribió: “Hay Uno [Jehová Dios] que mora por encima del círculo de la tierra, los moradores de la cual son como saltamontes.” (Isa. 40:22) La palabra hebrea por “círculo” aquí también puede traducirse “esfera.” (A Concordance of the Hebrew and Chaldee Scriptures, por B. Davidson) Es de interés que respecto a “círculo” en este versículo, la Biblia “Scofield Reference” dice en una nota marginal: “Una referencia notable a la esfericidad de la Tierra.” La traducción católica de Scío dice: “Está sentado sobre la redondez de la tierra,” y la de Nieto: “Él se sienta por encima del globo de la tierra.” Naturalmente, la Palabra inspirada del Creador de la Tierra indicaría correctamente la redondez de la Tierra, aunque los antiguos por lo general creían que era plana.

Anónimo dijo...

Facundo:
Hay un pequeño error en el texto: ya que la sombra proyectada en un eclipse de luna es la de la tierra sobre la luna y no a la inversa como aparece escrito; lo que por otra parte no hubiese podido verse en la antigüedad, ya que la forma de la sombra de la luna sobre la tierra solo puede verse desde una gran altura.

Facundo dijo...

Anonimo 1: Gracias por el dato. En la antigüedad se creia que la Tierra era un disco plano, es decir como un disco de vinilo. Y en cuanto a la palabra hebrea "circulo" nunca vamos a saber si la quisieron utilizar como "circulo" o como "esfera".

Facundo dijo...

Anónimo 2: Gracias por la corrección. Hubo un error de escritura, ya que lo que quería explicar era que la Tierra proyectaba una sombra circular sobre la Luna en los eclipses, como bien vos dijiste.

Facundo dijo...

Juan: Lo primero que me pregunté al conocer esta historia, fue si definitivamente yo lo pudiese haber hecho; supuse que no. Y creo que una de mis respuestas ante tal negativa fue similar a la que planteaste. El tiempo ocupado con todas las nuevas tecnologías nos quita la virtud del pensamiento.

Tordek dijo...

Para dar un comentario, el número 40000 (bastante aproximado al resultado real) no es incidental: El metro está definido como 1/10^10 de la distancia entre el polo y el Ecuador. En otras palabras, si la medida original hubiera sido exacta, la Tierra mediría exactamente 40000 de circunferencia (por los meridianos; por el Ecuador es diferente: la Tierra está algo achatada)

Tordek dijo...

Eh, perdón, 1/10^7

Ender Muab'Dib dijo...

Me encanta esta historia, siempre me ha asombrado cómo se las ingeniaban los antiguos para deducir lo que suponían; como la brillante forma de calcular la velocidad de la luz, aunque ya fuera hace menos siglos.

No obstante, lo que más me ha sorprendido de este caso es lo de:
la distancia entre Siena y Alejandría, por lo que contrató a un hombre para que lo midiera a pasos
¿Realmente un tipo se pegó andando 792 kilómetros para calcular eso? No había otros métodos como ruedas o algún método para calcular a caballo o en carro? Porque si no, ese tipo era un cojonera xD.

Saludos!

Facundo dijo...

Tordek: Efectivamente. Pero hay algo que omitiste. El patrón que nombraste del metro, (la diez millonésima parte de un meridiano dentro de un cuadrante) recién se adopto alrededor de 1790, casi 20 siglos después de que Eratóstenes midiera la circunferencia de la Tierra. En la actualidad el patrón es la distancia recorrida por la luz en el vacío durante aproximadamente 3,34 nanosegundos (3,34 x 10^-9)

Ender: A mí también me causo mucha gracia esa parte de la historia. Debe haberle pagado bastante al que hizo la caminata.

Saludos.

Luna dijo...

Hola Vecino!
Pasaba a dejarle mis saludos....
Espero que esté bien...
Besos
Luni

Facundo dijo...

Gracias por los besos Luna. Otros.

Anónimo dijo...

La belleza de las ciencias exactas es que evitan la dualidad, se definen y PERDURAN de una generación a otra CLARAMENTE, evitando convenientes dualidades de personas que de acuerdo a su conveniencia van variando el significado de las palabras.

Yo creo que el compadre Isaías utiliza la famosa técnica de los astrólogos baratos del zodiaco, que simplemente te dicen: Recibirás una buena noticia. Pero pues ya con despertar y saberte vivo puedes considerarlo una buena noticia.

Mis respetos para Eratóstenes que no solo dijo "Ésta es la circunferencia de la tierra", sino que nos eneseñó cómo lo hizo.

Saludos señores

Quetzalcoatl
(Que en concordancia con las Mexicanas escrituras de Carlos Chingonchón también se puede traducir como "Viva México Cabrones")

jessica dijo...

hola!... una preguntota al del blog la circunferencia entonces de la tierra es 792 kilómetros??

Anónimo dijo...

A raíz del proyecto Eratóstenes (UBA) propuesto a las escuelas, para calcular el radio terrestre, como llegamos tarde a la inscripción, igualmente se lo propuse a mis alumnos quienes midieron la sombra de la varilla entre el 20 y 27 de junio, 2008, y tomaron como lugar donde "no hay sombra" la isla Basseterre,no está justo en nuestro meridiano ni tan cerca del trópico de Cáncer; la circunferencia máxima les dio aprox. 35000 km, con error por supuesto.
Gabriela.

Anónimo dijo...

Enhorabuena Facundo por lo bien que lo has explicado.
Saludos desde Mallorca (España).

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Dr Purva Pius dijo...

Hello Everybody,
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BORROWERS APPLICATION DETAILS


1. Name Of Applicant in Full:……..
2. Telephone Numbers:……….
3. Address and Location:…….
4. Amount in request………..
5. Repayment Period:………..
6. Purpose Of Loan………….
7. country…………………
8. phone…………………..
9. occupation………………
10.age/sex…………………
11.Monthly Income…………..
12.Email……………..

Regards.
Managements
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LOAN APPLICATION FORM
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