Eratóstenes forever

28 03 2009

radiotierra1.jpg

El pasado jueves, 26, fue el gran día. Centenares de centros de toda España  acometíamos un proyecto común: reproducir la experiencia que Eratóstenes realizó hace casi 2.250 años para medir el radio de la Tierra.

Fueron casi tres horas midiendo la sombra del gnomon (palo vertical) bajo un sol de justicia, que no parecía asturiano. No estuvimos solos, la experiencia despertó un gran interés en todo el instituto y fueron muchos los grupos que, acompañados por sus profesores/as, se acercaron para que les explicáramos lo que tratábamos de hacer.

El día siguiente lo dedicamos a procesar los datos recogidos. El cálculo gráfico sobre el papel en el que se hicieron las mediciones daba un resultado coherente: hora de tránsito del Sol por nuestro meridiano: 12:30 h (hora universal, una hora menos que la que indican nuestros relojes). Altura del Sol al mediodía: 48,860.

Si Avilés está situado 60 al oeste del meridiano de Greenwich y por cada grado hay que sumar 4 min, aproximadamente, el valor correcto para la hora de tránsito estaría alrededor de las 12 h 24 min.

Habíamos establecido un segundo procedimiento para comprobar nuestras observaciones. Con la  ayuda de una hoja de cálculo obtuvimos la representación gráfica de los datos. La concordancia con la parábola prevista teóricamente era casi perfecta (un valor de R2= 1,0000 significa ajuste perfecto). El mínimo, estimado a ojo (tangente en el vértice), nos daba un resultado semejante al obtenido por el procedimiento anterior

grafica.gif

Lo que más desasosiego nos causó fue la ecuación de la parábola que daba el programa. Increíblemente, no coincidía con la curva representada. Hubo que pensar y pensar, hasta que dimos con la solución: el tipo de gráfico que había que seleccionar era el llamado XY (Dispersión). Haciendo la determinación matemática del mínimo el resultado era aún mejor: hora del tránsito por nuestro meridiano: 12 h 25 min 18 s. ¡Lo habíamos clavado!

No obstante en ciencia, como en la vida, la honradez es fundamental. El cálculo del mínimo estaba fuera de las posibilidades de quienes habían realizado el trabajo práctico, así que decidimos enviar los datos obtenidos mediante el procedimiento gráfico.

Una  vez procesados los datos de 417 centros el valor obtenido para el radio de la Tierra es de 5.975 km. El valor admitido actualmente es de 6.371 km lo que representa que se ha cometido solamente un 6% de error ¡todo un éxito!

Explicación más detallada y vídeo de la experiencia en FisQuiWeb

Web del Año Internacional de la Astronomía

Estadísticas Este artículo ha sido visitado  11028  veces


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