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ದುಂಡಾಕಾರವಾಗಿರುವ ಭೂಮಿಯ ದುಂಡಗಲ (diameter) 12,756 ಕಿಲೋ ಮೀಟರಗಳು ಮತ್ತು ಅದರ ತೂಕ 5.97219 × 10‌‍24 ಕಿಲೋ ಗ್ರಾಂ. ಇಂತಹ ಸಾಲುಗಳನ್ನು ಓದಿದೊಡನೆ ಮುಖ್ಯವಾಗಿ ಎರಡು ವಿಷಯಗಳು ಬೆರೆಗುಗೊಳಿಸುತ್ತವೆ. ಮೊದಲನೆಯದು ಇಷ್ಟೊಂದು  ದೊಡ್ಡದಾದ ಅಂಕಿಗಳು ಮತ್ತು ಎರಡನೆಯದು ಅವುಗಳನ್ನು ಅಳೆದುದು ಹೇಗೆ?.

Image EM1
ಇನ್ನೊಂದು ಅಚ್ಚರಿಯ ವಿಷಯವೆಂದರೆ ಭೂಮಿಯ ದುಂಡಗಲವನ್ನು ಮೊಟ್ಟಮೊದಲ ಬಾರಿಗೆ ಅಳೆದದ್ದು ಸರಿಸುಮಾರು 2200 ವರುಶಗಳ ಹಿಂದೆ! ಬನ್ನಿ, ಅವರಾರು? ಹೇಗೆ ಅಳೆದರು? ಎಂದು ತಿಳಿದುಕೊಳ್ಳೋಣ.
ಕ್ರಿ.ಪೂ. ಸುಮಾರು 200 ರಲ್ಲಿ ಈಜಿಪ್ಟಿನ ಎರತೊಸ್ತನೀಸ್ (Eratosthenes) ಎಂಬ ಗಣಿತದರಿಗ ಭೂಮಿಯ ದುಂಡಗಲವನ್ನು ಅಳೆದವರಲ್ಲಿ ಮೊದಲಿಗ. ಅದೂ ತನ್ನ ನಾಡಿನಲ್ಲೇ ಇದ್ದುಕೊಂಡು ಅರಿಮೆಯ ನೆರವಿನಿಂದ ಈ ಕೆಲಸವನ್ನು ಮಾಡಿ ತೋರಿಸಿದಾತ.

ಎರತೊಸ್ತನೀಸ್‍ರಿಗೆ ತನ್ನ ಸುತ್ತಮುತ್ತಲಿನ ಆಗುಹೋಗುಗಳು ತುಂಬಾ ಕುತೂಹಲ ಮೂಡಿಸಿದಂತವು. ಬೇಸಿಗೆಯ ಒಂದು ಗೊತ್ತುಪಡಿಸಿದ ಹೊತ್ತಿನಂದು ಸಿಯನ್ ಊರಿನ ಬಾವಿಯ ಮೇಲೆ ಹಾದುಹೋಗುವ ಸೂರ್ಯನ ಕಿರಣಗಳು, ಆ ಬಾವಿಯ ನಟ್ಟನಡುವೆ ಬೀಳುತ್ತಿದ್ದುದು ಮತ್ತು ಅದೇ ಹೊತ್ತಿಗೆ ಅಲ್ಲಿಂದ ಸುಮಾರು 750 ಕೀಲೋ ಮೀಟರಗಳಷ್ಟು ದೂರವಿರುವ ಅಲೆಕ್ಸಾಂಡ್ರಿಯಾದ ಕಂಬವೊಂದರ ಮೇಲೆ ಸೂರ್ಯನ ಬೆಳಕಿನಿಂದ ಉಂಟಾಗುವ ನೆರಳು ನೇರವಾಗಿರದೇ ಒಂದು ಕೋನದಲ್ಲಿ ಇರುತ್ತಿದ್ದುದು, ಎರತೋಸ್ತೇನಸ್ ರ ಕುತೂಹಲ ಕೆರಳಿಸಿದ್ದವು.

ಸೂರ್ಯನ ನೆಟ್ಟ ನೇರವಾದ ಕಿರಣಗಳು ಉಂಟುಮಾಡುವ ನೆರಳು ಸಿಯಾನ್ ಊರಿನಲ್ಲಿ ನೇರವಾಗಿ ಮತ್ತು ಅದೇ ಹೊತ್ತಿಗೆ ಅಲೆಕ್ಸಾಂಡ್ರಿಯಾದಲ್ಲಿ ಒಂದು ಕೋನದಲ್ಲಿದ್ದದ್ದು, ನಮ್ಮ ಭೂಮಿ ಚಪ್ಪಟೆಯಾಗಿರದೇ ದುಂಡಾಗಿದೆ ಅನ್ನುವಂತ ವಿಷಯವನ್ನು ಎರತೊಸ್ತನೀಸ್‍ರಿಗೆ ತೋರಿಸಿಕೊಟ್ಟಿದ್ದವು. ಗಣಿತವನ್ನರಿತಿದ್ದ ಎರತೊಸ್ತನೀಸ್‍ರಿಗೆ ಇದನ್ನು ಬಳಸಿಯೇ ಭೂಮಿಯ  ಸುತ್ತಳತೆಯನ್ನು ಅಳೆಯುವ ಹೊಳಹು ಹೊಮ್ಮಿತು.

Image EM2ಸಿಯಾನ್ ಊರಿನ ಬಾವಿಯ ಮೇಲೆ ಸೂರ್ಯನ ಕಿರಣಗಳು ನೇರವಾಗಿ ಬೀಳುತ್ತಿದ್ದ ಹೊತ್ತಿಗೆ ತನ್ನೂರು ಅಲೆಕ್ಸಾಂಡ್ರಿಯಾದಲ್ಲಿದ್ದ ಕಂಬದ ನೆರಳು ಬೀಳುತ್ತಿದ್ದ ಕೋನವನ್ನು ಎರತೋಸ್ತೇನಸ್ ಅಳೆದರು. ಕಂಬ ಉಂಟುಮಾಡುತ್ತಿದ್ದ ನೆರಳಿನ ಕೋನವು 7.2°  ಎಂದು ಗೊತ್ತಾಯಿತು.

ಅಲೆಕ್ಸಾಂಡ್ರಿಯಾ ಮತ್ತು ಸಿಯನ್ ಊರುಗಳ ದೂರ ತಿಳಿದಿದ್ದ ಎರತೋಸ್ತೇನಸ್ ಗಣಿತದ ನಂಟುಗಳನ್ನು ಬಳಸಿ ಭೂಮಿಯ ಸುತ್ತಳತೆ ಮತ್ತು ದುಂಡಗಲವನ್ನು ಈ ಕೆಳಗಿನಂತೆ ಎಣಿಕೆಹಾಕಿದರು.

Image EM3ಅಲೆಕ್ಸಾಂಡ್ರಿಯಾ ಕಂಬದ ನೆರಳಿನ ಕೋನ = 7.2°

ಒಂದು ಸುತ್ತಿನಲ್ಲಿ ಇರುವ ಕೋನಗಳು = 360°

ಅಂದರೆ, ದುಂಡಾಗಿರುವ ಭೂಮಿಯ ಸುತ್ತಳತೆ ಅಲೆಕ್ಸಾಂಡ್ರಿಯಾ ಮತ್ತು ಸಿಯಾನ್ ಊರುಗಳ ದೂರದ 360/7.2 = 50 ರಷ್ಟು ಇರಬೇಕು.

ಇನ್ನು, ಅಲೆಕ್ಸಾಂಡ್ರಿಯಾ ಮತ್ತು ಸಿಯನ್ ಊರುಗಳ ನಡುವಿನ ದೂರ = 5000 ಸ್ಟೇಡಿಯಾ
(ಸ್ಟೇಡಿಯಾ/Stadia – ದೂರವನ್ನು ಅಳೆಯಲು ಎರತೊಸ್ತನೀಸ್ ಬಳಸಿದ ಅಳತೆಗೋಲು)

ಹಾಗಾಗಿ,  ಭೂಮಿಯ ಸುತ್ತಳತೆ = 50 x 5000 = 250000 ಸ್ಟೇಡಿಯಾ = 40,000 ಕಿಲೋ ಮೀಟರಗಳು
(1 ಸ್ಟೇಡಿಯಾ = 0.15 ಕಿ.ಮೀ.)

ನಮಗೆ ಗೊತ್ತಿರುವಂತೆ, ಸುತ್ತಳತೆ = 3.142 x ದುಂಡಗಲ (Circumference = 3.142 x diameter)

ಹಾಗಾಗಿ, ಎರತೊಸ್ತನೀಸ್ ಎಣಿಕೆ ಹಾಕಿದ ಭೂಮಿಯ ದುಂಡಗಲ (diameter) = 40000/3.142 = 12730.7 ಕಿ.ಮೀ.

ಹೀಗೆ ಸುಮಾರು 2200 ವರುಶಗಳ ಹಿಂದೆ ಕೋನಗಳನ್ನು  ಬಳಸಿ ಎರತೋಸ್ತೇನಸ್ ಅಳೆದದ್ದು, ಹೊಸಜಗತ್ತಿನಲ್ಲಿ ಉಪಗ್ರಹಗಳನ್ನು ಬಳಸಿ ಕರಾರುವಕ್ಕಾಗಿ ಅಳೆಯಲಾದ ಭೂಮಿಯ ದುಂಡಗಲ 12,756 ಕಿಲೋ ಮೀಟರಗಳಿಗೆ ತುಂಬಾ ಹತ್ತಿರವಾಗಿದೆ ಎಂಬುದನ್ನು ನೋಡಿದರೆ ಅರಿಮೆಯ ’ಹಿರಿಮೆ’  ಮನದಟ್ಟಾಗುತ್ತದೆ.

(ಸೆಲೆ: heasarc.nasa.govhte.si.edu, en.wikipedia.org, emaze.com)

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