Galileo's telescope - The height of the mountains on the Moon

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Starting in autumn of 1609 Galileo (1564-1642) conducted observations of the Moon, of which he made some drawings of striking impact.
In open contrast to the Aristotelian tradition, which held that the celestial bodies are perfectly smooth and spherical, the surface of the Moon, observed through the telescope, showed cavities and prominences. Galileo had also noted the presence of small luminous zones in the dark part of the lunar disc in proximity to the terminator, the line of separation between the lighted part and the one in shadow. As dawn broke over the lunar surface, the luminous spots melded with the illuminated zone. Galileo correctly attributed this phenomenon to the presence of mountains, whose high peaks are touched by the sun's rays before the terrain below them, exactly as happens on the Earth when, at dawn, the mountain tops are already lit by the rays of the Sun while the valleys are still shrouded in darkness. With a simple but ingenious method, Galileo was able to calculate the height of the mountains on the moon. He estimated the distance of a mountain from the terminator as about one twentieth of the apparent diameter of the Moon. Then dividing by 20 the length of the true lunar diameter, known since antiquity, he obtained the length of the segment FA. By applying Pythagoras' theory to the right triangle GAF, he found the hypotenuse FG. It represented the distance of the top of the mountain from the centre of the Moon. By subtracting from this the radius of the Moon, he obtained the height of the mountain.


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