I have just got amazed because from a single place with four simple measurements Al-Biruni got the size of the Earth Al-Biruni (973-1038) developed a new method using trigonometric calculations to compute earths radius and circumference based on the angle between the horizontal line and true horizon from a mountain top with known height. He calculated the height of the mountain by going to two points at sea level with a known distance apart and then measuring the angle between the plain and the top of the mountain for both points. Birunis estimate of 6,339.9 km for the Earth radius had an error of 0,0026 and was 16.8 km less than the current value of 6,356.7 km. The idea came to him when he was on top of a tall mountain near Nandana in India. He measured the dip angle using an astrolabe and he applied to the law of sines formula. He also made use of algebra in his calculation. A = Highest point of mountain B = Lowest point of mountain h = Height of the mountain C = Lowest point of true horizon visible from point A O = Centre of Earth α = Dip angle r = Earths Radius Solution: The angle AOC = α. AO=(r+h) is the hypothenus in AOC triangle. r=(r+h).cos(α) Then the right side can be simplified to find r. r=h.cos(α)/(1-cos(α))
Posted on: Mon, 06 Oct 2014 21:36:25 +0000
Trending Topics
Recently Viewed Topics
© 2015