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Given the radius of the Earth, they could probably get the radius of the moon by looking at the curvature of the edge of the Earth's shadow upon the moon during

• abecedarius 14y ago
  Find the moon's distance by parallax, then the radius follows from the angle it subtends.
  • dalke 14y ago
    For parallax you need to take two measurements at the same time. Given that the distance to the moon is about 384,400 km, a 1,000 km baseline gives an angle of 1/384 radians = 0.15 degree. This requires some a rather sophisticated methods, such as clocks with good precision and a telescope. The method of Aristarchus is much more clever than that. At 1/2 moon, the earth/moon/sun forms a right angle. The angle moon/earth/sun could be measured as about 3 degrees - something that the ancient Greeks could measure. This gives a ratio of earth-moon/sun-moon distances between 18 and 20. Then during a lunar eclipse, you can measure the width of the cone of the earth's shadow vs. the moon's width. During a solar eclipse you can see that the moon's angular width is about that of the sun. That information, plus the measured radius of the earth, and a bit of geometry, gives you an estimate of the size of the moon. http://en.wikipedia.org/wiki/On_the_Sizes_and_Distances_%28Aristarchus%29 http://en.wikipedia.org/wiki/On_the_Sizes_and_Distances_%28A...