Height of the Moons Features The Height of the Moon\'s Features Galileo, turning

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Height of the Moons Features

The Height of the Moon's Features Galileo, turning his telescope to the Moon in 1610, was the first to show that the Moon was not flat, but had projections, mountains and craters. In this exercise we will calculate the height of some of the lunar features. When the Moon is full, the Sun is behind us and we don't see shadows on the moon. But at first or third quarter phase, when the Moon is half-full, the slant sunlight shows features on the terminator (the boundary between the light and dark parts of the moon), which can dramatically show their contours. Galileo's sketch of first quarter and third quarter moons. The first quarter terminator is sunrise; the third quarter terminator is sunset, (from the Starry Messenger) Have you ever used a shadow length to estimate the height of something? If you know the actual height of something (or someone) and can measure their shadow's length, then you can calculate the height of something else by measuring its shadow length. In the picture to the left, assume our girl is 1.1 meters high. What would that be in inches? Remember 1 inch = 2.54 cm. You can always multiply a number by ONE and get the same answer. We can just figure out a clever way to multiply by one to change the units! In this case we can use 1 = (100 cm/1m) and also (1 inch/2.54 cm). So in her case, 1.1 meters = 110 cm. Multiplying now by "1", 110cmx(1in/2.54 cm) = 110 in/2.54 = 43 in. Notice how the "cm" units cancel each other-yea! Ok, so if the girl is 1.1 m high, how tall is her shadow here?_ How tall is the flagpole's shadow?_? Let's use a PROPORTION. The ratio of her height h to her shadow length s is the SAME as the ratio of the flagpole's height H to its shadow length S. h/s = H/S So, multiplying both sides of the equation by S, we get (h * S)/s = H = h * (S/s). So we just measure S_and s_ (the shadow lengths on this page), divide them, and multiply by the height of the girl (1.1 m). What height do you get for the pole? (you may use a calculator):_

Explanation / Answer

Her shadow s = 2.2 m

Shadow of pole S= 12 m

Height of pole , H = h*S/s

                     = 1.1*12/2.2

                    = 6 m Answer

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