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02ps-12 Parallel Rays

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    When we were calculating the circumference of the earth,
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    our calculation was based entirely on the assumption that the sun's rays struck
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    Alexandria and Syene parallel.
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    Let's examine just how true or how good that assumption was.
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    Now, the drawing I've drawn here is totally out of scale.
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    I've drawn the earth huge and only a section of it.
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    I've drawn the sun absurdly tiny and much, much too close to earth.
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    For the sake of the geometry, this picture will work.
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    Now, we know that the distance from the earth to the sun is about 150,000,000 km.
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    Eratosthenes knew that the distance from Syene to Alexandria.
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    This distance was about 5000 stadia.
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    Remember 1 stadion is equal to about 185 meters.
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    I want to know what's this angle.
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    The reason why I want to know what this angle is
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    is because this angle somehow quantifies how parallel these lines are.
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    If they're truly parallel, this angle would be zero degrees.
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    This line would be coming in at the exact same orientation as this line.
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    Any deviation from 0 represents some error,
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    and we want to make sure that if it does deviate from zero
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    that it's still quite a small number.
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    For this problem, you're going to want to assume that this is a right triangle,
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    even though it doesn't quite look like one.
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    If we drew this more to scale, you would see that it truly is very close to being a right triangle.
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    So, we can still use our trigonometry.
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    Using the fact that this distance is 150 million km,
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    which you could say is the length of this leg here, if you like,
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    or that leg, since these are equal.
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    You know this length is 5000 stadia.
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    Can you tell me what's this angle?
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    We'll call this angle α.
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    Give your answer in degrees.
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    For this problem, I actually want you to round to 5 decimal places.
Title:
02ps-12 Parallel Rays
Video Language:
English
Team:
Udacity
Project:
PH100 - Intro to Physics
Duration:
01:49
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