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Anyone know why it gets dark so rapidly at this time of the year? Noticed this, this evening. With sunset at about 8:10pm, it was dark by 8:30pm.
It doesn't start to get remotely dark until 40-50 minutes after sunset during mid summer.
Think of the sun's altitude in the sky as a sine wave. At the winter solstice, the horizon (or X-axis) will be closer to the maximum point of the "function" (think graphs), and around the summer solstice the horizon (X-axis) will be closer to the minimum point. Derivatives always start approaching zero as they approach extreme points, which is why the sun is "slower" rising/falling around the solstices. At the equinoxes, the horizon (X-axis) will be right in the middle, and there you'll find the zeroes of the second derivative, which means the first derivative has its extreme points there and so the sun is rising/falling the fastest.
I'm sorry, we've recently worked through a chapter of derivatives and integrals in math class. It's been one of the most fun math chapters I've ever done...
Think of the sun's altitude in the sky as a sine wave. At the winter solstice, the horizon (or X-axis) will be closer to the maximum point of the "function" (think graphs), and around the summer solstice the horizon (X-axis) will be closer to the minimum point. Derivatives always start approaching zero as they approach extreme points, which is why the sun is "slower" rising/falling around the solstices. At the equinoxes, the horizon (X-axis) will be right in the middle, and there you'll find the zeroes of the second derivative, which means the first derivative has its extreme points there and so the sun is rising/falling the fastest.
I'm sorry, we've recently worked through a chapter of derivatives and integrals in math class. It's been one of the most fun math chapters I've ever done...
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