Spring, the Tropics, and Math

I missed posting on the first day of Spring this year, but what's the big deal?

Having had our wedding day on the Summer Solstice, and being a math nerd, I try to pay attention to special sun/math days.

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As a child growing up in Sacramento, things like rain forests and tropical islands held a dear place in my imagination. But what specifically is it about things "tropical" that inspires?

Beaches...blue ocean water...palm trees...like a marketing campaign for laundry detergent.

But what are the tropics?

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And what is spring?

Associated with the color green and rebirth, the season of spring comes after the (sometimes long and harsh) winter and before the (sometimes hot and stifling) summer. April showers and may flowers and all that. The days continue their push towards getting longer and longer.

The first day of spring is on the vernal equinox, and similarly, the first day of fall is on the autumnal equinox.

While doing research for some work to give my charges I learned exactly what the equinoxes are: they are the days when the amount of day and night are the same for opposing latitudes on the earth.

For example: Los Angeles and Sydney or similarly placed on the globe with respect to the equator, LA's at 35⁰ N and Sydney's at 35⁰ S, so on the equinox, the amount of day and night in LA and and Sydney will be the same.

Our spring is their fall, and vice-versa.

How do the tropics fit into this?

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There are a few demarcated horizontal lines on our global sphere. The equator is the most famous, as it cuts the sphere in half, and we've named the halves the northern hemisphere and the southern hemisphere.

At 23.5⁰ north and south of the equator are the lines that we call "tropics," the Tropic of Cancer is at 23.5⁰ N and the Tropic of Capricorn is at 23.5⁰ S. The area that makes up this equator sandwich is collectively known as "the tropics."

The zone represents a precarious historical position in western society: one one side, they are lauded as paradise; but alternately they've been seen as sub-human and uncivilized.

But why is it 23.5⁰ that marks where those tropic lines live?

Here's where the math comes in: the axial tilt of the earth is 23.5⁰. As in, have you ever noticed that a globe is tilted on the vertical axis? The result of the impact that created our natural satellite, the moon, the earth is tilted (and wobbles a smidgen) vertically. (The "wobbles" are sometimes blamed for different ice age events.)

The amount of separation from the vertical axis, 23.5⁰, means that on the summer solstice in either hemisphere, the sunlight comes down directly perpendicular to that hemisphere's tropic. 

On June 21st, the summer solstice for the northern hemisphere, the sunlight is coming straight down on the Tropic of Cancer. On December 21st, the summer solstice for the southern hemisphere, the sunlight is coming straight down on the Tropic of Capricorn.

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For complete mathematical disclosure: 

Another pair of horizontal circles on our globe are much closer to the poles, the Arctic and Antarctic Circles.

These are named and designated thusly: in the hemisphere's respective summer, there is no night, and in the respective winter, there is no day. Check out the graphic below:

NorHem bias!

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Spring is the way we humans chose to describe the transition from cold to hot and the tropics are about perpendicularity.

Also, the quarantine is going well...