The Tropic of Cancer

Where is it?

All of us who have looked at a map have noticed a little dotted line called the Tropic of Cancer. In fact, here in Mazatlan, this little dotted is less than 15 miles north of us. But what is it, and what if anything does it have to do with Cancer? The answer is both simple and complicated. The simple answer is that the Tropic of Cancer is 23.5 degrees north latitude. So what? The real answer is a bit more complicated, and very interesting.

Some History

Back in the old days, before television, cellular phones, and the internet, people who had a lot of free time on their hands used to look up at the stars and the sky. They noticed a bunch of remarkable things. One of the things they noticed was that the sun and the stars did not appear in the same place at the same time every day. In the northern hemisphere, from winter until summer, the sun gradually rose higher and higher in the sky each day, while from the summer until winter, the opposite happened. By carefully measuring how high the sun rose at mid day, they discovered that around June 21 (in our current calendar, but that is another story) the sun got as high as it was ever going to get, and that around December 21 the sun stayer lower in the sky than on any other day. To make matters worse, how high and how low the sun gets depends on where you live. For the folks living near the equator, on June 21 the sun was up in the northern sky, their day was long and hot, but things cooled off at night, while for the folks living up near the north pole, the sun was to the south and moved in a small circle. In fact they were in the middle of 6 months of constant daylight. Something funny is clearly going on.

What's the right question?

Suppose we ask the question, when is the sun directly overhead, that is, if we look straight up, when will we see the sun. Another way of asking this question is if we put a stick in the ground, sticking straight up, when will it cast absolutely no shadow. The answer is different depending upon where you live. If you live at the north pole, the answer is never, while if you live near the equator, the answer is twice a year, right around March 21 and September 22. However, if you live at the Tropic of Cancer, anywhere on the world at 23.5 degrees north, the answer to this question is that the sun is directly overhead only once a year, right around June 21st. Anyone living north of the Tropic of Cancer will never see the sun directly overhead, while anyone living south of the Tropic of Cancer (in the northern hemisphere) will see the sun directly overhead exactly twice. We live almost exactly on this dividing line.

Since a picture is worth a thousand words, take a look at the diagram below for exactly what is going on on June 21st. Our north pole is inclined by 23.5 degrees to the plane that contains the Earth's orbit around the sun. The equator and the line through the poles are at right angles, and the plane of the Earth's orbit around the sun makes an 23.5 degree (what a co-incidence) angle with the equator. Thus the Tropic of Cancer is the northernmost place in the world where the sun is ever directly overhead. Now only one mystery remains. What does this particular latitude have to do with Cancer. Well, it turns out that on June 21st, if you look up at night you will find the sun passes through constellation of Saggitarius. However, if you lived around 2000 years ago and looked up into the night sky you would find that the path of the sun that day took you right through the constellation of Cancer. Since the ancients had the privilege of naming things, this particular latitude is know as the Tropic of Cancer instead of the Tropic of Saggitarius. The next question is, why did it change? Perhaps we'll look into that next time.

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