How do we know the Earth’s axis is tilted 23.5 degrees?

This is a question one of my astronomy students asked last week. That’s a perfectly good question, and I want to answer it using a different style than the one I’m use to.

Imagine you have observed that on one particular day the sun at its highest point in the sky (local noon) is actually low above the southern horizon. Some days later, you notice that the noon-sun is higher, 23.5 degrees higher in the sky than it was for your first observation. Again, days pass and you notice at noon that the sun is even higher than before, another 23.5 degrees higher!

What is making this happen? Why is the sun changing its position in our sky?

Some ideas might be mystical: maybe angels and demons are fighting over the sun, holding their own celestial rugby match.

Some ideas might be more material: maybe the Earth is wildly wobbling on its axis.

A radical idea may be that the Earth is tilted: maybe our rotational axis is not exactly perpendicular to the orbital plane of the earth around the sun.

Is there a test we can conduct to see if the Earth may be wildly wobbling on its axis? Since we’re studying celestial objects oft times we must wait for the universe to do the testing for us and we just observe. Over time we notice that the changes in the position of the sun in our sky happen slowly and consistently.

Around December 21, the noon-sun is the lowest that it’s going to get. Just 3 months later, around March 21, the noon-sun position is 23.5 degrees higher than it was in December. Another 3 months (June 21) and the noon-sun is another 23.5 degrees higher. Again, another 3 months and the noon-sun has returned to it’s mid-position. And then it repeats, over and over.

Researching astronomical records you find the same pattern described far into recorded history. Would these observations rule-out the hypothesis that the Earth is wildly wobbling? The regularity of year after year, century after century, would seem to tell us the movement is not wild.

You start noticing other aspects of the sky, both during the days and the nights. You may notice that the star called Polaris stays pretty much in the same spot of the sky, night after night, year after year. If you travel to the North Pole you may find that on June 21, the noon-sun stays 23.5 degrees above the horizon all day. Another 3 months later and the noon-Sun barely brightens the horizon. Then the North Pole sky is dark for 6 months, but eventually, on March 21, the sun begins to reappear.

Would those observations lead the discerning observer to the conclusion that the Earth’s axis is tilted 23.5 degrees? We didn’t disprove the angelic rugby match!

I’m reading Scientific Inquiry and Nature of Science, edited by L. B. Flick and N. G. Lederman, and I’m exploring this way of thinking about astronomy.