Re: How are scientists able to determine the earth's tilt at 23.5 degrees?

Date: Tue May 18 16:35:48 1999
Posted By: Ricky J. Sethi, PhD
Area of science: Astronomy
ID: 921801910.As

Message:

Hi Denise,

Introduction

You might think that with modern technology (e.g., computers, satellites, lasers, telescopes, etc.), this would be a relatively trivial thing to determine today. And you'd be right. But it might surprise you to know that the very first (accurate) known measurements of the Earth's tilt were recorded over 2,000 years ago! And even more fascinating is the fact that you, too, can repeat that experiment today, using nothing more than a stick and some measuring tape!

History

Now that I've grabbed your attention (I hope), let's see how you can become the scientist and carry out this little experiment for yourself. But first, a little historical background. The gentleman alluded to earlier was one Eratosthenes of Cyrene (in modern day Libya in North Africa) who lived from about 276-194 BCE (Before Common Era). Eratosthenes was a brilliant man who not only deduced the tilt of the Earth but also calculated the circumference of the Earth and the distance to the Sun (among many other things). And he wasn't the only one, either. Abu Abdullah Al-Battani of Harran, who lived from about 868-929 CE (Common Era), also determined, with remarkable accuracy, the obliquity of the ecliptic (in addition to the length of the seasons, the true and mean orbit of the Sun, and many other things). Both of these brilliant scientists managed their incredible accomplishments without any satellites, computers, or even calculators!

Theory

So how the heck did they do it? Well, we can employ a similar (though understandly much less accurate :) method. First, let's examine some of the consequences of having a tilted Earth orbiting the Sun. What would this look like? Well, keeping in mind that the Earth is tilted with respect to the plane of the orbit, it would look something like Fig. 1:

Fig. 1

The above picture was taken from from this site about the reasons for the seasons. It shows, quite nicely, that the tilt of the Earth is really only in one direction. One of the consequences of this is that, at different times, you will get more or less sunlight depending on the orientation of the tilt of the Earth with respect to the Sun (i.e., depending on what time of the year, or season, it is). For example, in the summer, the Earth is tilted towards the Sun so it gets more solar energy from the Sun (since intensity = power/area). During the winter, on the other hand, the ground receives less energy. I've made a little diagram (Fig. 2, below) to show just the relative amount of energy the Earth receives during various parts of it's orbit (with apologies for my lack of artistic ability :). Just pick a spot, for example the northern hemisphere, and see how many rays of sunshine impact that area (as compared to the southern hemisphere, for example) during the various parts of the orbit.

Fig. 2

What you'll find is that at position 1, with the least rays in the northern hemisphere, it's Winter-time (Winter Solstice); at position 3, with the most rays in the northern hemisphere, it's summer-time (Summer Solstice); and positions 2 and 4, with equal rays in both hemispheres, are the equinoxes. So great... we know about the solstices and the equinoxes... but what now???

Experiment

Now for the actual experiment (at last!). We can use the information we learned in the Theory section to formulate a hypothesis and then test out that hypothesis with our experiment. We know that the Earth receives less energy in the winter months because of the longer angle that the northern hemisphere's ground makes with the Sun's rays (this is why we get less rays in the northern hemisphere during the winter solstice, position 1 in our Fig. 2). Similarly, the northern hemisphere's ground makes a sharper angle with the Sun's rays during the summer months, with the sharpest angle occuring at the summer solstice (position 3 in the diagrams above). These changing angles of the Sun's rays at different times of the year should result in different length shadows for the same stick measured at the same time (e.g., noon). That is, if we put our stick in the ground at a fixed location and measure the length of it's shadow at Noon at various times of the year (e.g., the solstices and the equinoxes), we should find that the length of the shadow of the stick at Noon changes, depending on what time of the year it is. This is shown in Fig. 3, below:

Fig. 3

So our hypothesis becomes that by measuring the different lengths of the shadows cast by the same stick measured at the same time of day (i.e., at Noon) but at different times of the year (i.e., the solstices and the equinoxes), we should be able to use simple trigonometry (Angular Height = arctan ([Length Of Stick]/[Length of Shadow])) to determine the angular variation of the Sun. And this angular change in the height of the Sun, as seen from Earth, is actually a measure of the tilt of the Earth when seen from a heliocentric point of view!

What you should find when you actually do the experiment is that the Sun's angular height varies about 23.5^o between either of the equinoxes and the solstices. For example, the difference in angular height of the Sun at the Winter Solstice and at the Autumn Equinox is 23.5^o (these are the first two rays in Fig. 3). Similarly, the difference between the Summer Solstice (the 3rd ray above) and the Vernal Equinox is also 23.5^o. As a side note, these angles are also the locations of the Tropic of Cancer and the Tropic of Capricorn!

Epilogue...

In summary, one of the ways to determine the obliquity (tilt) of the Earth (with respect to the plane of it's orbit), is to measure how much the shadow cast by a stick at noon varies with the time of year. That was a very good question and I hope this helped answer your question somewhat. I know parts of it might be murky and slightly confusing so you might want to elicit the help of an adult in going over those parts that I wasn't able to explain clearly. There are also some great sites out there on the tilt of the Earth and it's role in the seasons. Although I didn't find any sites on actually measuring the tilt, you might have better luck... just run a search for some keywords (e.g., Earth, tilt, seasons, Eratosthenes, etc.) at your favourite search engine and you should get plenty of additional perspectives on this. But, of course, the best way to learn anything is to actually do it... so grab a stick, make some measurements, and get ready to wait (patience is a huge part of what most scientists do) to confirm your hypothesis! And if you have any questions at all, please don't hesitate to drop me a line at rickys@sethi.org.

Best of luck!

Rick.

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