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## The Question

(Submitted July 14, 1997)

When is the Sun at its highest point and how did you determine the answer?

Thank you very much for your question about the Sun, it was a pleasure to answer. The short answer to your question is simply "noon." Astronomical noon is defined to be the time of day when the Sun is highest in the sky. For a northern latitude of 40 degrees (typical of North America) the Sun's noon position ranges from about 40+23=63 degrees South of straight-up in Late December to about 40-23=17 degrees South of straight-up in late June. That is why it is hotter in the summer than the winter. (Note: The Earth's spin axis is tilted by 23 degrees with respect to its circular orbit around the Sun; that is where the 23 degrees comes in.)

TIME ZONES AND DAYLIGHT SAVING TIME

Now, Astronomical Noon is not always at 12:00 local time. In the winter when we are on Standard Time it is within an 1/2 hour or so of 12:00 -- closer if you live near the middle of your time zone. If you live on the western edge of your time zone, Astronomical Noon is a little later than 12:00 because the Sun moves from East to West during the day. If you live on the Eastern edge it is earlier. (It could even be a few hours off if you live in parts of Alaska.)

On the other hand, during Daylight Saving Time astronomical noon is at around 1:00 pm., because we change our clocks so we can have more daylight in the evening when we are awake, and so the Sun does not rise too early in the morning when we are asleep.

THE SUN'S PATH IN THE SKY

There is another astronomical effect you should know about that can change the time that the Sun is highest in the sky. This is a little hard to explain, but it also has to do with us watching the Sun from a tilted perspective. The Earth spins on its axis about 366 and 1/4 times each year, but there are only 365 and 1/4 days per year. This is because we define a day not based on the Earth's period of rotation, but based on the average time from noon one day to noon the next. Gradually over the course of a year the Sun appears to go 'backwards' (West to East) around the Earth compared to the far away stars (this is because we are really going around the Sun). Subtracting this 1 time backwards from the 366 and 1/4 times forward, we get the typical 365 and 1/4 days per year.

So back to the point of the Sun at noon. The Sun appears to go around the Earth in a circle from West to East once per year in an orbit that is tilted by 23 degrees from the Equator (because the Earth's axis is tilted). This tilt means that sometimes the Sun appears to move mostly West-to-East, and very little North or South (like in late Dec and late June). While at other times is appears to move a good deal North or South (like in late March or late September), so it appears to move slower West-to-East.

So how what does this have to do with time and the Sun at noon? The time standard is to set our clocks to 12:00 when the Sun is highest in the sky on March 21st, since this is when it crosses the equator, also known as vernal equinox. But as you check the Sun's position at the same time, by your watch, on subsequent days, it appears to move West. This is because it appears to be moving slower than average West-to-East.

Conversely, in late December the Sun looks like it is turning around from moving South to moving back North again, known as the winter (to people living in the northern hemisphere) solstice. It does not appear to move either North or South, but it is moving faster than average West-to-East. Now following this argument we see that right after the equinox, in April and May, the Sun will be a little West of South at 12:00 (or it will be highest in the sky at a little before 12:00). However, by late June (the summer solstice) the Sun would have caught-up so it is now highest in the sky at 12:00 again. In July and August it is now East of South at 12:00 (or it will be highest in the sky at a little after 12:00). And then by late September (the Autumnal Equinox) it has fallen back to being South at 12:00 again.

There is a chart, called the Analemma (URLs below) that puts together all these effects to show the position of the Sun at noon each day throughout the year. You can recognize the Analemma because it looks like a figure 8.

(see http://www.alpheratz.net/murison/SunAltAz/WashDC1997.html)

YET EVEN ANOTHER EFFECT

If you are even more interested in this, there are some smaller effects because the Earth moves slightly closer and farther away from the Sun throughout the year. (We are closest to the Sun in January and farthest away in July). The motion toward and away from the Sun is very small compared to the distance to the Sun, yet still large compared to the size of the Earth. When the Earth is farther away from the Sun, it moves slower and when it is closer it moves faster. It is this effect that makes the Analemma not perfectly symmetrical -- it has a bigger loop on the bottom than the top. If the Earth had a perfectly circular orbit, the Analemma would be a perfectly symmetrical Figure 8 with the cross-over point directly above the Equator. As you can tell from the figures (URLs above) it is not symmetrical.

I hope this leaves you lots to ponder. We really enjoyed your question because it is so simple -- yet it can be answered simply, in more detail or excessive detail.

HOW YOU CAN MEASURE THIS YOURSELF

One way to determine when the Sun is highest is to find the time when shadows are shortest. Find a flagpole or other vertical object surrounded by level ground. Every ten minutes or so, place an object, marked with the time, at the tip of its shadow. When the shadow has stopped shrinking and is starting to get longer again, the object closest to the flagpole will be marked with the time at which the Sun was highest. If what we said above is correct, the shadow should be due North. Go test this yourself and see if we got it right!

Sincerely,

Jonathan Keohane