Changes in latitudes, changes in attitudes: Understanding the science of life on the equator

By Phillip Martin

When we arrive in Ecuador from northern climes it gradually dawns on us that sunrise and sunset come at just about the same time every day, all year long. While we almost universally enjoy the moderate, year round climate this brings us, some of us miss those long summer evenings; however I doubt many of us miss those short winter days. But why does the length of day change with the seasons, and why is it so much different here than back home?

There are days in Cuenca, called “los dias sin sombras” by the locals, when the sun is directly overhead and there are no shadows.

If you search Google for the answers the result you will likely get is because of the tilt of the earth’s axis. That’s all well and good, but it explains it about as well as saying a plane can fly because it has wings.

To address some of those questions I’ve prepared a few diagrams and some notes of interest that may help us understand what’s going on. I’m no expert on this, just someone whose brother likes astronomy. As for myself, I used to lie awake at night wondering where the sun went at night until finally it dawned on me.

Since the length of day is dependent upon which latitude on the earth’s surface one is standing on, it behooves us to contrast two different locations to identify why they are different. Some of the explanations are easier to visualize if we picture a location well away from Cuenca, as well as Cuenca itself. For this purpose I have chosen Minneapolis as a point of reference. I did this because this city lies on the 45th parallel — exactly halfway between the equator and the North Pole. This fact makes it much easier to locate on the diagram than would choosing Las Vegas, or New York, for example.

The diagrams below display the orientation of the earth at the solstices. The one with the June 21  date is called the summer solstice and the one with the December 21 date is called the winter solstice (for obvious reasons). These are the two dates which we traditionally say are the longest and shortest days of the year. The further north or south one goes from the equator  the truer that statement becomes but within the tropic latitudes things get squirrelly. In another box I’ll show you there are some discrepancies.

In the diagrams the yellow arrows represent the rays of the sun. The earth, of course, is divided in half. The light we will call day and the darkness we will call night.

The plane of the solar system is described by the elliptical orbit the earth makes around the sun. The earth’s axis is tilted 23.5⁰ in relation to this plane. For all practical purposes, this tilt is fixed in space. Yes, the earth wobbles, but you aren’t likely to notice as it takes 26,000 years to make one complete wobble. The tilt being fixed is why both diagrams show a tilt to the left (author’s choice). If you put the two diagrams side by side the December 21 diagram should be placed on the left and the 21 June diagram should be on the right. That way the sun would be right between the two.

As you can see, Cuenca is located just a little below the equator while Minneapolis is located well north of the equator.

June 21

December 21

Now we come to the critical part of the diagram. I have drawn a dashed line to illustrate the path that Minneapolis takes as the earth rotates each day. By looking at the June 21 diagram we can see that the length of this path is much longer in the daylight than it is at night.  Since the speed of rotation is constant at any given point it follows that the time to travel the longer path must also be longer. Thus the city has more hours of daylight in its summer.

The mirror image applies in the December 21 diagram.  Here we see that portion of the dashed line in the darkness is much longer than the portion in the light. Hence, the short winter days in Minneapolis.

The same principle holds true in describing why the length of day varies in Cuenca. But that difference is so small it becomes difficult to see in the diagram. If you look closely you will see that the dotted line crosses the divide between day and night just slightly to the left of the earth’s axis.

Cuenca’s location is fixed at 2.9 degrees south of the equator. However, its location on the solar plane varies throughout the year.

On June 21, Cuenca is 23.5+2.9 = 26.4 degrees south of the plane of the solar system.  On December 21, Cuenca is 23.5-2.9 = 21.4 degrees north of the plane of the solar system.

In March and September, Cuenca passes through the plane of the solar system. It is at the plane of the solar system where the sun’s rays fall perpendicular to the earth’s surface, that the sun is closest to the city.

In addition, the earth’s orbit around the sun is not perfectly circular. It is elliptical. In July it is 3 million miles farther from the sun than it is in January. For these two reasons Cuenca is farther away from the sun in June, July, and August than it is during December, January and February. This accounts in part for why July and August are the coldest months here.

Days when the sun is directly overhead in Cuenca

Date        Time

29 Sept.   12:06
30 Sept.   12:06
1 Oct.      12:05
12 Mar.   12:25
13 Mar.   12:25
14 Mar.   12:25

More Than 12 Hours
On the equator, the day and night stay approximately the same length all year round, but the day will always appear a little longer than 12 hours, due to the reasons given below.

On the equinoxes, the geometric center of the sun is above the horizon for 12 hours, and you might think that the length of the day (hours of daylight) would be 12 hours too.

However, “sunrise” is defined as the moment the upper edge of the sun’s disk becomes visible above the horizon – not when the center of the sun is visible. In the same sense, “sunset” refers to the moment the sun’s upper edge, not the center, disappears below the horizon. The time it takes for the sun to fully rise and set, which is several minutes, is added to the day and subtracted from the night, and therefore the equinox day lasts a little longer than 12 hours.

Refraction: Light Lingers
Another reason why the day is longer than 12 hours on an equinox is that the Earth’s atmosphere refracts sunlight.

This refraction, or bending of the light, causes the morning sun’s upper edge to be visible from Earth several minutes before the edge actually reaches the horizon. The same thing happens at sunset, when you can see the sun for several minutes after it has actually dipped below the horizon. This causes every day on Earth – including the days of the equinoxes – to be at least six minutes longer than it would have been without this refraction.

Which Way is North?
Do you find yourself getting disoriented from time to time? Subconsciously you may have used your shadow to help you know where places were. In North America your shadow always lies in a northerly direction. Thus, your brain could analyze visual feedback to tell you which direction you were going.

However, it in tropics it’s a little different. If you will refer to the two diagrams you will notice that in Cuenca your shadow lies in a northerly direction for half the year, but then it lies in a southerly direction for half the year. Thus your brain must factor in the time of year as well as the direction of your shadow in order to tell you which direction you were going.

Good luck.
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Phillip Martin is a former manufacturing and quality engineer in the United States of North Carolina, Tennessee, and Virginia. He has lived in Cuenca since 2013.