The Seasons

Note: You can consider this web page and the linked animation as an astronomy experiment, so you may find it useful to print this page.TheoryThe four seasons on Earth are caused by two factors: 1) variations in the Sun's total daylight and 2) variations in the heating effect of the Sun's light. These variations are caused by the Earth's axial tilt relative to its orbital plane, the Ecliptic Plane.By convention, we pretend that the Sun revolves around the Earth once a year along an orbital path called the Ecliptic. This fictitious orbit mimics the combined effect of the Earth orbiting the Sun while exhibiting its axial tilt.Experiment

The animation corresponding to the picture above, and is designed to teach important aspects of the earth's seasons. It starts on the first day of Spring (approximately March 21st), with a default observer latitude of 0 degrees (the observer is at the Equator).

If you press the Run button, the Sun will start "orbiting" the Earth counterclockwise (as viewed from above). You can stop the Sun anytime you want by pressing the Run button again. Each time the Sun passes through a season changing day (black dot on the "orbit" and black dot on the yearly clock), you will hear a sound and the black dot on the yearly clock will change to white. You can also "drag the Sun" around the Earth by dragging the clock hand (arrow) counterclockwise (it will only go one way).

There are three gauges in the middle of the animation: the angle alpha, EE and daylight hours. The angle alpha is the solar declination, the angle the line between the Sun's and Earth's centers makes with the Earth's equatorial plane. The EE gauge gives you the ground heating efficiency (energy efficiency) of the Sun's rays: the Sun is most efficient at heating the ground when it is shining directly overhead. The daylight hours gauge gives the approximate number of daylight hours for an observer at the latitude selected (twilight or indirect lighting is excluded).

In the lower left hand corner there is a slider that allows you to change the observer latitude (denoted as phi sub L). For now, leave it alone.

In the upper right hand corner you will see a little "light can" that represents the angle that the Sun's rays makes relative to Earth ground, looking South from wherever you are. This angle, called the solar altitude (indicated as beta), is equal to 90 degrees plus alpha minus phi sub L. Energy efficiency (in %) is equal to the sine of beta.

Daylight hours are also shown as a portion of the observer's latitude circle. The brown part shown is the Earth core, sliced off at the observer's latitude. The white outline of that core is a graphical representation of the illuminated portion of the observer's journey around the Earth (basically a day-night circle) for the latitude selected. For higher latitudes (positive or negative), the circle naturally gets smaller.

On the Earth image, look for latitude lines. The pinkish line in the middle is the Equator, the two lines directly above and below the Equator are the tropical latitudes (the Tropic of Cancer at +23.5 degrees, and the Tropic of Capricorn at -23.5 degrees), and the two outermost lines are the Arctic and Antarctic Circles (plus 66.5 degrees and minus 66.5 degrees respectively).

Notice that various parts of the animation will "pulse glow" and self-identify when you hover over them. For example, each black dot on the yearly clock self-identifies as a season changing day. In particular, the bottom dot is the Winter Solstice day, the shortest day for daylight in the Northern Hemisphere. On this day, the Sun shines directly over the Tropic of Capricorn (you can see this via the dotted line that connects the Sun's center with the Earth's center).

Now let's try out some scenarios. Leaving the observer latitude at 0 degrees, run the Sun around the Earth for a full year. What happens to the number of daylight hours at the Equator over the course of a year? Is this a surprise to you?

Now set the observer latitude to +90 degrees (the North Pole). Reset the animation and then run it over the course of a year. For what range of dates are there 24 hours of daylight? For what range of dates are there 0 hours of daylight? Does this information make any sense to you? While you are doing this test, be sure to look at the latitude circle part of the animation. Notice how small the brown part becomes, and whether there is a white circle around it or not. Is this consistent with the observations you've just made?

Now set the observer's latitude to -90 degrees (the South Pole). You should get the exact opposite results of your North Pole test.

Now set the observer latitude to 23.5 degrees (the Tropic of Cancer). On what day or days is the energy efficiency 100%? What are the angles alpha and beta on that day or days?

Now set the observer latitude to -23.5 degrees (the Tropic of Capricorn). On what day or days is the energy efficiency 100%? What are the angles alpha and beta on that day or days?

Now set the observer latitude to +66.5 degrees (the Arctic Circle). For what day or days is there 24 hours or daylight? Does this make sense to you?

Now set the observer latitude to -66.5 degrees (the Arctic Circle). For what day or days is there 24 hours or daylight? Does this make sense to you?

Press Reset to set the date back to the Vernal Equinox, and the observer latitude back to 0 degrees (the Equator). Leaving the date alone, vary the observer latitude from one end of the slider to the other. What happens to the number of daylight hours?

Questions

1) An equinox day is a day when the number of daylight hours is approximately twelve hours. Where on Earth is it true that every day is an equinox day?

2) A zenial day is a day when the Sun shines directly overhead, when beta is 90 degrees. For what range of latitudes is there at least one zenial day? What latitude experiences two zenial days?