Astronomy with a Stick / Day into Night

Astronomy with a Stick

AWS Unit 3: Making and Using Models

Introduction :: Activity 1 :: Activity 2

Activity 2

Objective

To demonstrate the effect of the inclined angle of the Earth's equator with respect to the plane of its orbit on the distribution of daylight on the surface of the Earth. This model presents a quantitative approach to why we have seasons.

Time Allotment

The length of time depends on how much of the demonstration is prepared before class and how much is done during the class.

Procedure

1. Review with the class the fact that the Earth rotates on its axis with the plane of its equator inclined at a 23.5° angle to the plane of its orbit around the Sun (the North Pole of the Earth is always pointed toward the North Star no matter which side of the Sun the Earth is on). In former years, the students will have done activities in which an inclined and rotating Earth is passed around a lamp to represent the Earth in its orbit around the Sun. You can repeat such a demonstration and note with the students when the northern hemisphere is lighted most directly by the Sun (our summer) and when the southern hemisphere is most directly lighted (our winter). They will see that in spring and fall the light is directly on the equator.
2. To prepare the model, begin by pasting the black construction paper to the cardboard. Then paste the yellow construction paper over the righthand-side of the black paper.
3. Now, mark the 12.5-cm disk that you cut from the manila folder. Be sure to include the following:

• A line across the center, labeled equator
• Points at the top and bottom, labeled 90°N and 90°S for the North and South Poles
• Lines drawn at 66.5° north and south of the equator and labeled Arctic and Antarctic Circles, respectively
• Lines drawn at 23.5° north and south of the equator and labeled Tropic of Cancer and Tropic of Capricorn, respectively
• A properly placed line to represent the latitude at which you live, labeled correctly

4. Push a pin (or paper fastener) through the center of the disk, through the center of the line between the black and yellow sheets, and through the cardboard backing.  The disk should rotate freely and evenly. Figure 10a. Earth as it would look if its axis were not inclined.
5. Mark a line on the yellow paper that is an extension of the equator when the North and South Poles are lined up with the line between the yellow and black paper.  Label that line "Plane of the Earth's Orbit." Draw arrows toward the disk from the outside edge of the yellow paper and label them "Rays from the Sun."
6. Place a ball on a desk to represent the Sun, and hold the model on one side of this Sun model. The yellow construction paper should be moved to face the ball. Align the disk representing the Earth so that the equator is in line with the plane of the Earth's orbit. This position illustrates the distribution of the sun's rays on the Earth at the time of the vernal and autumnal equinoxes. The direct rays extend between the Tropic of Cancer and the Tropic of Capricorn, and both poles are illuminated.
7. Now tilt the Earth disk 23.5°, either toward the model Sun or away from it. Ask the students to observe the areas illuminated by the Sun's rays in this position. They should see that the most direct rays from the Sun are striking the Earth on either the Tropic of Cancer or Tropic of Capricorn (depending on whether the teacher has begun with the North Pole tipped toward the Sun model or away from it). How much sunlight is striking either pole at this position? Do the Arctic and Antarctic Circles mark any special spots with regard to daylight and darkness? Figure 10c. Earth inclined 23.5°; southern hemisphere lighted by the Sun's rays.
8. Carry the model to the other side of the model Sun, being careful to keep the Earth's axis tipped in the same direction. At this point the black construction paper will be toward the Sun. Holding the disk stationary, turn the cardboard backing sheet so that the yellow construction paper is now toward the Sun. Ask the students to observe the areas illuminated by the Sun's rays in this position. Ask them if the most direct rays from the Sun are striking the Earth at the same latitude. They should see that now the most direct rays from the Sun are striking the Earth at a different latitude. If it was the Tropic of Cancer in part 6, then it will be the Tropic of Capricorn at this time. Have the students determine which month each position should represent. (The Sun strikes the Earth most directly at the Tropic of Cancer in June, and at the Tropic of Capricorn in December). Repeat the questions and observations regarding the Poles and Arctic and Antarctic Circles from part 6.
9. If a lighted Trippensee planetarium is available in the classroom, revolve the Earth slowly through the seasonal positions. Note that the Earth's axis is tipped, and because the North Pole always points to the same direction in space, sometimes the northern hemisphere is tilted toward the Sun, sometimes the southern hemisphere is tilted toward the Sun. This confirms the theories developed by the class, and reviews the materials.

Discussion

1. At the end of the unit, the students should be able to answer the question "Why do daylight hours vary in length where we live?" The variation of the length of daylight hours where we live is caused by the 23.5° angle of inclination of the Earth's equator from the plane of its orbit. These variations depend also on the latitude of our position on the Earth's surface.
2. The students should understand that this angle (called the obliquity of the ecliptic) affects where on the Earth the sun shines directly on any given day. The hours of daylight change because the Sun appears to stay above the horizon longer when the northern hemisphere is inclined toward the Sun; it appears to go below the horizon sooner when the Earth has moved around to the other side of the Sun and the northern hemisphere is inclined away from it. The more direct the rays, the longer the day and the warmer the season.

Resource

If you wish to work directly with the ephemeris constructed by the Naval Observatory, you can order it on a 3 1/2- or 5 1/4-inch, PC- or IBM-compatible, floppy disk directly from the National Audio Visual Center. Entitled Floppy Almanac (order #PB93505840), it contains the sunrise and sunset times and azimuths for places all around the world. The latest version available covers 1994-1996. It sells for $30, including postage to anywhere in the United States. You can order it by credit card by calling 800-553-6847 or visit the National Technical Information Service. A more expensive, but also perhaps more useful ephemeris is the Multiyear Interactive Computer Almanac (MICA) (Order #PB93-500163INC). This disk is a source of high-precision astronomical data and is a tool astronomers use when sky maps aren't enough. MICA provides high-precision astronomical data in tabular form for a wide variety of objects. The disk costs $55. The price outside U.S., Canada, and Mexico is $80. To order, contact NTIS at the toll-free number or web site listed above. Of course you can also try a free online ephemeris from the US Naval Observatory.

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