Middle School Astronomy Activity

Written by Judy Young and Bill Randolph

Lesson 5: MEASURING THE ANGLE OF THE SUN

THROUGHOUT THE SCHOOL YEAR

Note: This activity has many intersections with the National and State Science Education Standards.

NATIONAL SCIENCE EDUCATION STANDARDS, Grades 5-8 (NRC, 1996)

SCIENCE AND INQUIRY STANDARDS:

• Answer questions that can be solved by scientific investigations.

• Design and conduct scientific investigations.

• Use appropriate tools and techniques to gather, analyze and interpret data.

• Think critically and logically to make relationships between evidence and explanations.

EARTH SCIENCE STANDARDS:

• Most objects in the solar system are in regular and predictable motion.

• Explain how the tilt of the Earth and its revolution around the Sun results in uneven heating of the Earth, which in turn causes the seasons. Those motions explain such phenomena as the day, the year, phases of the moon and eclipses.

• Seasons result from variations in the amount of the sun's energy hitting the surface, due to the tilt of the earth's rotation on it axis and the length of the day.

MASSACHUSETTS STATE SCIENCE STANDARDS, Grades 6-8 (11/00)

EARTH SCIENCE STANDARDS:

• Compare and contrast properties and conditions of objects in the solar system to those on Earth.

• Explain how the tilt of the Earth and its revolution around the Sun results in uneven heating of the Earth, which in turn causes the seasons.

A. Learning Objectives:

• Collect and graph data throughout the year representing the height or angle of the Sun in relation to the horizon.

• Collect and interpret data which verifies that the Earth's axis is tilted at approximately 23°.

• Understand the angle of the Sun is responsible for climatic and seasonal changes.

• Understand the Sun is usually not due South at exactly noon.

B. Materials:

• Gnomon (fixed on a flat surface and accessible throughout the year)

• Ruler or tape measurer

• Booklet for recording observations (class or individual)

• Pencil or pen

• Protractor or graph paper

C. Background:

This lesson complements lesson 1 (Using Shadows to Find the Four Directions) and lesson 2 (Measuring Shadows). The success of this lesson depends on two factors: 1) measuring the length of shadow at the same gnomon throughout the year and 2) taking measurements of the gnomon's shadow when the Sun is directly south, i.e. when shadow aligns with N-S direction. You will need to have completed Lesson 1 (Finding the Four Directions) to locate the N-S line.

You might begin this lesson by asking your class some pre-assessment questions that relate to the tilt of the Earth's axis:

• How high is the Sun at noon today?
• How high is the Sun at noon in the winter versus the summer?
• What causes the Sun to be at different heights or angles above the horizon at noon from winter to summer?
• What causes the seasons?
• Encourage the class to develop their ideas into data collecting experiments. Then conduct as many of these experiments as feasible. Student-centered experiments can lead to: creating a common vocabulary, insight into student misconceptions, and cognitive readiness for alternative explanations, such as the scientific viewpoint.

Because of the abstract nature of astronomy, the more measurements the students record, the more likely they are to be successful at interpreting their data. Ideally, this activity will allow individual students or the whole class to collect data once a week throughout the school year. A student or a pair of students could take turns collecting data from a shared gnomon on campus; the actual time needed to measure the gnomon's shadow only takes a few minutes. Alternatively, students could also create their own gnomon at home and collect data on the weekends.

Teacher's Note:

There are two distinct parts of this activity, either or both of which can be done. It is very instructive to measure the changing angle to the Sun at noon throughout the year. This alone makes a coherent lesson.

For interested classes and teachers an additional part of this activity is keeping track of when the Sun is due South, and learning about the "Equation of Time." If you are familiar with the analemma (the figure 8, which is made by measuring the Sun's shadow length at noon throughout the year), it incorporates the equation of time because shadow measurements are always made at noon. However, because of the Earth's slightly elliptical orbit around the Sun, and our changing speed in that orbit, the Sun deviates from due South at noon (EST) by as much as 15 minutes throughout the year. The graph of this deviation is called the "Equation of Time" (not an equation of the true sense) and is reproduced here to guide you as to when the Sun is due South each day for measuring the gnomon's shadow.

Figure 5-1: Equation of Time

This graph shows the time when the Sun is seen due South throughout the year. In making the graph of time when shadows are measured, you will need to account for Daylight Savings Time. If you begin this activity in Sept./Oct., before we go off Daylight Savings Time, remember that times have been shifted and use the right side in Figure 5-1. This also applies for measurements made after April. Between November and April, when we are on Eastern Standard Time, no adjustments are needed, so use the left side in Figure 5-1.

D. Procedures:

1. Recording Data

During this activity the students will use a gnomon as explained in Lesson 1. Students will record three pieces of data each time they make observations: the length of the gnomon's shadow, the date and time when the gnomon's shadow lines up on the north-south line. Enter the data collected onto a table which includes the yearly observations, such as Table 1. This table also includes a space for entering each determination of the angle to the Sun. 2. Data Analysis

Lesson 3 describes the procedures for using the gnomon's shadow to measure the angle of the Sun above the horizon. Determine the angle to the Sun for each measurement of the gnomon's shadow and enter the result in Table 1 and in the graph below. Record your observations in Figure 5-3 indicating the time when the Sun is due South, i.e. when the gnomon's shadow points North). Notice that this time can be as much as 15 minutes before or after 12:00 noon EST or 1 p.m. EDT.

Figure 5-3. Equation of Time (corrected to Standard Time)

Eastern Standard Time (EST) appears in bold; Eastern Daylight Time is italics. 3. Illustrating the Data by Month:

It is useful to illustrate the changing angle to the Sun throughout the year in a single graph showing the gnomon, the shadow, and the angle to the Sun. An example is shown in Figure 5-3. The date, time, shadow length and angle to the Sun can be listed, and the shadow lengths can be labeled with dates and drawn accurately to scale. The angle to the Sun is illustrated effectively next to the raw data columns.  4.) Interpreting the Data and Results:

Understanding the Significance of the Angle to the Sun

Over the course of the school year, students have recorded and observed how the angle to the Sun changes from month to month or season to season. It is relatively easy for the students to use their data to calculate that the Earth's axis is 23°.

Here are the steps your students can do to arrive at this conclusion. Let's assume your students have made the following recordings:

On September 21 the Sun was 48° above the horizon

On December 21 the Sun was 25° above the horizon

On March 21 the Sun was 50° above the horizon

On June 21 the Sun was 70° above the horizon

At a very minimum the students will see that the angle to the Sun changes throughout the year. Hopefully they associate the higher the angle to the Sun and the longer daylight hours to coincide with the warmer temperatures. The highest noon-time angle of the Sun also corresponds to the longest day of the year around summer solstice and the smallest angle occurs near the winter solstice. Additionally, the angle to the Sun near the two equinoxes is roughly in between the angle to the Sun on the two solstices. Using the example angles given above, the average angle to the Sun on the Equinoxes is approximately 49°. Students should calculate how much higher the angle to the Sun is in June from this average as well as how much lower it is in December.

A simple example of these would look like:

70° in June minus the equinox average of 49° = +21° in June.

25° in December minus the average of 49° = +24° in December. If you take the average between 21° and 24°, it equals 22 1/2°, which is very close to the actual tilt of the Earth's axis of 23 1/2°.

The angle to the Sun at our latitude of 42° is never straight up, or 90°, from the horizon. It reaches it highest angle during summer solstice (June 21) at 71°, and its lowest angle on winter solstice (December 21) at 24°. The angle to the Sun at the two equinoxes is 48°. Therefore, the difference between the angle to the Sun at the solstice and the equinox is 23°. Hopefully the students understand the difference between the Sun's angle from winter and summer solstice is 48 + 23° or 48 - 23° minus 48°. Again, 48° is the angle to the Sun at the two equinoxes.

Understanding the Importance of the Equation of Time:

The equation of time is the difference between noon and the time the Sun is actually due- south. Again, this is measured by recording the time when the gnomon's shadow lines up on the North-South line. The Earth's elliptical orbit and varying speed in the orbit cause the Sun to be due south alternately ahead of or behind mean solar time (noon). The difference between the two kinds of time can accumulate to about 15 minutes. Often the equation of time is plotted on globes of the Earth as a figure 8, called an analemma, and is placed in the region of the South Pacific Ocean (because there is space).  A project conceived by Dr. Judith S. Young Professor of Astronomy, University of Massachusetts, Amherst e-mail: Judith Young   Last Update: 7/15/2003