University of Michigan - Department of Astronomy

Version: tropics

Seasons Worksheet


Before class, please study Figure 1 in the Introduction in color to learn and be familiar with the given features in the planetarium. Also, please review and be familiar with the terms below from the Coordinate Systems activity.

In this activity, you will explore how the Sun's position and apparent motion vary seasonally and depend on the observer's latitude. You will be using the local sidereal time (LST; see the Timekeeping and Telescopes at the Detroit Observatory Activity) as an approximation of solar time. In the planetarium, the LST is determined by reading the RA on the equator that is crossing the meridian (see Figure 1). There are tick marks every 10 minutes, with longer marks for the hour and half hour.

The date is based on the Sun's position on the ecliptic. In the planetarium, the ecliptic is labeled with the calendar dates, but watch the direction: the Sun moves eastward through the stars! Note that the position of the Sun is only accurate to about 2 days (e.g., the computer may set the Sun's position for March 21, but the Sun may actually appear to sit on March 19.) When asked for the date, record the position of the Sun that you observe, but keep this inaccuracy in mind when doing the activity.

The cardinal directions (N, E, S, W) are azimuthal directions on the horizon, where the north and south cardinal points are defined by the intersection of the meridian with the horizon (Figure 1). East and west are defined to be 90 and 270 degrees clockwise on the horizon, when facing north, which is 0 degrees azimuth. When facing down toward the Earth, east is to the right of north. However, when facing the sky, east will appear to the left of north, instead of to the right!

Azimuth is measured in degrees from the north cardinal point on the horizon (0 degrees azimuth), toward east. It is represented by the horizontal arrow in Figure 1. The azimuthal direction can be given roughly, using the cardinal directions. For example, an object's azimuthal direction can be estimated as north-northeast (NNE), or west-southwest (WSW). In this activity, the azimuthal direction is used to determine rising and setting directions for celestial objects.

Altitude is measured in degrees above the horizon, and is represented by the vertical arrow in Figure 1. It is most easily measured when an object is on the meridian because the meridian is exactly perpendicular to the horizon. In the planetarium, it is conveniently marked in degrees. Please note: The wall in the planetarium cuts off the horizon 2 degrees above the true horizon.

Part 1: Navigating the Planetarium

The questions in this first part are meant to help you understand how to get the information you need for the rest of the activity. Please think about how you get the answers as you proceed.


  1. From what azimuthal direction is the Sun rising?

  2. What is the local sidereal time?

Local noon

  1. What is the date?

  2. Is the Sun above, below, or on the celestial equator? (circle one)

  3. Is the shown date the March equinox, June solstice, September equinox or December solstice? (circle one)  How do you know?

  4. What is the altitude of the Sun when it is on the meridian?

Once you know the correct answers and how to get them, fill in the appropriate row in Table 1.

Part 2: Ann Arbor

  1. Your GSI will show the Sun's motion on key seasonal dates. Use the same methods that you used in Part 1 to fill out the remaining rows in Table 1.
Table 1: Observing the Sun from Ann Arbor


Rise position (azimuthal direction)

Rise time


Altitude at noon

Set position (azimuthal direction)

Set time

Hours of daylight

March Equinox








June solstice








September Equinox








December solstice








  1. What season starts on each date in Table 1, in Ann Arbor?

Part 3: Other Latitudes

  1. The GSI will now present the sky from other latitudes at noon on the June solstice. Record the position at which you see the Sun at each location in Table 2.
Table 2: Observing the Sun on the June solstice.
Latitude Altitude at noon Azimuthal direction at sunrise Azimuthal direction at sunset
North Pole      
Arctic Circle      
Tropic of Cancer      


Tropic of Capricorn      
  1. What season starts on each date in Table 1, in Santiago, Chile?

Concluding Questions

Complete any sections of Table 1 that have not been filled in. Figures 2 and 3 in the Introduction may be helpful in answering some of the following questions.
  1. Reviewing your answers to Part 3, how does your latitude affect the observed maximum altitude of the Sun in the sky on the summer solstice? Be as specific as you can. Explain how this relates to the average temperatures at the equator and poles.

  2. Compare the number of daylight hours in Ann Arbor in summer and winter. Together with your answer to the previous question, explain how these factors are related to the average temperature in these seasons.

  3. If you are standing on the North Pole on the December solstice at noon, can you see the Sun? Explain.

  4. Which latitude has the least variation in the length of day and night, throughout the year: the equator, Tropic of Cancer, or arctic circle? Which has the most? Explain.

  5. Using Figure 3 in the Introduction, show how to find the latitudes of the arctic and antarctic circles, in degrees. Please copy the relevant parts of Figure 3 below and explain clearly, showing the results.

Last modified: 8/28/14 by SAM and MSO. Additional material from EMP

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