Time and the SunEarth Science B

Name: ______________________Date: _______________________

The altitude of any object in the sky is its vertical angle above the horizon. We consider the horizon to be 0°, and the zenith, the point in the sky straight overhead, to be 90°. An outstretched fist is about 10° in apparent diameter, so nine fists should measure the angle between horizon and zenith.

In Figure 1, the sky resembles a dome under which an observer is positioned. The zenith is directly overhead. The height in degrees of the north celestial pole equals the observer’s location. The meridian is the line extending from south, through the zenith, to the north point on the horizon.

The sun’s altitude varies throughout the day, reaching its highest altitude around noon (Figure 1, directly on the meridian). However, the sun is rarely exactly south when a wall clock says noon. Clock time is known as average solar time, and it forms an approximation of time by the sun which is known as apparent solar time. Solar time is either ahead of or behind clock time depending on the season of the year. The difference between solar time and clock time is known as the equation of time. A graph of the equation of time is displays the classical figure-8 shape known as the analemma. The analemma has been photographed (Figure 2):

The height of the sun at solar noon appears to shift with the seasons. The sun will appear highest when it is positioned directly overhead at the Tropic of Cancer, located at 23.5° N compared to the equator. The sun will appear lowest when it is positioned directly overhead at the Tropic of Capricorn, located 23.5° S compared to the equator. The sun appears at its middle height when positioned directly overhead at the equator.

Figure 2: The first analemma photo, taken by Dennis DiCicco from 1978 to 1979, using one piece of film

In this lab, you will prepare a graph of the analemma using our latitude and the latitudes of other locations where the sun is directly overhead.

1. Our latitude can be determined by the altitude of the North Star (Polaris) on a clear night. Record you location and latitude below:

Location: ____________________

Latitude: ____________________

2. You will use your latitude, which you recorded above, to complete the table in Figure 3. The second column of Figure 3 shows the latitude on earth where the sun is directly overhead (altitude 90°) at solar noon on each date. To complete the third column, you need to determine how far away you are (in degrees of latitude) from each location. For locations south of the equator, this means adding that latitude to your latitude; for locations north of the equator, this means subtracting that latitude from your latitude.

Example: For Jan 10: If you are 40° N of the equator, you are 40° + 22.1°, or 62.1° from the location where the sun is overhead.

Use your latitude to complete column 3 of Figure 3.

3. Now you will determine the altitude of the sun for each of the dates listed in Figure 3. Your distance in latitude from the latitude where the sun is overhead is the same as the difference between the local height of the sun and the zenith (90°). To obtain the sun’s local altitude, subtract the values in column 3 from 90.

Example: For Jan 10: If you are 40° N and are 62.1° from the latitude where the sun is overhead, the local altitude of the sun is 90° – 62.1° or 27.9°.

Complete column 4 of Figure 3 using the above directions.

Figure 1

Figure 3:

DateLatitude where Sun is Overhead at Solar

Noon

Your Distance from Latitude in Column 2

Altitude of Sun at Solar Noon at Your

Latitude

Clock Time at Solar Noon (h)

10-Jan 22.1° S 64.1° 25.9° 12:07

20-Jan 20.3° S 12:11

30-Jan 17.9° S 12:13

10-Feb 14.6° S 12:14

20-Feb 11.2° S 12:14

5-Mar 6.4° S 12:12

10-Mar 4.4° S 12:11

20-Mar 0.5° S 12:08

30-Mar 3.4 N 12:05

10-Apr 7.6° N 12:02

20-Apr 11.2° N 11:59

30-Apr 14.5° N 11:57

10-May 17.4° N 11:56

20-May 19.8° N 11:56

30-May 21.6° N 11:57

10-Jun 22.9° N 11:59

20-Jun 23.4° N 12:01

30-Jun 23.2° N 12:04

10-Jul 22.3° N 12:05

20-Jul 20.8° N 12:06

30-Jul 18.7° N 12:06

10-Aug 15.8° N 12:05

20-Aug 12.7° N 12:04

30-Aug 9.3° N 12:01

10-Sep 5.3° N 11:57

20-Sep 1.4° N 11:54

30-Sep 2.5° S 11:50

10-Oct 6.3° S 11:47

20-Oct 10° S 11:45

30-Oct 13.5° S 11:44

10-Nov 16.9° S 11:44

20-Nov 19.5° S 11:46

30-Nov 21.5° S 11:49

10-Dec 22.8° S 11:53

20-Dec 23.4° S 11:57

30-Dec 23.2° S 12:02Shaded: Label the 20th of each month on your graph (but plot all values)

4. You now have complete data to graph an analemma for your latitude. Set up your graph with Clock Time at Solar Noon along the horizontal axis, and the Sun’s Altitude at Solar Noon along the vertical axis. Notice that the vertical axis is unlabeled. The values you use depend upon your data. To figure out the values you should use, find the highest and lowest altitudes for the sun in your table (column 4). Make the lowest value on your graph the closest even multiple of 10 that is below your lowest value. In a similar manner, select the next even multiple of 10 above your highest altitude value. Your finished vertical axis will read 10, 20, 30, and so on, or 20, 30, 40, and so on, or 30, 40, 50, and so on, depending on your original latitude. Each square represents 2°. Label your vertical axis according to the above directions.

For the horizontal axis, begin with noon in the center, and number before and after noon accordingly. Each square represents 2 minutes. Label your horizontal axis.

5. For each date, graph the clock time of solar noon (column 5) against the altitude of the sun at solar noon (column 4). Label the points that represent the 20th of each month with the date. When you are finished, connect the points by order of date.

6. When you finish the lab, answer the questions below:

Questions:

1. Fill in the table: On your graph, find the maximum and minimum altitudes of the sun. Determine the dates that each occurred, the latitudes where the sun was overhead, the approximate season, and the closest Tropic (Cancer or Capricorn):

Maximum Altitude Minimum AltitudeAltitude Value

Date Occurred

Latitude Overhead

Approximate Season

Tropic

2. Using your data, find the altitudes and dates when the sun is overhead closest to the equator at solar noon. Name the season that begins close to each of these dates.

Nearest Equator Nearest EquatorAltitude Value

Date Occurred

Approximate Season

3. During which seasons is apparent solar time ahead of clock time?

4. During which seasons is apparent solar time behind clock time?

5. Explain how the analemma photo was taken.

Analemma on Mars: Other planets can create analemma patterns. If you lived on Mars, you could observe the sun forming a teardrop pattern throughout a Martian year. An analemma pattern results from a planets tilt and the eccentricity of its orbit, or how non-circular its orbit is. A planet with no tilt would display no seasonal variation in the height of the sun. A planet with a circular orbit would produce no equation of time, or no difference between average time and solar (sundial) time.” Examine the Mars analemma diagram to answer the following:

6. In the Mars Analemma diagram, each dot represents 10 Martian days or “sols.” How many sols are in a Martian year?

7. Use the solar declination scale to determine the approximate tilt of the Martian axis.

8. At what Martian latitudes would its “tropics” be located?

9. If the amount of the equation of time is related to how elliptical a planetary orbit is, than which planet, Mars or Earth, has the most elliptical orbit? Use each equation of time to explain your answer.

10. Mercury has 0° tilt and a highly elliptical orbit. Describe the appearance of an analemma on Mercury.

The Analemma for _______° N

Noon

Clock Time at Solar Noon

Sun’s Altitude at Solar Noon (degrees)