Lab 4 Earth-Sun Relationships; Declination, Seasons, and Daylength

Use the analemma to determine the latitude of the zenith, to the nearest ½ degree (or 30

minutes), for the dates (below). Include the appropriate hemisphere.

For example: on October 20 the zenith is situated at 10° South latitude

1. November 10:

2. May 11:

3. March 21:

4. July 15:

Identify the (two) dates during the year that the zenith is situated over the each latitude,

below.

For example: at 16° South latitude the zenith (or 90°solar beam) occurs on November 7 and February 6.

5. 9° South latitude:

6. 20° South latitude:

7. 20° North latitude:

8. 7° North latitude

Find January 18th on the analemma and follow the vertical line up to the top of the graph;

the vertical line is labeled “10M” on the “Sun slow” side of the chart. This means that the

Sun will reach its “noon” zenith (with the solar beam directly overhead) at 12:10 P.M., or

10 minutes “late” due to the combined effects of eccentricity and solar vs. sidereal

rotation (as discussed earlier).

For each date, below, indicate if the noon Sun is fast or clow and provide the clock time

that the Sun will achieve zenith:

For example, on October 13 the zenith will be “fast” by 13 minutes and occur at 11:47 AM

(13 minutes before noon or 11:47 AM) so the answer for October 13 is: Sun Fast, 11:47 AM

9. March 8:

10. May 20:

11. October 21:

12. June 15:

The pertinence of the tangent rays is that, depending on the season, from the latitude of

the tangent ray to the pole (in one hemisphere) there will be 24 hours of daylight while in

the other hemisphere, from the tangent ray to the pole, there will be 24 hours of darkness

(see Figure 4, below).

Figure 4. Illustration showing parallel rays of incoming radiation and, due to Earth's axial

tilt and curvature, areas with 24 hours of daylight (66.5° South latitude to the South Pole)

and 24 hours of darkness (66.5° North latitude to the North Pole) during the December

Solstice.

For example, the analemma indicates that the latitude of the zenith (solar declination,

subsolar point or 90° solar beam) on August 2 is situated at 18° North latitude: 90 - 18 =

72

On August 2 the tangent rays are situated at 72° North latitude AND at 72° South

latitude.

From 72° North latitude to the North Pole, the Sun does not dip below the horizon ( with

24 hours of daylight) and from 72° South latitude to the South Pole, the Sun does not rise

above the horizon (with 24 hours of darkness).

Indicate the latitude of the tangent rays for the following declinations (zeniths):

13. 10° South latitude:

14. 23° 30’ North latitude:

15. 15° South latitude:

16. 6° North latitude:

Given the dates above (#s 13-16) indicate whether there will be 24 hours of daylight or 24

hours of darkness from the tangent ray to the pole for the Northern Hemisphere.

For example, if the zenith is situated over 18° North latitude and the tangent ray is

situated at 72° North latitude, there will be 24 hours of daylight from the tangent ray (at

72° North latitude) to the North Pole.

17. Given a zenith of 10° South latitude, the Northern Hemisphere tangent ray (from #13)

to the North Pole will experience 24 hours of daylight or darkness?

18. Given a zenith of 23° 30’ North latitude, the Northern Hemisphere tangent ray (from

#14) to the North Pole will experience 24 hours of daylight or darkness?

19. Given a zenith of 15° South latitude, the Northern Hemisphere tangent ray (from #15)

to the North Pole will experience 24 hours of daylight or darkness?

20. Given a zenith of 6° North latitude, the Northern Hemisphere tangent ray (from #16)

to the North Pole will experience 24 hours of daylight or darkness?

A relationship exists between the answers for 13-16 and 17-20 that can be useful in

determining whether there is 24 hours of daylight or darkness from the tangent ray to the

pole. This pattern can be identified by considering the answers to problems 21 and 22:

21. If the zenith is situated north of the Equator then, from the Northern Hemisphere

tangent ray to the North pole, there will be 24 hours of: daylight or darkness (select one).

22. And, if the zenith is situated south of the Equator then, from the Northern Hemisphere

tangent ray to the North pole, there will be 24 hours of: daylight or darkness (select one).

Daylength Hours

Because of Earth's axial tilt, the number of daylight hours, or the time between sunrise and

sunset, varies throughout the year. Interestingly, the daylight hours at a given latitiude in

one hemisphere are inversely proportional to the same latitude in the opposite

hemisphere.

Table 1 (below) provides sunrise and sunset times for given latitudes during the Winter

and Summer Solstices. Calculate the number of “daylength” ( hours & minutes) during the Winter and Summer Solstices at each latitude. Answers should include two duration times

(daylength during the Winter Solstice and daylength during the Summer Solstice) and the

sum of the daylength hours (at a given latitude for the Summer Solstice and Winter

Solstice) should equate to 24 hours. One way to accomplish this is to simply double the

afternoon hours & minutes for each latitude and solstice. This works because, given the

sunrise and sunset times on the table below, daylength hours are evenly split at noon

(which, considering an earlier portion of this lab, is typically not the case). Again, the sum

of daylight hours and minutes for the Winter and Summer Solstices (for a given latitude)

must equate to 24 hours.

Table 1. Daylength for selected latitudes in the Northern Hemisphere during the solsitces.

#s 23-26: Calculate the number of daylight hours and minutes during the Winter and Summer Solstices for each latitude in Table 1 (above).

Using information from Table 1 (above), calculate the number of daylight hours and

minutes for the latitudes and dates listed below. Assume 4 minutes of time change for each arc-degree of latitude. Pay attention to the hemisphere (and specific solstices).

For example: Using the completed table, calculate the daylength hours & minutes for

Eugene, Oregon (44° N) on June 21.

If June Solstice daylength hours at 40° N are 9 hours, 8 minutes, and we assume 4 minutes

for each are-degree of latitude, then 4 (degrees) x 4 (minutes) = 16 minute difference

between 40° N and 44° N. And, because daylength increases poleward during northern

hemisphere June Solstice, we add the 16 mintues to hours and minutes to the daylength at

40° N.

Answer: Eugene will experience 9 hours, 24 minutes of daylight during the June Solstice.

27. Dawson, Yukon Territory, Canada (64° N) on Dec 21:

28. Adelaide, South Australia (35° S) on June 21:

29. Bangkok, Thailand (14° N) on March 22:

30. DVC (37°N) on June 21: