Reddin's change theory

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LAB MODULE 3: EARTH SUN RELATIONSHIP

Note: Please refer to the GETTING STARTED lab module to learn tips on how to set

up and maneuver through the Google Earth ( ) component of this lab.

KEY TERMS

The following is a list of important words and concepts used in this lab module:

Analemma Equation of time Solstice

Aphelion Equinox Sphericity

Axial parallelism Insolation Subsolar point

Axial Tilt International Date Line Sun Angle

Circle of illumination NDVI Sun-fast, Sun-slow

Coordinated Universal Time (UTC) Perihelion Time zones

Daylight saving time Revolution

Declination of Sun Rotation

LAB MODULE LEARNING OBJECTIVES

After successfully completing this lab module, you should be able to:

● Compute differences in time between two location

● Recognize and demonstrate how time zones work

● Differentiate the changes in the circle of illumination over the course of a

year

● Identify and describe the reasons for the seasons

● Infer vegetation as an indicator for seasonality

● Read and interpret an analemma

● Calculate the Sun’s declination for a given location and date

● Compute the equation of time for a given location

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INTRODUCTION

This lab module examines fundamental Earth-Sun relationships. Topics include time

zones, the equation of time, analemma, declination, solstice and equinox, the

reasons for seasons, and the seasonal migration of the subsolar point. While these

topics may seem disparate, you will learn how they are inherently related.

The modules start with four opening topics, or vignettes, found in the

accompanying Google Earth file. These vignettes introduce basic concepts related to

Earth-Sun relationships. Some of the vignettes have animations, videos, or short

articles that will provide another perspective or visual explanation for the topic at

hand. After reading each vignette and associated links, answer the following

questions. Please note that some components of this lab may take a while to

download or open, especially if you have a slow internet connection.

Expand EARTH-SUN RELATIONSHIPS, and then expand the INTRODUCTION

folder. Double click Topic 1: Earth-Sun Relations.

Read Topic 1: Earth-Sun Relations.

Question 1: Looking at the maps, which of the following best showcases the

uneven balance of insolation – and resulting seasonality - on planet Earth?

A. Most of the northern hemisphere is free of ice and snow year round

B. Most of the northern hemisphere is covered in ice and snow year round

C. Most of the northern hemisphere shows ice and snow advancing in the

July

D. Most of the northern hemisphere shows ice and snow retreating in July

Read Topic 2: Reason for Seasons. (Note: If you are having issues watching

the animation, please check to see if the movie has been downloaded rather than

automatically playing via the webpage)

Question 2: Why does each hemisphere receive the same amount of energy

from the Sun on the March and September equinoxes?

E. The subsolar point is aligned with the Tropic of Cancer

F. The subsolar point is aligned with the Tropic of Capricorn

G. The subsolar point is aligned with the Equator

H. The subsolar point is aligned with the North Pole

Read Topic 3: Time Zones.

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Question 3: What was the main reason for instituting standard time (time

zones)?

A. To end confusion in communities using their own solar time

B. To help astrologers forecast urban growth patterns

C. To reaffirm England’s world dominance

D. To validate the Meridian Conference of 1884

Read Topic 4: Human Interactions.

Question 4: Name 3 reasons ancient cultures used stone structures or

modified natural formations regarding Earth-Sun or Earth-Moon relationships.

A. To chart seasons, create calendars, and celebrate birthdays

B. To monitor eclipses, mark deaths, denote holidays

C. To chart seasons, monitor eclipses and create calendars

D. To celebrate birthdays, mark deaths and denote the end of days

Collapse and uncheck the INTRODUCTION folder.

GLOBAL PERSPECTIVE

I. Coordinated Universal Time (UTC)

The Earth is divided into 24 time zones, one for each hour of the day. Earth’s 24

time zones are approximately 15° wide – a width calculated from the number of

degrees in a sphere divided by the number of hours in a day (360°/24hr =

15°/hour). Noon (12pm) occurs roughly when the Sun is at its highest point in the

sky each day. For example, noon in New York is three hours before noon in Los

Angeles because there is (approximately) a three hour difference in when the Sun

is at its zenith.

Expand the GLOBAL PERSPECTIVE folder and then expand and select the

Universal Time Coordinated folder.

Time zones are as much a Sun-Earth relationship as they are a human construct

used to standardize time. The Prime Meridian - which signifies 0 degrees latitude

and passes through Greenwich, England - is the starting reference line for time

zonation. Time zones are relative to Greenwich Mean Time (GMT) or more

appropriately, the Coordinated Universal Time (UTC). Examples are New York City,

USA in the winter at UTC -5 (or 5 hours behind UTC), or Manila, Philippines at

UTC+8 (or 8 hours ahead of UTC). In other words, when it is 8am in New York, it is

9pm in Manila.

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As you can see in Google Earth, time zones do not always follow straight lines from

pole to pole because of political, economic, or geographic reasons. Time zone

anomalies include the following:

Time Zone Anomaly Example

Time zone extends far greater or lesser

than 15 degrees.

China is one time zone.

Time zones shifts significantly eastward

or westward.

Iceland shifts 2 time zones to be UTC 0.

Time zone does not follow the 1-hour

system. Instead, a partial time-zone unit

is used.

Newfoundland, Canada is 3:30 UTC

(summer 2:30 UTC), while Nepal is 5:45

UTC

Double-click São Paulo, Brazil. You might have to pan northward to find the

time zone label near the Equator.

Question 5: In what UTC time zone is this city located?

A. UTC -2

B. UTC -3

C. UTC +2

D. UTC+3

Question 6: If UTC 0 time is 1pm, what is the standard time for this city?

A. 10 AM

B. 11 AM

C. 3 PM

D. 4 PM

Double-click Cape Town, RSA. You might have to pan northward to find the

time zone label near the Equator.

Question 7: In what UTC time zone is this city located?

A. UTC -1

B. UTC -2

C. UTC +1

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D. UTC+2

Question 8: If UTC 0 time is 1pm, what is the standard time for this city?

A. 11 AM

B. 12 PM (NOON)

C. 2 PM

D. 3 PM

Double-click Kuala Lumpur, Malaysia. You might have to pan northward to

find the time zone label near the Equator.

Question 9: Which of the following best describes the time zone anomaly

affecting this city and country?

A. Time zone extends far greater or lesser than 15 degrees

B. Time zone shifts significantly eastward or westward

C. Time zone does not follow the standard 1 hour system

D. There is no time zone for the given location

Question 10: What is the primary reason for this time zone anomaly?

A. Political boundaries of Malaysia

B. Economic trade for Southeast Asia

C. Railway schedules

D. International law

Question 11: In what UTC time zone is this city located?

A. UTC-7

B. UTC-8

C. UTC +7

D. UTC +8

Question 12: If UTC 0 time is 1pm, what is the standard time for this city?

A. 8 PM

B. 9 PM

C. 5 AM

D. 6 AM

Double-click, and select, Pitcairn Islands

Question 13: Which of the following best describes the time zone anomaly

affecting these islands?

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A. Time zone extends far greater or lesser than 15 degrees

B. Time zone shifts significantly eastward or westward

C. Time zone does not follow the standard 1 hour system

D. There is no time zone for the given location

Question 14: What is the primary reason for this time zone anomaly?

A. Geographic location of the islands

B. Economic trade for the islands

C. International law

D. Strict moral code

Question 15: In what UTC time zone are these islands located?

A. UTC -6

B. UTC -8.5

C. UTC +6

D. UTC +8.5

Question 16: If UTC 0 time is 1pm, what is the standard time for these

islands?

A. 4:30 PM

B. 9:30 PM

C. 4:30 AM

D. 9:30 AM

Collapse and uncheck the Universal Time Coordinated folder.

II. Daylight Savings

Double-click, and select, Daylight Saving Time

Many regions in the world have adopted daylight saving time (DST), or the

advancing of UTC time for a given location. This is especially true for North America

and Europe. As an example, New York, New York moves from Eastern Standard

Time (EST) to Eastern Daylight Time (EDT) between the months of March and

November. The standard time during daylight saving time is adjusted from UTC -5

(EST) to UTC -4 (EDT).

Question 17: If it is 12 PM (noon) in Manila, Philippines (UTC +8), what is

the time during EDT in New York (UTC -4)?

A. 12 AM

B. 4 PM

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C. 8 PM

D. 8 AM

III. International Date Line

Double-click the International Date Line folder and then check the IDL folder.

The International Date Line (IDL) is an imaginary line that runs from pole to pole on

more or less the 180°E/W longitude. Notable exceptions to this occur from 50°N to

75°N and from the Equator to 50°S.

If you cross the IDL traveling westwardly (from east to west), you need to add a

day to your time. In other words, a Thursday becomes a Friday. If you cross the

IDL traveling eastwardly (from west to east), you would subtract a day. For

example, a Friday becomes a Thursday. To think of it another way, the Earth

“starts” the day (12:01 am) on the west side of the IDL, and takes a full 24 hours

for 12:01 am to reach the east side of the IDL.

Double-click and select IDL North.

Question 18: Why does the IDL deviate from 180° E/W in this location?

A. To account for the faster rotational speed toward the North Pole

B. The IDL is following the 180° E/W meridian – there is no deviation in this

location

C. To follow the bathymetry of the ocean in this location

D. To have the islands of Alaska in the same time zone as the rest of Alaska

Double-click and select IDL South.

Question 19: Why does the IDL deviate from 180° E/W in this location?

A. To account for the faster rotational speed toward the Equator

B. To follow the bathymetry of the ocean in this location

C. To have the islands of Kiribati in the same time zone.

D. To separate the islands countries on the west side of the IDL from the

island countries located east of 180° E/W

Collapse and uncheck the GLOBAL PERSPECTIVE folder.

REASONS FOR SEASONS

There are five distinct reasons for the seasons – tilt (at 23.5 degrees), revolution

(around the Sun), rotation (every 24 hours), axial parallelism (fixed alignment

during revolution around Sun), and sphericity (the Earth’s shape). These five

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reasons account for the four divisions of the year - spring, summer, autumn (fall),

and winter – commonly marked by distinct weather patterns, temperatures

fluctuations, vegetation greeness and so on. The degree of these seasonal change

becomes more apparent as you move away from the Equator (as seasonality in

tropical regions is minimal).

In this section, we will examine three of the five reasons for the seasons – axial tilt,

revolution, and rotation.

I. Axial Tilt

Because of the tilt of the Earth, the amount of energy Earth receives from the Sun

is dependent on location and time of year. On the equinoxes (March 20 and

September 22 or 23), the Sun is directly overhead (the sub-solar point) and all

areas on Earth receive the same 12 hours of solar energy (sunlight). On the

solstices (June 20 or 21 and December 21 or 22), the subsolar point is on the tropic

of cancer (23.5 degrees North) or the tropic of capricorn (23.5 degrees South),

resulting in the most unequal distribution of solar energy on Earth.

Expand and select the REASONS FOR SEASONS folder. Double-click

Overview and then read the text and watch the animation.

Question 20: What is the relationship between the seasons and the position

of the sub-solar point?

A. The sub-solar point is furthest north during the spring equinox

B. The sub-solar point is furthest north during the autumn equinox

C. The sub-solar point is furthest north in summer (June) solstice

D. The sub-solar point is furthest north in winter (December) solstice

Question 21: Explain how Earth’s seasons would be if the Earth did not tilt

on its axis.

A. Annually, there would be more than four seasons

B. Annually, there would be no more seasons

C. Annually, there would be one dry season and one wet season

D. Annually, there would one “hot” season on Earth

II. Revolution

It takes 365.24 days for the Earth to complete one revolution around the Sun. And

although the Earth’s orbit is elliptical , the variation in distance between the Earth’s

orbit nearest to the Sum (perihelion) or farthest from the Sun (alphelion) is not

great enough to account for the seasons.

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Question 22: Assume the Earth was tilted and rotated, but did not revolve

around the Sun. How would this influence the location of sub-solar point over

a given year?

A. The sub-solar point would not move

B. The sub-solar point would move daily instead of annually

C. The sub-solar point would move between the tropics just like it does

today

D. There would be no sub-solar point

III. Rotation

Earth completes one rotation approximately every 24 hours. This rotation is what

gives us days and nights.

Double-click Circle of Illumination. This figure shows the circle of illumination,

or the day-night line, for June 21.

At 9:00pm EST in New York, South America is in darkness, while North America is

still in day light. If we fast forward 2 hours to 11pm EDT in New York, the circle of

illumination has moved westward. Indeed, the Earth’s rotation helps ensure the

Sun’s energy is spread over the Earth’s surface.

Question 23: Assume the Earth was tilted and revolved, but did not rotate.

What would the seasons be like if the Earth did not rotate?

A. No change to the current seasons/seasonality on Earth

B. There would be one season on Earth

C. There would a constant summer-type season on one side of Earth and a

constant winter-type season on the other side of Earth.

D. Earth would experience a summer-type season (with sunlight) for about 6

months and a winter-type season (with no light) for about 6 months

Click Back to Google Earth, which is located in the top-left corner in the

Google 3D viewer.

We are now going to go through one rotation on Earth.

Zoom out as far as you can until the Earth is as small as Google Earth allows.

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Click Show sunlight acrosss the landscape ( ). A time stamp displays at

the top of the slide bar. (Note: Verify that the Historical Imagery is off

because it can hide the Show sunlight acrosss the landscape slide bar).

Using your mouse, place the cursor on the Earth and move it around until the

Sun is behind the Earth. Then, set North in the default position (press N).

Question 24: How does the circle of illumination look to the portion of the

Earth currently facing you?

A. The portion of the globe facing me is illuminated

B. The portion of the globe facing me is not illuminated (shadowed)

C. The western portion of the globe facing me is illuminated

D. The eastern portion of the globe facing me is illuminated

Move the slide bar slowly over the next 24 hours.

Question 25: What is the direction of Earth’s circle of illumination?

A. Predominately westward (right to left)

B. Predominately eastward (left to right)

C. Predominately northward (bottom to top)

D. Predominately southward (top to bottom)

Turn off Show sunlight acrosss the landscape ( ).

Collapse and uncheck the REASON FOR SEASONS folder.

NDVI

Expand the NDVI folder.

This folder contains a series of images showing Normalized Difference Vegetation

Index (NDVI) for the year 2011. NDVI is a relatively simple way of displaying where

vegetation is most green, which means that the vegetation is alive and producing

greenness from its leaves and other plant parts. In general, the darker the green is

for a given area, the more vegetation cover and/or growth exists for that area.

In this section you will be looking at three locations – Africa, North America, and

Southeast Asia. To start, let’s go to North America in January.

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Double-click North America.

Remember that in the Northern hemisphere, the Sun is lower in the sky in January,

and thereby receives less direct sunlight (solar energy). As a result, the green

appears absent at higher latitudes.

Systematically click through the months (January through December) and note

the green areas in North America. (Note: The images might take some time to

load; as a hint, cycle through the months individually rather than checking all of

them at one time).

Question 26: Which of the followings months is the majority of North

America dark green?

A. January

B. April

C. July

D. October

Question 27: How does this month (you selected in Question 25)

correspond to the sub-solar point of the Sun?

A. The sub-solar point near the equator

B. The sub-solar point near its most northern position

C. The sub-solar point near its most southern position

D. The position of the sub-solar point does not matter

Double-click and select Africa.

Systematically click through the NDVI months (January through December) and

note the green areas in Africa.

Question 28: In which of the following month is the large green

(vegetation) area reach furthest South?

E. January

F. April

G. July

H. October

Question 29: How does the northernmost point correspond to the sub-solar

point of the Sun?

A. The sub-solar point is over the equator

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B. The sub-solar point is at its most northern position

C. The sub-solar point is at its most southern position

D. The position of the sub-solar point does not matter

Double-click and select Borneo.

This is the island of Borneo (center) and the surrounding islands that make up the

Philippines (to the north) and Indonesia (to the south) in Southeast Asia. The island

of Borneo straddles the Equator.

Systematically click through the NDVI months (January through December) and

note the green areas in Borneo.

Question 30: What is the overall trend in NDVI for the year?

A. The NDVI is distinctively lower in March

B. The NDVI is distinctively higher in September

C. The NDVI varies little over the entire year

D. The NDVI is distinctively lower in December

Question 31: With respect to Sun angle, why do we see such an NDVI trend

for the island of Borneo? (Choose the one that is incorrect)

A. There is little variation in Sun angle because Borneo is at the equator

B. Borneo basically receives the same amount of solar radiation year round

C. Borneo receives rainfall throughout the year

D. Few, if any clouds, obscure the Sun from Borneo year round

Collapse and uncheck the NDVI folder.

ANALEMMA

An analemma is a chart that you use to track the Sun’s declination and to

determine the equation of time. The Sun’s declination is the latitude of the Sun’s

solar point for a given date. The Sun’s solar point is the where the Sun is directly

overhead (90°) at mean solar time.

The Earth’s orbit is elliptical and, as a result, revolves around the Sun at varying

speeds depending on the time of year. In June and July, the Earth revolves slower,

compared to December and January. Hence, as the speed of revolution varies, we

need the equation of time to determine the difference between observed solar time

(the time when the Sun is at its highest point in the sky for your location) and

actual time:

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● If the Sun is at its highest point before noon (12:00pm), then the time is

said to be Sun-fast.

● If the Sun is at its highest point after 12:00pm, time is said to be Sun-slow.

An analemma will tell us how fast (or slow) the Sun is relative to noon.

Expand the Analemma folder and then click Introduction to view the

introduction animation.

I. Sun Angle

Expand Sun Angle.

Assume we are in Atlanta, Georgia, USA (33.95°N, 83.32°W). This city is in the

Northern hemisphere. It also implements daylight saving time, so “noon” is

technically at 1pm. Using the example in the animation, we can read the graph to

determine the Sun’s declination on August 1 is 18°N. In other words, the Sun is

directly overhead (Sun’s solar point) at 18°N. However, we are not located at 18°N

but farther north at ~34°N. This means that the Sun is not directly overhead but at

an angle, known also as an altitude angle or solar elevation angle. So what is the

Sun’s altitude angle at its highest point in Atlanta, Georgia (~34°N) on August 1?

To answer this question we can use the following equation:

Altitude Angle = 90° - latitude ± declination

When our location and the Sun’s declination are in the same hemisphere (North or

South), we add the declination value in the equation. When they are in opposite

hemispheres, we subtract the declination value. In our example then, we are in the

same hemisphere, so we add. We know our latitude is 34 degrees and the

declination is 18 degrees, so answer is:

Altitude Angle = 90° - 34° +18° = 74°

Altitude Angle = 74°

So, on August 1 in Atlanta, Georgia, the Sun angle at its highest point would be

74°.

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Suppose we were in Cape Town, South Africa (33.92°S, 18.45°E) on August 1.

Rounding the latitude to 34°S, what is the Sun angle at noon?

Altitude Angle = 90° - 34° - 18°

Altitude Angle = 38°

As we can see, the Sun’s altitude angle on August 1 at noon is much lower in Cape

Town, South Africa than in Atlanta, USA.

Using this equation, answer the following questions.

Double-click and select Location A.

Question 32: What is the latitude (degrees only) for Location A?

A. 0°E

B. 0°S

C. 78°W

D. 78°N

Question 33: What is the Sun’s altitude angle for Location A on September

21?

Altitude Angle = 90° - latitude ± declination =

A. 90° - 0 – 0 = 90°

B. 90° - 90 + 0 = 0°

C. 90 – 78 – 0 = 12°

D. 90 +78 – 0 = 168°

Double-click and select Location B.

Question 34: What is the latitude (degrees only) for Location B?

A. 68°E

B. 68°N

C. 133°W

D. 113°N

Question 35: What is the Sun’s altitude angle for Location B on December

21?

Sun Altitude Angle = 90° - latitude ± declination =

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A. 90° - 68 – 22 = 0°

B. 90° - 68 + 22 = 44°

C. 133 - 90 - 22 = 21°

D. 113 - 90 -22 = 41°

II. Equation of Time

In addition to determining the Sun’s altitude angle of a given latitude, we can use

the analemma to determine the time at which the Sun is directly overhead for a

given date.

Click Equation of Time and view the animation.

On May 1, the equation of time is 3 minutes Sun–fast, meaning the Sun reaches its

highest point 3 minutes before noon (11:57 AM).

Question 36: Is the equation of time Sun-fast or Sun-slow on the March

equinox? By how many minutes?

A. Sun-fast by 4 minutes

B. Sun-fast by 12 minutes

C. Sun-slow by 8 minutes

D. Sun-slow by 0 minutes

Question 37: What time does the Sun reach its highest point on November

25?

A. 12:00 + 16 minutes = 12:16 PM

B. 12:00 - 13 minutes = 11:47 AM

C. 12:00 - 16 minutes = 11:44 PM

D. 12:00 + 13 minutes = 12:13 PM

Question 38: What time does the Sun reach its highest point on June 15?

E. 12:00 + 0 minutes = 12:00 PM

F. 12:00 + 4 minutes = 11:56 AM

G. 12:00 - 4 minutes = 11:56 PM

H. 12:00 + 12 minutes = 12:12 PM

Collapse and uncheck the Analemma folder. You have completed Lab Module 3.