Name:__________________________________________ Class:_________________ Date:_______
Earth Science- Ms. Gill
Unit 2: Earth’s Dimensions
Do Now: Read the following article about Mt. Chimborazo, then answer the questions that follow.
Title: Mt. Chimborazo
Date: February 19, 2009
Photographer: Thomas McGuire
Summary Author: Thomas McGuire
There are several ways to measure a mountain’s height. While Mt. Everest, on the border of Nepal and China
(Tibet province), is the highest mountain in the world above sea level, it’s not the place on the Earth’s surface most
distant from the point at the very center of Earth. Due to Earth’s daily rotation on its axis, our planet bulges about
22 km (14 miles) at the Equator. As a result, the distance from the top of Mt. Chimborazo (in Ecuador) to the point
at Earth’s center is actually about 2 km greater than to the top of Mt. Everest. In fact, nearby tropical beaches
along the Pacific Ocean are actually farther from Earth’s center than is the top of Mt. Everest.
If Earth were a drop of liquid rotating once a day, its shape would be the same. That is, under the long-term
centrifugal forces, Earth takes the shape of a sphere slightly flattened at the poles. However, Earth is so close to
being a perfect sphere that it appears perfectly round from any point in space. Due to the combined effects of
Earth’s oblate shape and centrifugal force, a person who weighs 68 kg (150 lbs) at the North Pole would weigh
about half a pound less at the equator. But his or her mass wouldn’t change. This is one reason that scientists
generally measure matter by mass rather than by weight, which is dependent on the force of gravity. Furthermore,
although Earth has a mass of 6 septillion kg (13 septillion lbs), our planet is weightless in space.
1) A) Look at the satellite image of earth on the right.
Can you see Mt. Everest or Mt. Chimborazo?
Explain why earth is said to have a relatively smooth surface.
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B) Can you tell that earth is an oblate spheroid in this image?
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2) Draw an exaggerated picture in the box provided to illustrate
the earth’s shape as described in the underlined sentences above.
Label the equator, core and both mountains in your diagram.
Did you know that my students that score best on exams
are often one that draw diagrams to illustrate their
reading comprehension!
3) Where on Earth would someone weigh more, the poles or the equator? Explain.
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4) Which is the Earth more like a football or a ping pong ball? Explain.
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5) Mt. Chimborazo is taller than Mt. Everest. Accept or Reject. Provide your
evidence:_________________________________________________________________________
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The Size of the Earth:
Objective: Now that you have accepted the notion that Earth is a oblate sphere it is important that you
understand how you can calculate the circumference of the Earth!
Historic Background: Over 2000 years ago, Eratosthenes, the Chief Librarian in Syene, Egypt made a surprisingly
accurate measurement of the Polar Circumference of the Earth. It all started when he noticed that the sun does
not cast a noon time shadow from his flag pole once a year, on June 21st.
1) Think about it, where must the sun be located in the sky in order for it not to cast a shadow?
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Perplexed, Eratosthenes contacted his friend, Maximus, who lives in Alexandria on the Northern Coast of Egypt to
discuss this phenomenon. Maximus laughed at Eratosthenes “What are you talking about! Of course there is a Noon
time shadow, here, there always is!” Hmmm, thought Eratosthenes, “What could this mean? Is it possible that the
sun is so far away that the rays were essentially parallel, and thereby create different angles with the Earth’s
curved surface?”
2) Examine Diagram #1 below, is it possible that a pole in Alexandria could cast a shadow, while a pole in Syene
does not on the same day, June 21st? Explain:
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Diagram #2: Map of Egypt
Diagram #1:
‘
Syene
●
After much thought, Eratosthenes concluded that he could use the length of noon shadow on June 21st cast by a
flag pole in Alexandra to calculate the angle between the Sun’s ray and this flag pole (angle α). Using the laws of
trigonometry and the fact that the Sun’s rays directly line up with the flag pole in Syene, he figured out that this
angle α is equal to the interior angle between Syene and Alexandra (angle α’). Using the angle between the two
cities and the distance between them, he could easily calculate the circumference of the Earth, using simple
geometry. So he contacted Maximus again and asked him to measure the length of the Noon time shadow on June
21st in Alexandria.
3) Examine diagram #1 again, note the two angles labeled
α and α ’ are they equal? ___________
Explain:
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4) Suppose they are equal, how would that enable you to calculate the circumference of the earth? What
other information do you need?
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5) What could you measure that would enable you to get the degree value for angle “α”?
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6) Examine Diagram #2 the map of Egypt, using the scale on the map calculate the distance between
Alexandria and Syene in Kilometers : ________________________________
Explain how you got your answer:
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7) Looking at the scale on the map, what do you think is a common mistake that students make when reading a
scale?
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Maximus reports that the length of the shadow and using simple trigonometry, Eratosthenes calculates the angle
the sun’s ray’s make with the flag pole in Alexandria to be 5.4 degrees.
Since there are 360 degrees in a circle, we can set up a proportion to use the distance between Alexandra
and Syene and the angle created with the sun to calculate the circumference. Angle/ distance between cities
= 360° / circumference
Show Work Here:
7. Based on this information, what is the polar circumference of Earth?___________________________
Although we are very impressed with Eratosthenes’s calculation, we are still curious to see if the Equatorial
circumference of Earth is the same. To calculate this, we need to travel south to visit Gabon, an a country on the
equatorial west coast of Africa. We observed that high noon occurs at this location (on the equator) at 12:00 noon
Greenwich Mean Time (GMT). Next we call our friend that lives 1,669.83 km due East of Gabon in Kenya. Our
friend reports that it is 1:00 PM (GMT) in Kenya.
HINT: If a circle has 360°, and a day has 24 hours; how many degrees does the earth spin in an hour? ___
Hmmm, so if we know the degrees covered in hour, and we know the distance covered along the equator for
that amount of degrees, can we set up a proportion to figure out the distance covered in the 360 degrees
around the equator?
Show Work Here:
8. Based on this information, what is the Equatorial Circumference of Earth?_________________________
9. Degree of Flattening= (difference of polar & equatorial circumference) /equatorial radius x 100%
What is the degree of flattening?_______
(hint use your ESRT)
10. Is this a noticeable difference when looking at a satellite image of earth from space? Yes or No?
Closure activity:
Create three questions based on this activity that you think might appear on your test. Be sure to include the
answer:
1.
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Answer: ___________________________________________________________
2. ________________________________________________________________________________
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Answer: ___________________________________________________________
3. ________________________________________________________________________________
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Answer: ___________________________________________________________