Geometry Of The Earth

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| By Jjnevinski

Jjnevinski

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Questions: 5 | Attempts: 219 | Updated: Mar 20, 2023

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Geometry of the Earth Long before Columbus, a Greek scholar names Eratosthenes (274-194BC) calculated the circumference of Earth by making some simple observations about shadows at noon and applying some insights from geometry.

The size of Earth has been estimated and measured many time since then. The French Academy of Sciences tried to make an accurate measurement in the late 1700s in order to create a new unit of measure, the meter. They proposed to define the meter as one ten-millionth of the distance from the North Pole to the equator.

Today we can measure Earth's circumference very accurately using Read moredata from satellites and making calculations on computers. The circumference at the equator is 24,901.55 miles. Earth is not a perfect sphere, however, because its rotation causes it to bulge a little at the equator. So the circumference from pole to pole is a bit smaller, about 24,859.82 miles.

Questions and Answers

1.

How many centuries before the French Academy of Sciences measured the circumference of Earth did Eratosthenes live?
- A.
  
  22 centuries
- B.
  
  20 centuries
- C.
  
  18 centuries
- D.
  
  16 centuries
Correct Answer
B. 20 centuries

Explanation
Late 1700s means about 1800. Eratosthenes lives about 200 BC or -200.
1800 - -200 = 2000 or 20 centuries.

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2.

How much greater is the circumference of Earth at the equator than the circumference at the poles?
- A.
  
  About 20 miles
- B.
  
  About 40 miles
- C.
  
  About 80 miles
- D.
  
  About 200 miles
Correct Answer
B. About 40 miles

Explanation
24,901.55 - 24,859.82 = 41.73 or about 40 miles.

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3.

Earth is divided into 24 time zones. About how wide is each time zone at the equator?
- A.
  
  1031 miles
- B.
  
  1036 miles
- C.
  
  1038 miles
- D.
  
  1042 miles
Correct Answer
C. 1038 miles

Explanation
24,901.55/24 = 1037.56 or 1038 miles.

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4.

Which is the best estimate of the diamter of Earth from pole to pole?
- A.
  
  3960 miles
- B.
  
  4530 miles
- C.
  
  6300 miles
- D.
  
  7920 miles
Correct Answer
D. 7920 miles

Explanation
Circumference = 3.14xDiameter. So Diamter = Circumference/3.14. 24,859.82/3.14 = 7917.14 miles or 7920 miles.

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5.

A geostationary satellite move in an orbit 22,300 miles above the equator. The satellite moves at a rate such that it stays at the same point about the Earth as Earth rotates on its axis. What is the appoximate speed of the satellite?
- A.
  
  700 miles per hour
- B.
  
  7000 miles per hour
- C.
  
  10,000 miles per hour
- D.
  
  14,000 miles per hour
Correct Answer
B. 7000 miles per hour

Explanation
We can calculate the radius of Earth by dividing the circumference at the equator by 2 & 3.14. 24,901.55/2 = 12,450/ 3.14 = 3965 miles. If we add the distance the satellite is from the equator, we will determine the radius of the satellite: 3965 + 22,300 = 26,255 miles. We can then calculate the circumference of the satellite by multiplying its radius by 2 and 3.14: 26265 * 2 = 52,530 * 3.14 = 164,944 miles. Finally, since this is the distance the satellite travels around (by perspective) in 24 horus, we can determine the speed by dividing by 24: 164,944/24 = 6873 miles per hour or about 7000 miles per hour.

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Geometry Of The Earth

How many centuries before the French Academy of Sciences measured the circumference of Earth did Eratosthenes live?

How much greater is the circumference of Earth at the equator than the circumference at the poles?

Earth is divided into 24 time zones. About how wide is each time zone at the equator?

Which is the best estimate of the diamter of Earth from pole to pole?

A geostationary satellite move in an orbit 22,300 miles above the equator. The satellite moves at a rate such that it stays at the same point about the Earth as Earth rotates on its axis. What is the appoximate speed of the satellite?