Whether the new measurements lead to more accurate calculation if Erathosthenes had measured the difference in the angles of the noonday sun between Syene and Alexandria to be 10 degrees instead of 7 degrees with reference to Figure 21.3 in the textbook.

Question

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Answer 1

Question

Chapter 21, Problem 1GST

a)

To determine

Whether the new measurements lead to more accurate calculation if Erathosthenes had measured the difference in the angles of the noonday sun between Syene and Alexandria to be 10 degrees instead of 7 degrees with reference to Figure 21.3 in the textbook.

a)

Expert Solution

Answer to Problem 1GST

Although Erathosthenes measured the difference in the angles of the noonday sun between Syene and Alexandria to be 10 degrees instead of 7 degrees that would not be an accurate calculation.

Explanation of Solution

Erasthosthenes (276-194 B.C.E) is the one who successfully attempted to establish the size of the Earth. His calculations were very close to the modern values.

Erasthosthenes calculated the angles of the noon day sun at two different Egyptian cities, namely Syene and Alexandria. They were roughly north and south of each other. He identified that the difference between the two angles is 7 degrees or 1/50 of a circle.

Therefore, he described the circumference of the Earth would be 50 times the distance between the two cities. He calculated the Earth’s circumference as 39,400 kilometers and the modern value of circumference is 40,075 kilometers.

b)

To determine

Whether the new measurements lead to an estimate for the circumference of the Earth that is larger or smaller than the original Erathosthenes’ estimates.

b)

Expert Solution

Answer to Problem 1GST

As the angle increases to 10 degrees, it is 1/36 of a circle. Hence, the circumference of the Earth would be 36 times the distance between the two cities. Thus, the new measurements lead to an estimate for the circumference of the Earth, which is smaller than the original Erathosthenes’ estimates.

Explanation of Solution

Erasthosthenes calculated the angles of the noon day sun at two different Egyptian cities, namely Syene and Alexandria. They were roughly north and south of each other. He identified that the difference between the two angles is 7 degrees or 1/50 of a circle.

Therefore, he described that the circumference of the Earth would be 50 times the distance between the two cities. He calculated the Earth’s circumference as 39,400 kilometers and the modern value of circumference is 40,075 kilometers.

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Answer 2

Question

Chapter 21, Problem 1GST

a)

To determine

Whether the new measurements lead to more accurate calculation if Erathosthenes had measured the difference in the angles of the noonday sun between Syene and Alexandria to be 10 degrees instead of 7 degrees with reference to Figure 21.3 in the textbook.

a)

Expert Solution

Answer to Problem 1GST

Although Erathosthenes measured the difference in the angles of the noonday sun between Syene and Alexandria to be 10 degrees instead of 7 degrees that would not be an accurate calculation.

Explanation of Solution

Erasthosthenes (276-194 B.C.E) is the one who successfully attempted to establish the size of the Earth. His calculations were very close to the modern values.

Erasthosthenes calculated the angles of the noon day sun at two different Egyptian cities, namely Syene and Alexandria. They were roughly north and south of each other. He identified that the difference between the two angles is 7 degrees or 1/50 of a circle.

Therefore, he described the circumference of the Earth would be 50 times the distance between the two cities. He calculated the Earth’s circumference as 39,400 kilometers and the modern value of circumference is 40,075 kilometers.

b)

To determine

Whether the new measurements lead to an estimate for the circumference of the Earth that is larger or smaller than the original Erathosthenes’ estimates.

b)

Expert Solution

Answer to Problem 1GST

As the angle increases to 10 degrees, it is 1/36 of a circle. Hence, the circumference of the Earth would be 36 times the distance between the two cities. Thus, the new measurements lead to an estimate for the circumference of the Earth, which is smaller than the original Erathosthenes’ estimates.

Explanation of Solution

Erasthosthenes calculated the angles of the noon day sun at two different Egyptian cities, namely Syene and Alexandria. They were roughly north and south of each other. He identified that the difference between the two angles is 7 degrees or 1/50 of a circle.

Therefore, he described that the circumference of the Earth would be 50 times the distance between the two cities. He calculated the Earth’s circumference as 39,400 kilometers and the modern value of circumference is 40,075 kilometers.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 21, Problem 1GST

a)

To determine

Whether the new measurements lead to more accurate calculation if Erathosthenes had measured the difference in the angles of the noonday sun between Syene and Alexandria to be 10 degrees instead of 7 degrees with reference to Figure 21.3 in the textbook.

a)

Expert Solution

Answer to Problem 1GST

Although Erathosthenes measured the difference in the angles of the noonday sun between Syene and Alexandria to be 10 degrees instead of 7 degrees that would not be an accurate calculation.

Explanation of Solution

Erasthosthenes (276-194 B.C.E) is the one who successfully attempted to establish the size of the Earth. His calculations were very close to the modern values.

Erasthosthenes calculated the angles of the noon day sun at two different Egyptian cities, namely Syene and Alexandria. They were roughly north and south of each other. He identified that the difference between the two angles is 7 degrees or 1/50 of a circle.

Therefore, he described the circumference of the Earth would be 50 times the distance between the two cities. He calculated the Earth’s circumference as 39,400 kilometers and the modern value of circumference is 40,075 kilometers.

b)

To determine

Whether the new measurements lead to an estimate for the circumference of the Earth that is larger or smaller than the original Erathosthenes’ estimates.

b)

Expert Solution

Answer to Problem 1GST

As the angle increases to 10 degrees, it is 1/36 of a circle. Hence, the circumference of the Earth would be 36 times the distance between the two cities. Thus, the new measurements lead to an estimate for the circumference of the Earth, which is smaller than the original Erathosthenes’ estimates.

Explanation of Solution

Erasthosthenes calculated the angles of the noon day sun at two different Egyptian cities, namely Syene and Alexandria. They were roughly north and south of each other. He identified that the difference between the two angles is 7 degrees or 1/50 of a circle.

Therefore, he described that the circumference of the Earth would be 50 times the distance between the two cities. He calculated the Earth’s circumference as 39,400 kilometers and the modern value of circumference is 40,075 kilometers.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 21, Problem 1GST

a)

To determine

Whether the new measurements lead to more accurate calculation if Erathosthenes had measured the difference in the angles of the noonday sun between Syene and Alexandria to be 10 degrees instead of 7 degrees with reference to Figure 21.3 in the textbook.

a)

Expert Solution

Answer to Problem 1GST

Although Erathosthenes measured the difference in the angles of the noonday sun between Syene and Alexandria to be 10 degrees instead of 7 degrees that would not be an accurate calculation.

Explanation of Solution

Erasthosthenes (276-194 B.C.E) is the one who successfully attempted to establish the size of the Earth. His calculations were very close to the modern values.

Erasthosthenes calculated the angles of the noon day sun at two different Egyptian cities, namely Syene and Alexandria. They were roughly north and south of each other. He identified that the difference between the two angles is 7 degrees or 1/50 of a circle.

Therefore, he described the circumference of the Earth would be 50 times the distance between the two cities. He calculated the Earth’s circumference as 39,400 kilometers and the modern value of circumference is 40,075 kilometers.

b)

To determine

Whether the new measurements lead to an estimate for the circumference of the Earth that is larger or smaller than the original Erathosthenes’ estimates.

b)

Expert Solution

Answer to Problem 1GST

As the angle increases to 10 degrees, it is 1/36 of a circle. Hence, the circumference of the Earth would be 36 times the distance between the two cities. Thus, the new measurements lead to an estimate for the circumference of the Earth, which is smaller than the original Erathosthenes’ estimates.

Explanation of Solution

Erasthosthenes calculated the angles of the noon day sun at two different Egyptian cities, namely Syene and Alexandria. They were roughly north and south of each other. He identified that the difference between the two angles is 7 degrees or 1/50 of a circle.

Therefore, he described that the circumference of the Earth would be 50 times the distance between the two cities. He calculated the Earth’s circumference as 39,400 kilometers and the modern value of circumference is 40,075 kilometers.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 21, Problem 1GST

a)

To determine

Whether the new measurements lead to more accurate calculation if Erathosthenes had measured the difference in the angles of the noonday sun between Syene and Alexandria to be 10 degrees instead of 7 degrees with reference to Figure 21.3 in the textbook.

a)

Expert Solution

Answer to Problem 1GST

Although Erathosthenes measured the difference in the angles of the noonday sun between Syene and Alexandria to be 10 degrees instead of 7 degrees that would not be an accurate calculation.

Explanation of Solution

Erasthosthenes (276-194 B.C.E) is the one who successfully attempted to establish the size of the Earth. His calculations were very close to the modern values.

Erasthosthenes calculated the angles of the noon day sun at two different Egyptian cities, namely Syene and Alexandria. They were roughly north and south of each other. He identified that the difference between the two angles is 7 degrees or 1/50 of a circle.

Therefore, he described the circumference of the Earth would be 50 times the distance between the two cities. He calculated the Earth’s circumference as 39,400 kilometers and the modern value of circumference is 40,075 kilometers.

b)

To determine

Whether the new measurements lead to an estimate for the circumference of the Earth that is larger or smaller than the original Erathosthenes’ estimates.

b)

Expert Solution

Answer to Problem 1GST

As the angle increases to 10 degrees, it is 1/36 of a circle. Hence, the circumference of the Earth would be 36 times the distance between the two cities. Thus, the new measurements lead to an estimate for the circumference of the Earth, which is smaller than the original Erathosthenes’ estimates.

Explanation of Solution

Erasthosthenes calculated the angles of the noon day sun at two different Egyptian cities, namely Syene and Alexandria. They were roughly north and south of each other. He identified that the difference between the two angles is 7 degrees or 1/50 of a circle.

Therefore, he described that the circumference of the Earth would be 50 times the distance between the two cities. He calculated the Earth’s circumference as 39,400 kilometers and the modern value of circumference is 40,075 kilometers.

Answer 6

Chapter 21, Problem 1GST

a)

To determine

Whether the new measurements lead to more accurate calculation if Erathosthenes had measured the difference in the angles of the noonday sun between Syene and Alexandria to be 10 degrees instead of 7 degrees with reference to Figure 21.3 in the textbook.

a)

Expert Solution

Answer to Problem 1GST

Although Erathosthenes measured the difference in the angles of the noonday sun between Syene and Alexandria to be 10 degrees instead of 7 degrees that would not be an accurate calculation.

Explanation of Solution

Erasthosthenes (276-194 B.C.E) is the one who successfully attempted to establish the size of the Earth. His calculations were very close to the modern values.

Erasthosthenes calculated the angles of the noon day sun at two different Egyptian cities, namely Syene and Alexandria. They were roughly north and south of each other. He identified that the difference between the two angles is 7 degrees or 1/50 of a circle.

Therefore, he described the circumference of the Earth would be 50 times the distance between the two cities. He calculated the Earth’s circumference as 39,400 kilometers and the modern value of circumference is 40,075 kilometers.

Answer 7

Chapter 21, Problem 1GST

a)

To determine

Whether the new measurements lead to more accurate calculation if Erathosthenes had measured the difference in the angles of the noonday sun between Syene and Alexandria to be 10 degrees instead of 7 degrees with reference to Figure 21.3 in the textbook.

Answer 8

a)

Expert Solution

Answer to Problem 1GST

Although Erathosthenes measured the difference in the angles of the noonday sun between Syene and Alexandria to be 10 degrees instead of 7 degrees that would not be an accurate calculation.

Answer 9

a)

Expert Solution

Answer 10

a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Erasthosthenes (276-194 B.C.E) is the one who successfully attempted to establish the size of the Earth. His calculations were very close to the modern values.

Erasthosthenes calculated the angles of the noon day sun at two different Egyptian cities, namely Syene and Alexandria. They were roughly north and south of each other. He identified that the difference between the two angles is 7 degrees or 1/50 of a circle.

Therefore, he described the circumference of the Earth would be 50 times the distance between the two cities. He calculated the Earth’s circumference as 39,400 kilometers and the modern value of circumference is 40,075 kilometers.

Answer 13

b)

To determine

Whether the new measurements lead to an estimate for the circumference of the Earth that is larger or smaller than the original Erathosthenes’ estimates.

b)

Expert Solution

Answer to Problem 1GST

As the angle increases to 10 degrees, it is 1/36 of a circle. Hence, the circumference of the Earth would be 36 times the distance between the two cities. Thus, the new measurements lead to an estimate for the circumference of the Earth, which is smaller than the original Erathosthenes’ estimates.

Explanation of Solution

Erasthosthenes calculated the angles of the noon day sun at two different Egyptian cities, namely Syene and Alexandria. They were roughly north and south of each other. He identified that the difference between the two angles is 7 degrees or 1/50 of a circle.

Therefore, he described that the circumference of the Earth would be 50 times the distance between the two cities. He calculated the Earth’s circumference as 39,400 kilometers and the modern value of circumference is 40,075 kilometers.

Answer 14

b)

To determine

Whether the new measurements lead to an estimate for the circumference of the Earth that is larger or smaller than the original Erathosthenes’ estimates.

Answer 15

b)

Expert Solution

Answer to Problem 1GST

As the angle increases to 10 degrees, it is 1/36 of a circle. Hence, the circumference of the Earth would be 36 times the distance between the two cities. Thus, the new measurements lead to an estimate for the circumference of the Earth, which is smaller than the original Erathosthenes’ estimates.

Answer 16

b)

Expert Solution

Answer 17

b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Erasthosthenes calculated the angles of the noon day sun at two different Egyptian cities, namely Syene and Alexandria. They were roughly north and south of each other. He identified that the difference between the two angles is 7 degrees or 1/50 of a circle.

Therefore, he described that the circumference of the Earth would be 50 times the distance between the two cities. He calculated the Earth’s circumference as 39,400 kilometers and the modern value of circumference is 40,075 kilometers.