Help with Eratosthenes' Astronomical Measurement!

  • Thread starter Thread starter monkeymocha
  • Start date Start date
  • Tags Tags
    Measurement
Click For Summary
SUMMARY

The discussion centers on solving a problem related to Eratosthenes' method of measuring the Earth's circumference using the angle of the Sun between Alexandria and Syene. The distance between the two cities is specified as 860 km, and the problem requires calculating the difference in the angle of the Sun in degrees. The answer choices provided range from 3.29 x 10^-4 degrees to 0.329 degrees. A diagram illustrating the triangle formed by the Sun and both cities is recommended to aid in visualizing the problem.

PREREQUISITES
  • Understanding of basic trigonometry
  • Familiarity with Eratosthenes' measurement technique
  • Knowledge of angular measurement in degrees
  • Ability to interpret geometric diagrams
NEXT STEPS
  • Study Eratosthenes' method for measuring the Earth's circumference
  • Learn about angular measurements and their applications in astronomy
  • Explore basic trigonometric principles relevant to angle calculations
  • Practice drawing and interpreting geometric diagrams in astronomy contexts
USEFUL FOR

This discussion is beneficial for students of astronomy, educators teaching geometry and trigonometry, and anyone interested in historical methods of measuring the Earth.

monkeymocha
Messages
1
Reaction score
0
Astronomy Help! :(

I'm sure that compared to all the other problems posted here, this Astronomy problem is incredibly easy, but I'm TERRIBLE at sciences and mathematics and really need some help.

The problem is: "Although the distance to the Sun is obviously much larger than the distance between Alexandria and Syene, it is not infinite. This results in a small error in Eratosthenes' measurement, which is given by the difference in the angle of the Sun between Alexandria and Syene. What is the difference in the angle in degrees? (assume a distance between Alexandria and Syene of 860 km. It may help to draw a diagram.)"

The answer choices are:
a) 3.29 x 10^-4 degrees
b) 2.07 x 10^-3 degrees
c) 5.75 x 10^-6 degrees
d) 0.329 degrees
e) 3.29 x 10-2 degrees


This problem is referring to how Eratosthenes measured the circumference of the Earth by using the distance from Alexandria and Syene and the angles of the sun. See http://www.eg.bucknell.edu/physics/astronomy/astr101/specials/eratosthenes.html for details.

I honestly have no idea where to even begin. I'm not even sure what the problem is even asking. If anyone could just point me on the right track, I would really be happy! Thank you!
 
Physics news on Phys.org


Draw the diagram (Sun and both cities). There is a triangle that contains angle in question.

--
methods
 

Similar threads

  • · Replies 10 ·
Replies
10
Views
16K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
Replies
3
Views
2K
  • · Replies 1 ·
Replies
1
Views
5K
Replies
9
Views
2K
  • · Replies 49 ·
2
Replies
49
Views
6K
  • · Replies 1 ·
Replies
1
Views
2K