Drawing on Eratosthenes' method, if two observers are due north and south of each other and are separated by 400 km, what is the circumference of their spherical world if they see the same star on their meridian at altitudes of 23 degrees and 47 degrees respectively, and at the exact same time?

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Estimating the circumference of a body based on Eratosthenes' method:

Two observers positioned at S1 & S2 on a North-South meridian see a star (observed at the same time) at altitudes of 47 deg and 23 deg respectively. If their physical separation S1-S2 is 400 km what is the circumference of their world.

First we can assume that the starlight is ...

Solution Summary

Determining the circumference of an observers world using angles of inclination of two stars and Eratosthenes theorem

This problem is about the proof of Theorem 1 implies Theorem 2 as discussed in class. Regard Theorem 1 as a statement P and Theorem 2 as the statement "Q implies R". Then the statement "Theorem 1 implies Theorem 2" can be expressed as:
"P implies (Q implies R)".
Theorem 2" is can be expressed as P implies (Q implies H)".
a

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To see the description of the problem in its true format, please download the attached question file.

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Please see the attached file for the fully formatted problem.
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See the attached file. Solution to 11.6.2(a) is needed.

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Problem:
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Thank you!

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