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Easy scientific measurement

by NateTheGreat
Tags: measurement, scientific
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NateTheGreat
#1
Oct7-08, 12:58 AM
P: 4
1. The problem statement, all variables and given/known data

The Shadow cast by a vertical pillar in Alexandria at noon during the summer solstice is found to be 1/8 the height of the pillar. The distance between Alexandria and Syene is 1/8 the Earth's radius. Is there a geometric connection between these two 1-to-8 ratios?

2. Relevant equations

Not sure exactly what kind of answer they are looking for here.
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tiny-tim
#2
Oct7-08, 04:28 AM
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Quote Quote by NateTheGreat View Post
The Shadow cast by a vertical pillar in Alexandria at noon during the summer solstice is found to be 1/8 the height of the pillar. The distance between Alexandria and Syene is 1/8 the Earth's radius. Is there a geometric connection between these two 1-to-8 ratios?
Hi NateTheGreat! Welcome to PF!

You've left out that at noon during the summer solstice, the sun at Syene is directly overhead.

(I know that 'cos this is a well-known experiment by Eratosthenes in about 200 BC )

Does that help?
NateTheGreat
#3
Oct7-08, 12:10 PM
P: 4
Quote Quote by tiny-tim View Post
Hi NateTheGreat! Welcome to PF!

You've left out that at noon during the summer solstice, the sun at Syene is directly overhead.

(I know that 'cos this is a well-known experiment by Eratosthenes in about 200 BC )

Does that help?
Ah! So then would that explain why they are both 1/8 of the Earth's radius? I'm trying to figure out what they mean by a "geometric connection"?

Sakha
#4
Oct7-08, 01:45 PM
P: 295
Easy scientific measurement

Look at this flashy simulation of the experiment, it is a demo but you can see from it the basic geometry used.

Here


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