<blockquote>
<p>&quot;We pick two locations on the same latitude&quot;.</p>
</blockquote>
<p>Erathostenes used different latitude but same longitude to know Earth's circumference.</p>
<p>If you do the experiment with the same latitude you'll get as Oscar Lanzi said :</p>
<blockquote>
<p>&quot;the circumference ... of your latitude circle&quot;</p>
</blockquote>
<p>And thus to know Earth true circumference you'll need to do the maths trick he said.</p>

CC BY-SA 4.0
2021-09-15T21:34:06.257Z
2021-09-15T21:34:06.257Z
Tom Garet
<p>You can use the fact that the Earth's rotation period is known.  Then divide that period (use the solar day of 24 hrs 00 minutes instead of the sidereal day of 23 hrs 56 minutes) by the actual amount of time between your two solar noons and multiply the resulting factor by your 1260 km distance.</p>
<p>The result is the circumference ... of your latitude circle.  To get the circumference of a great circle and thus the Earth, you need to divide the calculated number above by the cosine of your latitude.  To get the latitude perform your experiment on an equinox and measure the shadow angle at solar noon.</p>
<p>Have fun, good luck!</p>

CC BY-SA 4.0
2020-08-07T17:19:25.143Z
Thank you! Doing the same experiment at the solar noon at both places was the idea that I was missing. But just to make sure I got this right: The difference in time will give me an angle along the longitude and comparing the angles of the shadows will give me an angle for the latitude. And you're saying to get the "diagonal" angle I need to divide the first by the cosine of the second?
Fullk33
CC BY-SA 4.0
2020-08-07T17:38:06.420Z
You should divide the circumference of your latitude  circle by the cosine of the latitude angle.  So convert the angle from the difference in solar noon times into a circumference, which corresponds to your latitude circle, then divide by the cosine of the angle you get from the shadow measurement.  By this method you do not calculate the great circle arc directly.
Oscar Lanzi
CC BY-SA 4.0
2020-08-10T01:12:22.247Z
Where does 1260 km come from? Is it somehow based on knowing the answer already?
JohnHoltz
CC BY-SA 4.0
2020-08-10T01:39:50.843Z
@john that figure is given in the question.
Oscar Lanzi
CC BY-SA 4.0
2020-08-10T14:22:44.053Z
Sorry about that. I should not use my phone to read because the screen is too small. :-(
JohnHoltz
CC BY-SA 4.0
2020-08-07T10:03:34.587Z
2020-08-07T10:03:34.587Z
Oscar Lanzi
<p>I have done a bit of research on this topic already and the easiest way seems to be the <a href="https://en.wikipedia.org/wiki/Eratosthenes#Earth%27s_circumference" rel="nofollow noreferrer">experiment by Eratosthenes</a>. We pick two locations on the same latitude (of which we know the distance) and then measure the length of the shadow of a vertical stick at solar noon to get two angles. We can then figure out the difference between these angles and plug it into the formula:</p>
<p><span class="math-container">\begin{align}
\frac{\text{angle}}{360°}&amp;=\frac{\text{distance}}{\text{circumference of the earth}}\\[3mm]
\text{circumference of the earth}&amp;=\frac{360°}{\text{angle}}\times\text{distance}\\
\end{align}</span></p>
<p>Now I would like to do a similar experiment. My family has friends who live 1260km west (and a little south) from us. Is there a way for us take a measurement at the same time and calculate the circumference of the earth? Obviously the formula above does no longer apply since we never have the same solar noon.</p>

CC BY-SA 4.0
2020-08-07T15:30:45.260Z
eratosthenes need to use the same latitude to correlate time with reports, you have a phone so you can do the same thing with different longitudes.
John
<measurements><earth-observation>
Measuring the circumference of the earth - revisited
Fullk33
# Measuring the circumference of the earth - revisited

(Asked by: username_0 on 2020-08-07)

I have done a bit of research on this topic already and the easiest way seems to be the [experiment by Eratosthenes](https://en.wikipedia.org/wiki/Eratosthenes#Earth%27s_circumference). We pick two locations on the same latitude (of which we know the distance) and then measure the length of the shadow of a vertical stick at solar noon to get two angles. We can then figure out the difference between these angles and plug it into the formula:

\begin{align}
\frac{\text{angle}}{360°}&=\frac{\text{distance}}{\text{circumference of the earth}}\\[3mm]
\text{circumference of the earth}&=\frac{360°}{\text{angle}}\times\text{distance}\\
\end{align}

Now I would like to do a similar experiment. My family has friends who live 1260km west (and a little south) from us. Is there a way for us take a measurement at the same time and calculate the circumference of the earth? Obviously the formula above does no longer apply since we never have the same solar noon.

**Tags:** measurements, earth-observation

> **Comments:**
> **username_1**: eratosthenes need to use the same latitude to correlate time with reports, you have a phone so you can do the same thing with different longitudes.  

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## 2 answers

### Answer by username_3 on 2020-08-07. Score: 6 | Accepted answer

You can use the fact that the Earth's rotation period is known. Then divide that period (use the solar day of 24 hrs 00 minutes instead of the sidereal day of 23 hrs 56 minutes) by the actual amount of time between your two solar noons and multiply the resulting factor by your 1260 km distance.

The result is the circumference ... of your latitude circle. To get the circumference of a great circle and thus the Earth, you need to divide the calculated number above by the cosine of your latitude. To get the latitude perform your experiment on an equinox and measure the shadow angle at solar noon.

Have fun, good luck!

> **Comments:**
> **username_0**: Thank you! Doing the same experiment at the solar noon at both places was the idea that I was missing. But just to make sure I got this right: The difference in time will give me an angle along the longitude and comparing the angles of the shadows will give me an angle for the latitude. And you're saying to get the "diagonal" angle I need to divide the first by the cosine of the second?  
> **username_3**: You should divide the circumference of your latitude  circle by the cosine of the latitude angle.  So convert the angle from the difference in solar noon times into a circumference, which corresponds to your latitude circle, then divide by the cosine of the angle you get from the shadow measurement.  By this method you do not calculate the great circle arc directly.  
> **username_4**: Where does 1260 km come from? Is it somehow based on knowing the answer already?  
> **username_3**: @username_1 that figure is given in the question.  
> **username_4**: Sorry about that. I should not use my phone to read because the screen is too small. :-(  

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### Answer by username_2 on 2021-09-15. Score: 0

> "We pick two locations on the same latitude".

Erathostenes used different latitude but same longitude to know Earth's circumference.

If you do the experiment with the same latitude you'll get as username_3 said :

> "the circumference ... of your latitude circle"

And thus to know Earth true circumference you'll need to do the maths trick he said.


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