21 mars 2019 4 21 /03 /mars /2019 15:33

## Eratosthenes experiment at Draguignan

To beginning with the experiment we consult Geoportail to find :

Coordinates of the Lycée Jean Moulin

• latitude 43.53459 °
• longitude 6.471098 °

For the following we use the protocol of this site https://eratosthenes.ea.gr/.

The length oh our stick is H = 1, 000 m and the length of our shadows is S = 0,970 m.

So we can calculate the angle with

tan(angle) = S / L

and

angle = Arctan (S / L) = Artan (0,97/1,00) = 44.12 °

The stick (H = 1,000 m) is cut in a piece of wood by comparaison of a reproduction of the etalon meter of Breteuil pavillon :

https://fr.wikipedia.org/wiki/M%C3%A8tre

Les élèves de seconde astronomie font la mesure avec Mme Antonsanti et M Decap (qui se cache).

This Year we decided to work with a shool at Sao Tomé and Principe in the Guinea Gulf. You can find their measures here : http://fisicaequimica.com/2019/03/18/eratosthenes-experiment-2019-eratostenes-2019/

We can resume :

Resultados / Results (Portuguese School of São Tomé and Príncipe):

H = 97 cm, S = 6 mm, angle = 0,35°

We need now the distance between Sao Tomé and Draguignan. We use National Geographic Map MAker interactive to find the distance between Draguignan and SaoTomé.

The distance D = 4809 km beetween Draguignan and Sao Tomé.

We can also notice that Draguignan is in the North Hemispher and Sao Tomé too. But Sao Tomé is just next to the Equator Line.

The coordinates of the Portugues Sao Tomé School is

• latitude 0,3528255 °
• longitude 6,7192194 °

First of all, the value of angle beetween Draguignan and Sao Tomé :

Difference angle = 44.12 - 0.35 = 43.77 °

Know, we have all results to find the length of Earth circonference like Eratosthen did few centuries ago.

We can now find the Perimeter of the Earth

Perimeter P = 4809 * 360/43.77 = 39550 km

 distance along the Earth (km) Angle Draguignan-Sao Tomé 4 809 43.77 ° Perimeter 39 550 360 °

We can know compare our result with the number find in Wikipedia : https://fr.wikipedia.org/wiki/Terre

The official meridional Perimeter : P = 40 008 km

It's al little bit less than Equatorial Perimeter ( 40 075,017 km) because af the aellipsoïdal form of the Earth.

The Relative mistake is : Delta P/P = (40 008 - 39 550)/40008 * 100 = 1.14 % = 1.2 %

What is a really good Measure !!

Thanks a lot to our Friends from Sao Tomé.

To recap :

 Town Latitude Longitude H (cm) S (cm) Angle Draguignan 43.53459 ° 6.471098 ° 100.0 97.0 42.12 ° Sao Tomé 0,3528255 ° 6,7192194 ° 97 0.6 0.35 °

D = 4809 km beetween Draguignan and Sao Tomé.

Difference angle = 44.12 - 0.35 = 43.77 °

Perimeter = 4809 * 360/43.77 = 39550 km

Relative Mistake = 1,2 % !!