A CIESE Collaborative Project

# 2012 Letters, Reports and Photos

## Introduction (About Rukmini Devi Public School)

We, Rukmini Devi Public School (RDPS), are one of the premier educational institutes in North-West Delhi, India, imparting quality education to children up to 10 + 2 level. We aim to provide our students and staff an opportunity to enrich their international understanding and awareness of sharing common values and make them better citizens of the Global Village. We continuously motivate our students to connect with the schools abroad so that they can express and discuss their ideas, exercises and opinions with other fellow students.

Latitude: 28.42° N                                                                                       Longitude: 77.8° E

Hypothesis: ( Noon day Project)

In this project, we will estimate the circumference of the earth, using a method developed about 2,200 years ago, by Eratosthenes, a Greek mathematician and the librarian of the great library at Alexandria, in Egypt.

We can use Eratosthenes' method to calculate the circumference of the earth ourselves. We can even make the calculation when the sun casts a shadow at noon in experimental places. The goal of this project is to estimate the circumference of the earth by setting up a mathematical proportion from simple measurements.

The circumference of the earth at the equator is 24,902 mi / 40,076 km. So, with our experiment we should reach to the same conclusion. Let us do the experiment and calculate its inference.

## Final Report

We are grade 8 students from Rukmini Devi Public School, located in the capital city-Delhi of India (Latitude: 28.42° N and Longitude: 77.8° E) and doing this project as part of our subject “Collaborative Projects” in our school.

Firstly, our teacher explained us the set up and steps to measure the angle of the sun and circumference of the earth. We did our experiment on 25 September’ 2009 which was close to the Equinox day i.e 22 September’ 2009. Equinox is the time when the sun crosses the plane of the earth's equator, making night and day of approximately equal length all over the earth. We were fortunate to have sunny sky.

We were divided into groups of three to measure the angle of the sun. Out of 3 groups, we submitted the data, which was considered as best in comparison to the actual data. Here’s the procedure and measurements taken by that best group:

We started our experiment at 11.45 a.m.  We took a meter stick and marked the shadow after every 2 minutes of interval for the first 10 minutes and then at an interval of 10 minutes till 12.45 p.m., the shadow started increasing. Then, we found the length of shortest shadow which came out to be 50.40 cm, which was cast by the stick at 12.05 p.m. Then by making right angle triangle between length of stick and shortest shadow of the stick, we measured the angle of the sun. The angle of the sun was measured to be 27.8°.

We took data from website of The Churchill School School situated in NY, U.S.A to calculate the circumference of the earth, which was done as follows:

Latitude of Delhi, India = 28.42° N,  Angle of Sun measured = 27.8°

Latitude of NY, USA = 40.7° N, Angle of Sun measured = 40°

Central angle = 40° – 27.8° = 12.20°

Number of slices needed to make a full circle by central angle = 360 / 12.20 = 29.5

The distance between these two places along a north-south line = 40.7°– 28.42° = 12.28°.

Now, as each angle of latitude = 111 km. Therefore, total distance between these two places along a North-South line = 12.28 x 111= 1363.08 km, which can be taken as 1363 km.

So if the length of the "slice" is about 1388 km and there are about 30 slices, then the projected circumference is 1363 x 29.5= 40,208 km.

Therefore, the circumference of the earth came out to be 40,208 km, which is about 0.5% error, since the average circumference of earth is 40,008 km.

It was a real fun and enriching experience to measure the circumference of the earth using a method that was first used by Eratosthenes.  Through this project, we came to know that angle of sun we measured was less than the latitude of our place. As a further enhancement to the project, when we will take up this project next time, we would also find longitude by shadow measurements.  The evidence of the observations taken for The Noon Day Project is shared on the link given below:

We certainly look forward to work on it in future.

Thanks, The Noon Day Collaborative Project Group, Rukmini Devi Public School, Delhi, India

## Weld Central Middle School, Colorado, USA

Dear Participants of the Noon Day Project,

We are writing from Weld Central Middle School.  We are planning on doing an exciting project on measuring the circumference of the earth, called the Noon Day Project.  We are hoping you'll join us on this exciting journey to help us with this research.  Let's make new calculations and discoveries!

We are in Keenesburg, Colorado.  Our latitude is 40.0 degrees North, and our longitude is 104.5 degrees west.  Our school is in the middle of a plain and also by a busy highway.  We come from a farming community.  Our school colors and flag colors are red, white, and blue.  We are hoping to get precise answers and have some help from you in getting our measurements right.  I hope that you are willing to work with us to find the right measurements.  Let's make new calculations and discoveries!

Thank You for your time and consideration.

Sincerely, Weld Middle School

## Collège Antonin Perbosc, France

Hello,

We are currently in Jeanne d'Albret High School in France. We are 10th graders in a special section called the European English section. Students in our High School speak French of course. The difference between the other students and us is that in addition, we have physics and chemistry lessons in English.

Jeanne d'Albret High School is located in Saint-Germain-en-Laye, which is a small town in the Département des Yvelines (this is the region) to the west of Paris. St-Germain's latitude is 48.9°N and its longitude 2.08°E.

A lot of people in St-Germain speak English because many expatriates come to live here and study at the International High School. In our town we have a historical palace where a very famous French king called Louis XIVth was born. Actually, Louis XIVth is mainly famous for building the world-renowned Château de Versailles, which is very near where we live.

We thought it would be a challenge to measure the circumference of the Earth without even leaving the school. By participating in the Noon Day Project, we expect to develop our team spirit and we hope to find a value which is very close to the real circumference of the Earth.

We are enthusiastic about sharing a human experience thanks to this scientific project.

We look forward to finding a partner to finalise our calculations!

Best wishes to all!

The 208 class in Jeanne d'Albret

### Final Report

Our results

 Lafrançaise France Collège Antonin Perbosc 44°08’N 01°15’E
 september 22nd 100 cm 96 cm 43°49’ = 43.831°

our partner school

 Alor Akar Malaysia SMK Alor Akar 03°50’N 103°21’E
 september 22nd 100 cm 6.5 cm 3°43’ = 3.719°

Calculation

Distance Alor Akar - Lafrançaise  4478 km

Difference between angles : 43.831° - 3.719°  = 40.112°

Circumference : 4478 x 360 / 40.112 =  40189 km

http://www.eratosthenes.eu/spip/spip.php?rubrique184