Introductory letter to the ciese projects (2014-15)

Introduction (About Rukmini Devi Public School)

Rukmini Devi Public School (RDPS), is one of the premier educational institutes in North-West Delhi, India, imparting quality education to children up to 10 + 2 level which helps in building strong foundation. Strong foundation means learning of skills that matters in students’ lives irrespective of the time period whether it is the 21st Century or centuries to come. Therefore development of Attitudes (A), Communication Skills (C), and Thinking Skills (T) is incorporated in the school curriculum to ‘ACT’ upon equipping the young for maneuvering future opportunities and challenges. In response to the process of globalization, RDPS has made sustained efforts to bring an international perspective to its activities. It can be substantiated by school's involvement in Multicultural Students & Staff Exchange Programmes & Collaborative Projects with the various schools in countries - UK, Germany, France, Italy, Singapore and other countries. The students under these Exchange Programmes work on different projects related to Socio- economic, Cultural, Historical, Geographical structure of the country. The “Survey Based Projects” are also undertaken by the students in which the real time data is collected, analyzed and compared with the participants all over world. The school’s “Moto” is to provide 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.

Latitude: 28.70° N Longitude: 77.14° E

Hypothesis: (Noon day Project)

Earth is spinning on its own axis and it appears that with continuous spinning the circumference of earth may change. For e.g. If we think about a ball rotating on a string continuously and this would create a force that holds the ball out on the end of the string and it may flatten out slightly, bulging at the equator.

Over 2,000 years ago Eratosthenes made a remarkably accurate measurement of the earth's circumference. This project requires collaboration of students in places at different latitudes of the earth to make some simple measurements, share data, use a spreadsheet to make comparisons, and then replicate and share their results of the circumference of earth.

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 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.

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^th September’ 2014 which was close to the Equinox day i.e 22 September’ 2014. 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 four to measure the angle of the sun. Four groups, have submitted the data, which was considered as best in comparison to the actual data. Here’s the procedure and measurements taken by the four groups:

We started our experiment at 11.45 a.m. We took a 100 cm 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 82.5 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 32.5°.

We took data from website of The Sunset Spiderman School situated in OR, 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 =32.5°

Latitude of OR, USA = 45.46° N

Angle of Sun measured = 48.5°

Central angle = 48.5° – 32.5° = 16°

Number of slices needed to make a full circle by central angle = 360^o / 16^o = 22.5

The distance between these two places along a north-south line = 45.46°– 28.42° = 17.04

Now, as each angle of latitude = 111 km. Therefore, total distance between these two places along a North-South line = 17.04 x 111= 1888.11 km, which can be taken as 1888 km.

So if the length of the "slice" is about 1388 km and there are about 30 slices, then the projected circumference is 1888 x 22.5= 42,480 km.

Therefore, the circumference of the earth came out to be 42,480 km, which is about 6.2% error, since the average circumference of earth is 40,008 km.

All the four groups had the similar observations.

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:

gbartus@stevens.edu

We certainly look forward to work on it in future.

Thanks,