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
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: 28.70° N and Longitude: 77.14° 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 25th March’ 2015 which was close to the Vernal Equinox
(Spring Equinox) day i.e. 20th March’ 2015.
The equinox is the point
where one season turns to the other. The word is Latin for 'equal night' and
refers to the fact that, on the equinox, day and night is of equal length.
There are two equinoxes each year, with the vernal equinox usually occurring on
21 March. Vernal comes originally from the Latin word for 'bloom' - it refers
to the fact that, in the northern hemisphere, this equinox marks the end of
winter and the beginning of spring. The name is less meaningful in the southern
hemisphere, where this equinox actually marks the beginning of autumn, but
nonetheless the traditional name vernal is commonly retained.
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 62.5
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 22.8 cm, which was cast by the stick at 12.00 noon. 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 30.2°.
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 = 28.70° N
Angle of Sun measured =30.2°
Latitude of OR, USA = 40.76° N
Angle of Sun measured = 42.15°
Central angle = 42.15° – 30.2° = 11.95°
Number of slices needed to make a full circle by central angle = 360o
/ 11.95o = 30.12
The distance between these two places along a north-south line = 40.76°–
28.70° = 12.06
Now, as each angle of latitude = 111 km. Therefore, total distance
between these two places along a North-South line = 12.06 x 111= 1338.66 km,
which can be taken as 1888 km.
So if the length of the "slice" is about 1338.66 km and there
are about 30.12 slices, then the projected circumference is 1338.66 x 30.12 = 40,320
km.
Therefore, the circumference of
the earth came out to be 40,320 km, which is about + 0.78% 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 more 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 I the form of images 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,
Observations taken by Students
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