COMPETITION CANCELLED DUE TO BAD WEATHER

"Scientist of the day competition" on 23rd Sept at Jantar Mantar cancelled due to bad weather.

Measuring the Earth - Experiment

Measuring  Earth

This instructional video is also on Youtube here

Since ancient times people were curious about the place they were living on ….The mother planet- Earth. After discovering the shape of earth, i.e. round, there were very few people who could think of measuring its size. Eratosthenes was one who first measured the circumference of the earth quite accurately.

Eratosthenes Background and his Experiment

Eratosthenes was a Greek living in Alexandria, Egypt, in the third century, BC. He knew that on a certain day at noon in Syene, a town a considerable distance to the south of Alaxandria, the sun shone straight down a deep well. This observation meant that the sun was then directly overhead in Syene, as shown in Figure 1. Eratosthenes also knew that when the sun was directly overhead in Syene, it was not directly overhead in Alexandria, as shown in Figure 2. Notice in both drawings, the sun’s rays are shown as parallel.           

                        

                              

                    

 Figure 1                               Figure 2

How Eratosthenes Found the Circumference of Earth      

He was the first person to actually execute the idea of measuring circumference of earth and give the radius of the earth quantitatively. His idea was very simple.

He first made some simple assumptions:

·        The earth is spherical

·        The distance to the sun is very large compared to the size of the earth

·        So the rays of the Sun falling on the earth are all parallel to each other

How did he do it, more than two thousand years ago? Take a look at Figure 3. Syene is represented by point “S,” and Alexandria by point “A”. In Figure 3, the arc length between S and A is d, and the angle corresponding to the arc SA is angle Q. The radius of Earth is R.

                                                            
                                                                     

Eratosthenes perform the experiment at noon time. As he knew about the amazing fact about the zero shadow happening at Syene. It was very clear in his mind that the shadow can be zero only at the noon time. At other timings of the day we will certainly find some or the other shadow because of the daily movement of the sun. So, to find out whether the shadow becomes zero at Alexandria as well one had to observe it only at the noon time.                                      

                             

                                                                                                     

He observe at point S (in Syene) sun ray is perpendicular to the surface of Earth so casting no shadow and the sun is directly overhead there as shown in figure 4.






Therefore :

Noon shadow length at Syene on summer solstice day = 0 and sun is overhead.

He also measured the shadow of a tower A in Alexandria at noon shown in Figure 4.

The tower at A, which is perpendicular to Earth’s surface, and the ray of sunlight at point S both point to the center of Earth, and the rays of sunlight are parallel. So the angle between the sunlight and the tower is equal to Q (Alternate interior angles are equal.) Therefore: 
Q = Angle between Gnomon and Sun ray

Eratosthenes hired a person who walked from Alexandria till Syene and measured the distance, which cames out to be 718 km. Therefore :

d = Distance from the place where sun is overhead

If he had walked around the whole earth this curve would be 360 ⁰ and the length he walked would be the circumference of the earth.

Therefore one can easily find out circumference of earth by using simple unitary method. According to this method if angle between Alexandria and Syene is 7º which is 50^th part of the total angle at the centre of the earth…then the distance between the above two places is also just 50^th of the total circumference. This can be written as the following formula:

Circumference of earth(C)/distance between two places(d)= 
360º / angle between Gnomon and sunray(angle Q)

Rearranging for the circumference C, 
C = 360/Q X d

Measuring the Circumference of Earth by you at Jantar Mantar

You will also measure the circumference of the earth using the same method as Eratosthenes did. He measured it on the day of summer solstice but you will be measuring circumference of our planet on the day of equinox using the same technique.

So far you must have understood that, Eratosthenes used unitary method which is quite simple to implement. You only need to know the angle between place where you are doing the experiment and the place where sun is overhead and distance between these two places. Putting these values in the following formula will give us circumference of earth: 

C = 360/Q X d

Let us now see how you will find he circumference of earth at Jantar Mantar -

Experiment

Material needed

1. Gnomon with base X 1
2. A plumb line (tie a nut with a thin thread) X 1
3. Drawing board X 1
4. White chart paper, sharp pencil, fine thread, board pins, protector, meter scale
5. Spirit Level X 1                       
6. India Map X 1(along with the scale mentioned on it)                             

 

PREPARATION:

1. Fix the chart paper on drawing board with the help of board pins
2. Unscrew the gnomon stick from the base and measure the full length of Gnomon stick several times. Record the Average length in millimetres. This is the height of the gnomon, H
3. Stick the gnomon base (yellow colored plastic piece) on the board using board pins in such a way that it should not move throughout the observations.
4. Mark with pencil, the centre of the hole where you are going to screw in the gnomon.
5. Screw the gnomon stick back in base.
6. Make a plumb line by attaching weight to the end of a string and try to make the gnomon stick as vertical as possible. For this you may stick some paper padding under base of the gnomon.
7. Position the board under the sun in such a way that the shadow of the tip of the gnomon is falling on the chart paper only and has plenty of space to move around without going off the chart paper.

Marking the shadow

1. Between 11:30am to 1pm mark the tip the shadow formed by the gnomon every 5 minutes.

2. Remove Gnomon from board.

3. Measure the shortest distance from the curve to the base of the pencil in millimetres several times. Record the average. This is the length L of the shadow

Measuring the Sun Angle ‘a’:

It is very simple to measure the sun angle. After conducting the experiment and measuring the length of shortest shadow you need to draw a right angle triangle with sides proportional to the Gnomon height H and shadow length L. For this draw a horizontal line CP=L; Draw a line AC perpendicular to it at one end, of length H. Join AP.

Measure the angle CAP i.e. ‘a’. This is the angle between your location and the place where sun is overhead on equator.

Measuring the Distance ‘d’

As you will be doing this experiment on the day of equinox, you already know that the sun is traveling above the equator, which means you need to find the distance between your place and equator along the longitude.

Finding this distance is also very simple as you just need an Indian map along with its scale (All maps carry a scale written on it which vary from map to map, e.g. 1cm = 150Km). You need to find the distance between Delhi and equator along with the same longitude and then multiply that to the map scale. This will give you the value of  ‘d’

Alternatively you may also measure it before hand with the help of ‘Google Earth’ or any other map. One map will also be given as a  reference.

* We will provide you the facility of both, google map and a large map showing India and equator on the competition site as well.

 Measuring Circumference:

Using the following formula you will measure the circumference of the earth:

C/d = 360/a

C =  360/a X d

Where C – circumference,  a- sun angle, d- distance between Delhi and place where sun is overhead.

You have measured the earth!