Page 15 - Curiosity_June_2020_FB

(a city at the north of Syene, Fig. 1) to measure the angle of shadow of walls
of well and hence deduced the angle between the Sun and the zenith (Fig. 2). Two of the assumptions made by Erato- sthenes were inaccurate: (1) Alexandria and Syene are on the same longitude (actually, their longitude differs by approximately 3 degrees) and (2) Syene is exactly on Tropic of Cancer and hence there was zero shadow in Syene on 21 June (actually, Syene is little north of Tropic of Cancer).
At the local noon, when Sun crosses the meridian (the line in sky joining north, zenith, and south), Eratosthenes got Sun’s angle with the zenith (point in the sky exactly overhead) as 7 degrees. He also measured the distance between Syene and Alexandria and calculated circumference of Earth using a simple
formula:
Distance between Syene and Alexandria = 7 Circumference of Earth 360
(7 degrees being the angle between Sun and the zenith and 360 degrees for the full circle)
The ratio of the same is compared with the distance between two places and circumference. The answer he got was around 98% accurate!
This experiment is quite simple
and can be performed using a simple apparatus. Thus, to utilize the pres- ent national lockdown period, Vigyan Prasar, in association with Jyotirvidya Parisanstha, conducted a nationwide experiment to measure the circumfer- ence of Earth with the VIPNET Clubs across the nation. These VIPNET clubs performed the experiment from their homes. Around 81 VIPNET clubs
Map created using Google Maps https://bit.ly/2XA2LMg
enthusiastically responded to this idea and participated in the experiment. The map shows the locations of the observ- ers across India.
The experiment was conducted on 13 May 2020, which was the ‘zero shadow day’ at Pune (location of Jyotirvidya Parisanstha). It is the day when Sun’s position in sky matches the latitude of
a place, and hence Sun comes at the zenith at local noon. As a result, the shadow of an exactly vertical object disappears at local noon.
At different observing locations on the same day, participants measured the angle of Sun from their zenith at local noon. As all the locations of observers and Pune are not on the same longitude, thus, only the latitude vector of the distance between the observers’ location and Pune was considered in calcula- tions. An example is shown in Figure 4, where an observer is located at Kolkata. As shown in the figure, only the latitude vector of distance is considered because on the entire latitude of Pune, there
was zero shadow day on 13 May. So, an imaginary point was considered, which is the intersection point of the latitude of Pune and longitude of Kolkata. That imaginary point and observer in Kolkata being on the same longitude, their local noon will be at the same time, and then there will not be any error in further calculations.
To measure the angle between the Sun and the zenith at noon, observers made simple setups at their home. For performing the experiment, they needed a gnomon, which is here an object that, by the position or length of its shadow, can act as an indicator, especially of
the hour of the day. All the observers used a simple erected gnomon, placed
it on a graph paper or plain paper, and measured the length of the shadow of the gnomon at their local noon. Figure
5 explains the concept of this simple measurement. With the help of height of gnomon and length of the shadow, the angle between Sun and zenith was
June 2020
15
Figure 3