Operation Eratosthenes II "Measuring Earth with one stick"
Thailand - Cambodia
Spring Equinox 21 - 23 March 2025
Introduction
Operation Eratosthenes is an astronomical practice to measure the size of Earth’s circumference by using the angle of the sun at two locations located in the same longitude in north – south formation. This work is dedicated to the ancient Greek astronomer Eratosthenes 276 – 194 BC who invented the method of measuring Earth’s circumference by using sun angle between the two cities in Egypt Alexandria and Syene. He learnt that angle of the sun in Alexandria is 7.2 degrees where angle at Syene is zero that means Earth must be a sphere.
Eratosthenes was the first person to calculate the circumference of the Earth. He did this by measuring the angle of shadows cast by a stick in two different cities on the same day.
How he did it
1. Measured the distance between two cities
2. Measured the angle of a stick's shadow in each city at noon on the summer solstice
3. Used the ratio of the distance between the cities and the angle of the shadows to calculate the Earth's circumference
Eratosthenes made a remarkably precise measurement of the size of the earth. He knew that at the summer solstice the sun shone directly into a well at Syene at noon. He found that at the same time, in Alexandria, Egypt, approximately 787 km due north of Syene (now Aswan), the angle of inclination of the sun’s rays was about 7.2 With these measurements he computed the diameter and circumference of the earth as we will do.
Principle of Astronomy
Let’s have a touch of simple astronomy of Earth and sun
Earth orbiting around the sun and caused 4 seasons
Earth is tilted at 23.5 degrees and spinning 24 hours a day
How we see the morning sun at the horizon
Sun path at different season
Shadow formation on the spring and fall equinox is a straight-line
The shadow formation at solar noon is aligned exactly north – south
Shadow formation of winter is a curve on the northern side
Shadow formation of summer is a curve on the southern side
Shadow plot on spring equinox, by placing small gravel stones at the tip of the shadow in every 10 minutes
Finally, a straight-line E – W is formed
Shadow formation in winter season is a curve
Shadow formation in summer is also a curve
Angle of solar noon = angle of local latitude
Angle of solar noon = angle of local latitude
Operation Eratosthenes I
This operation was conducted in March 21, 2012 by using two ancient Khmer temples named Prasat Phupek Sakon Nakhon Province Thailand N 17.19 E 103.93 and Prasat Bayon in Angkor Thom Cambodia N 13.44 E 103.85. The result was very satisfactory at 38,451 Km with only 3.9% error from the actual 40,0008 Km Earth’s circumference.
Result of Operation Eratosthenes I March 21, 2012
Operation Eratosthenes II
This is a second operation conducted on March 21
- 23, 2025 to measure Earth’s circumference by using two ancient sites namely Phra Tad Chai Buri located at Nakon Phanom Province Thailand N 17.65 E 104.46 and Prasat Preah Vihear located at Preah Vihear Province Cambodia N 14.39 E 104.80
It is an intercontinental astronomical project operated by 3 colleagues
1.Ajarn Woravit Tongsiri deputy chairman of Sakon Nakhon Civilization Club is stationed at Phra Tad Chai Buri Nakon Phanom Province Thailand
2.Mr Oeur Sopheap a Professional tour Guide positioning at Prasat Preah Vihear Cambodia
3.Ajarn Sansonthi Boonyothayan Chairman of Sakon Nakhon Civilization Club taking the role of coordinator from Iowa State, USA
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Question …… What is the reason of choosing these two places?
Answer …….. The two sites are located at the same
Longitude of E 104 in north – south formation
Question …… Why this operation is scheduled on spring equinox March 21 – 23, 2025
Answer …… Due to an astronomical reason, shadow formation is in straight line that make an easy to identify the angle of the sun at solar noon
Question ….. Can we conduct this operation in anywhere else?
Answer …… Yes of course, we can choose any location on the Earth that located on the same Longitude, but here we are focusing on historical background and story behind
Question …… can you do this operation on any day?
Answer …… yes, we can perform it in any day when sky is clear but shadow formation is a curve (not straight-line) it will be somewhat difficult to find the angle of solar noon
Question …… what is the main problem of the operation
Answer …… human and mechanical error are the main factors that resulted in miscalculation
Eratosthenes formulation of Earth’s circumference
We have to find an angle of the sun at solar noon on the two sites: angle (a) and angle (b)
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Since Earth is a sphere, so the angle of solar noon at (a) and (b) are not the same
Astronomical Opreration at
Phra Tad Chai Buri, Nakon Phanom ProvinceThailand
Brief history
This is a Buddhist temple located in Chai Buri District of Nakhon Phanom Province Thailand next to Mekong River, The Phra Tad is built in BE 2351 or AD 1808 during the Lang Chang Empire. This is a location where River Song Kram met with Mekong River and created the two -color water.
The word “Phra Tad” is literally Thai-Laos language to name a Buddhist Stupa. There is a legend of eternal love of Tow Mor and his wife’s name Sunantha, he built this stupa to witness their love. Many young couples always visited this place for blessing their love and fortune.
Sun path on spring equinox
A stick is installed on the ground next to the Phra Tad
Small gravel stones are placed at the shadow’s tip in every 10 minutes to mark a shadow formation
Draw a straight line through the formation of small gravel stones and the shadow’s tip
Create geometric figure to find the angle of the sun at solar noon
Applied Pythagorean rule to find angle of the sun at
solar noon and here we have angle (a) = 17.3540
Recheck with a protector to confirm angle (a) =
17.3540
Repeat "action 2" with the same methodology
Shadow formation is a straight-line
Create geametric figure
Applied Pythagoras formulation, a = 17.3488
Comfirm with aprotector
The Thai custom of blessing fortune for the operation is a tradition
The Buddhist abort and local community are sharing their best wishes, and here science and belief are well coordinated
The colorful cultural of Chai Buri District
Astronomical Operation at Prasat Praeh Vihear Cambodia
Brief history of Prasat Preah Vihear (Cr: UNESCO)
Situated on the edge of a plateau that dominates the plain of Cambodia, the Temple of Preah Vihear is dedicated to Shiva. The Temple is composed of a series of sanctuaries linked by a system of pavements and staircases over an 800 metre long axis and dates back to the first half of the 11th century AD. Nevertheless, its complex history can be traced to the 9th century, when the hermitage was founded. This site is particularly well preserved, mainly due to its remote location. The site is exceptional for the quality of its architecture, which is adapted to the natural environment and the religious function of the temple, as well as for the exceptional quality of its carved stone ornamentation
We made a decision to choose the operating site at the Gopura IV because there is a clear E – W incised line on the floor, the shadow’s path of a vertical object will coast along this line
I had been to Prasat Preah Vihear on October 1, 2005
With the help of this young lady named Nong Hong
Yok who worked as a local guide, I found E – W line
on the floor of Gopura
Photo of Nong Hong Yok in 2005 and 2025
The straight-line E – W line is marked at the center of
Magnetic compass shows East – West direction
small gravel stones are placed at the shadow’s tip every 10 minutes to form a straight-line E – W
Guide Oeur Sopheap pointing at the shadow’s tip
Sun's shadow on equinox is seen as a straight - line E - W
Applying the Pythagorean rule to find the angle of the sun at solar noon
We got angle of the solar noon = 14.3109
Recheck with the protector
Distance between Phra Tad Chai Buri Thailand and
Prasat Preah Vihear = 362 Km
Since Earth is a sphere so angel of sunlight at Phra Tad Chai Buri (a) and Prasat Praeh Vihear (b) are not the same
Formulation of Eratosthenes to measure Earth’s circumference
Final result of Operation Eratosthenes, we have
42,861 Km with Error 7.13%
Frankly speaking “The Operation Eratosthenes” is a layman method of astronomical and mathematical work using extremely low cost tools hardly 200 Baht or 6 USD. However, the result of Earth’s circumference with 7% error is very acceptable in comparison with the sophisticated and high-technology of NASA
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