Opration Chou Li Episode III

        Measure Earth Axis Tilt With One Stick

          3,000 years ago a chinese astronomer name "Chou Li" was the first man who found "Earth Axis Tilt" by astronomical calculation. He observed the lenght of shadow at solar noon on winter and summer solstice then came out with accurated figure of Earth's tilt  (http://curious.astro.cornell.edu/physics/148-people-in-astronomy/history-of-astronomy/general-questions/995-who-and-when-discovered-that-the-earth-s-axis-is-on-a-23-degree-tilt-intermediate) It is the reason why this experiment is named "Operation Chou Li"    

 

 

How to conduct "Operation Chou Li"

We belived that Chou Li must have been observing the astronomical phenomena called winter solstice and summer solstice repeatedly for many years, finally he came to conclusion of how to calculate the earth's axis tilt

 

This is what Chou Li must have seen on winter solstice and summer solstice

 

Logically Chou Li must have observing the shadow of a pole and recorded angle of incidence on summer solstice and winter solstice then came out with this equation 

 

This is what Chou Li must have been observing and derived the equation  

 

As an astronomy teacher in English Program at Tad Narai Wittaya School Sakon Nakhon Province northeast of Thailand, I did repeated "Chou Li equation" to measure Earth's axis tilt with "one stick"  

Step 1 

Determine angle of incidence at solar noon on winter solstice 20 Dec 2017 with the help of Pythagoras's theory and here I found 38.8116 degree

 

The shadow of a stick at solar noon is directed to geographic north 

 

Angle of incidence at solar noon is calculated by Tangent A

 

Step 2

Determine angle of incidence at solar noon on summer solstice 21 June 2018 and 21 June 2017, here I got 5.6368 degree and 6.3715 degree respectively

 

 

The stick shows lenght of shadow at solar noon on summer solstice 21 June 2018 (the shadow is directed to geographic south) 

 

Calculating angle of incidence at solar noon on summer solstice 2018 

 

M-5 English Program students at Tad Narai Wittaya School Sakon City were participating in astronomical experiment on summer solstice 21 June 2017

 

The shadow at solar noon on summer solstice 21 June 2017 shows the length of 11.2 cm 

 

Calculating angle of incidence at solar noon on summer solstice 21 June 2017

 

Step 3

Using an ancient astronomical equation of Chou Li, here we have Earth's axis tilt 22.2267 (error 5.16%) and 22.5940 (error 3.59%) from the 2 experiments 21 June 2018 and 21 June 2017 respectively

Normally these errors are caused by what we called "human and mechanical error" due to

1.The sun shadow is somewhat "fuzzy"

2.The stick may not installed exactly vertical (90 degree) to the ground 

3.The ground may not exactly level with the Earth's surface

4.Recording the sun shadow at "precised solar noon" is distracted by the cloudy sky

(the actual figure of Earth's axis tilt = 23.4368 https://en.wikipedia.org/wiki/Axial_tilt)

 

Earth's axis tilt from 2 experiments from 2017 and 2018 

 

Scenario of winter and summer solstice at Nong Han Zodiacal Solar Calendar

 

Zodiacal Solar Calendar at Nong Han Sakon City

 

Instruction of the Zodiacal Solar Calendar 

 

Winter Solstice 20 Dec 2017

 

Summer Solstice 21 June 2018

 

 Scenarion of winter and summer solstice

 

Sundial shows 08:30 on summer solstice 

 

Summer solstice 23 June 2018 solar time is slower than clock time (- 06 min) 

 

Conclusion

Operation Chou Li is an integrated learning in science and social science due to the multidisciplinary approach of astronomy mathematic and history. Student will have fun in learning mathematic with story behind.