We are all aware of the fact that the Earth's axis is tilted from the normal. This tilt is the cause of the seasons. Today , to relieve myself of boredom I decided to calculate this tilt of the Earth's axis using a very tall lamp post and its shadow both of which could be observed from my bedroom window.
The Tilt
I started with the shadow. I measured the length of the shadow using my normal 6.5 inch (15 cm) ruler. It recorded a length of 3.5 cm. Careful to hold my head so that it's spatial co-ordinates remain reasonably constant I measured the height of the lamp post. I knew that all angles on the triangle I constructed(See illustration below) would be exactly the same as those in the triangle formed by the original lamp post and shadow because I was working with similar triangles.
So I did the math.
Theta would be the arctan of (8/3.5).
θ = 66.4°
The angle of tilt (φ):
φ = 90 - 66.4°
φ = 23.6°
________
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The actual angle of tilt of the Earth's axis is 23.45°. The error in my calculation is therefore 0.6% which is absolutely fantastic.
And that is the story of how I measured the angle at which the Earth's axis tilts away from the normal.
I started with the shadow. I measured the length of the shadow using my normal 6.5 inch (15 cm) ruler. It recorded a length of 3.5 cm. Careful to hold my head so that it's spatial co-ordinates remain reasonably constant I measured the height of the lamp post. I knew that all angles on the triangle I constructed(See illustration below) would be exactly the same as those in the triangle formed by the original lamp post and shadow because I was working with similar triangles.
Theta would be the arctan of (8/3.5).
θ = 66.4°
The angle of tilt (φ):
φ = 90 - 66.4°
φ = 23.6°
________
-----------
The actual angle of tilt of the Earth's axis is 23.45°. The error in my calculation is therefore 0.6% which is absolutely fantastic.
And that is the story of how I measured the angle at which the Earth's axis tilts away from the normal.
2 comments:
Excellent calculations. But you should have specified the conditions at which your observation is true. I had guesses it but i wanted to make sure.
I guess the most challenging bit would have been to measure the length of the shadow from where you observed it.
I'd like to taunt Kian Seng with this, really. :P
But the honour's yours. xD
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