Tuesday, 8 December 2009

The Tilt of the Earth's Axis

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°

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.
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