Thursday, 17 December 2009

Another Calculation

Today I decided to do another calculation of interest related to the Earth. 

I chose to calculate the speed of rotation of the Earth. I needed some reference point and therefore chose to calculate the speed of one point on the Equator. I considered  the day of the Equinox i.e the day on which the duration of daylight and night time would be exactly the same(12 hours). I imagined myself on a desert island in the sea which is located exactly on the equator. On the day of the Equinox the sun would travel 180 degrees from the west to the east. From this assumption I obtained a crucial figure: The angular velocity of the Earth. Since 180 degrees in pi radians the angular velocity would be pi/12 radians per hour.
The radius of the earth is 6367.5 km. The velocity of one point on the Equator would therefore be (pi/12) * (6367.5) = 1674.365 km/hr or 463.05766716974556587756670701464 m/s.

But that was easy I did not even have to make any physical measurements. I decided to make a very interesting calculation: The difference between the speed of my feet and the speed of the top of my head. I state the radius of the Earth in meters: 6367500 m. my height is 1.67 m. 
The speed of the top of my head is.  463.05778861......(I am not displaying all 32 digits in my calculator display but I use all the digits for my calculation.)
Subtracting the speeds I find that my head is 0.0001214458271179387663942735177012 m/s faster than my foot. So during the day my foot only travels   40008182.443466016891821763486064 m while my head travels 40008192.936385479881731179951293 m. Subtracting, I get that my head travels 10.5 meters more than my foot in one day!!

Now I apply Einstein's Relativistic equation for time dilation:

The relative speed between my head and  my foot or v is 0.0001214458271179387663942735177012 m/s.
c is the speed of light. Let t-zero be 1. 
I get t-v to be  1.0000000000000000000000000820529 seconds
This means that for every second that passes for my head 1.0000000000000000000000000820529 seconds pass for my foot.

The average life expectancy of the world is 65 years. If I live to be 65, my head will have lived a total of 2049840000 seconds while my foot will have lived a total of 2049840000.000000000000000168195316536 seconds.
This means that at the end of 65 years my foot will be older than my head by 1.7 * 10^-16 or  



I think you would agree that this is a truly astounding revelation.

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