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Sometimes I get so bored that I just try to calculate certain experiments I've heard without know the solution. Like using the basic formula to calculate the speed of the moon around the Earth. This time I tried to calculate the differences between 2 clocks, on put on the highest building in the world (Burj Khalifa) with 828m of the ground and one in its basement so 0m.
First of all, I went searching for some variables I need to use :
I also found the formula I needed to use :
To find the Velocity, I used the simple formula
and
So, I'm trying to find the velocity of those 2 clocks relative to the center of the earth. And because one clock is further (as we see in the formula, if the angular speed is constant) it would have a faster velocity so it should go faster in time.
Velocity clock basement :
Velocity clock on top :
Then I chose for a timeframe of an hour = 3600s
That means I need to calculate the space they have done with their velocity :
Now we should have all the variables for the formula I first mentioned, so let's fill it in :D
For the clock in the basement :
So 4.33192 nanoseconds faster than the center of the earth.
Now for the clock on top :
So 4.33329 nanoseconds faster than the center of the earth.
There seems to be a theoretical a difference of 1.37 picoseconds after 1h on the clocks.
First of all, this is my first time trying to solve such a question, I just graduated high school. But I'm really interested in this field of physics.
If I made a mistake somewhere I would love to hear it, also English grammar mistakes will be visible, my apologize for those also.
Have a great day further.
First of all, I went searching for some variables I need to use :
 Rotation of the Earth = 23h 59min 04s = 86164 s
 Radius of Earth = 6378 x 10^{3} m
 Speed of light = 299 792 458 m/s
I also found the formula I needed to use :
To find the Velocity, I used the simple formula
So, I'm trying to find the velocity of those 2 clocks relative to the center of the earth. And because one clock is further (as we see in the formula, if the angular speed is constant) it would have a faster velocity so it should go faster in time.
Velocity clock basement :
Velocity clock on top :
Then I chose for a timeframe of an hour = 3600s
That means I need to calculate the space they have done with their velocity :
Now we should have all the variables for the formula I first mentioned, so let's fill it in :D
For the clock in the basement :
So 4.33192 nanoseconds faster than the center of the earth.
Now for the clock on top :
So 4.33329 nanoseconds faster than the center of the earth.
There seems to be a theoretical a difference of 1.37 picoseconds after 1h on the clocks.
First of all, this is my first time trying to solve such a question, I just graduated high school. But I'm really interested in this field of physics.
If I made a mistake somewhere I would love to hear it, also English grammar mistakes will be visible, my apologize for those also.
Have a great day further.
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