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Physics
Special and General Relativity
Calculating Velocity: Moon Around Earth & Clocks in Burj Khalifa
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[QUOTE="Anakin Delabelle, post: 6061227, member: 651258"] 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 ([B]Burj Khalifa) with 828m [/B]of the ground and one in its basement so 0m. First of all, I went searching for some variables I need to use : [LIST] [*]Rotation of the Earth = 23h 59min 04s = 86164 s [*]Radius of Earth = 6378 x 10[SUP]3[/SUP] m [*]Speed of light = 299 792 458 m/s [/LIST] I also found the formula I needed to use : [INDENT] [IMG]https://wikimedia.org/api/rest_v1/media/math/render/svg/cd0ef0ab32cb75d24e1baca01106d02f0d0ae0bd[/IMG] [SIZE=7][I][/I] [I] [IMG]https://wikimedia.org/api/rest_v1/media/math/render/svg/d047edd48fc8cbe8c6277b0115d66be121e46ed9[/IMG][/I][B] [/B][/SIZE] [/INDENT] To find the Velocity, I used the simple formula [IMG]https://wikimedia.org/api/rest_v1/media/math/render/svg/b5edc54db08559dc3e33cb3cc568126e12b46521[/IMG] and [SIZE=6][IMG]https://wikimedia.org/api/rest_v1/media/math/render/svg/e463711972f03d38362b2a4f330ed8a9d4b172b9[/IMG] [/SIZE] [SIZE=4]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.[/SIZE] Velocity clock basement : [ATTACH=full]231048[/ATTACH] Velocity clock on top : [ATTACH=full]231049[/ATTACH] Then I chose for a timeframe of an hour = 3600s That means I need to calculate the space they have done with their velocity : [ATTACH=full]231050[/ATTACH] [ATTACH=full]231051[/ATTACH]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 : [ATTACH=full]231052[/ATTACH][B][ATTACH=full]231053[/ATTACH] [B]So 4.33192 nanoseconds faster than the center of the earth.[/B] [/B]Now for the clock on top : [ATTACH=full]231054[/ATTACH][ATTACH=full]231055[/ATTACH] [B]So 4.33329 nanoseconds faster than the center of the earth.[/B]There seems to be a theoretical a difference of [B]1.37 picoseconds after 1h on the clocks.[/B] 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. [/QUOTE]
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Calculating Velocity: Moon Around Earth & Clocks in Burj Khalifa
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