Question

Suppose two highly precise, identical clocks are synchronized and one clock is placed at the North Pole and one clock is placed at the equator. After 100 years, how much will the clocks differ in time? You can assume Earth is a perfect sphere of radius 6.37 x 10⁶ m and makes one revolution in exactly 24 hours.

(You will have to use a spreadsheet program that holds a lot of decimal places rather than your calculator to find your answer.)

Answer 1

at first, find the speed of the second clock:

v = r_e ?_e

   = r_e * ((2?/T))

= 6.37e6 * (2*3.14/(24*60*60))

= 463.00463 m/s

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?t = ? ?t_p

    = 1/(?(1-(v/c)²)) ?t_p

    = 1/(?(1-(463.00463/3e8)²)) * (100)

    = 100.0000000003572888 yrs

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the clocks difference = 100.0000000003572888 - 100

                               = 3.57288812336366443e-10 years

                                = 3.57288812336366443e-10 *365.25*24*60*60

                               = 1.13 * 10^-2 s