Jan-Feb, 2003 Calculations

Straw-Man

 

Proposed Mathematics of Atomic Time (UTC) measurement comparison calculations:

 

Assuming our clocks run at a uniform rate (some straight line of any slope) then:

 

Measure "r" as the difference between of Atomic time and individual Clock time = r₁, r₂, r₃…. r_N. at time period N.  Assumes clocks are not set back to atomic time at the beginning of each time period. (+ = Clock reading faster than Atomic Time.  - = Clock reading slower than Atomic time)

 

First derivative or slope in (sec/day) is then R_N =  r₁/d₁,   (r₂ - r₁)/d₂,   (r₃ - r₂)/d_3,  . . . Where d_N = Number of days (to at least several decimal places) between each measurement N.

 

Second derivative or acceleration of time (sec/day²) is then:

C_N =  (R₂ - R₁)/d₂, (R₃ - R₂)/d₃, . . . (R_N - R_N-1)/d_N)

 

Next select the most reliable clocks using the resulting standard deviation as a reference. Average all Second derivative C_N readings for selected clocks during each time period or  AC_N = (C₂ + C₃ + C₄….+ C_N)/(N-1)   Where C_N is second derivative for each of  N-1 clocks.

 

First Integral of average AC_N or FI_N = AC₁*d_1,  (AC₁*d₁+AC₂*d₂)_,  (AC₁*d₁+AC₂*d₂+ AC₃*d₃)_, . . . 

 

Integral of  FI_N  or SI_N= FI₁*d_1,  (FI₁*d₁+FI₂*d₂)_,  (FI₁*d₁+FI₂*d₂+ FI₃*d₃)_, . . . 

This second integral then becomes the filtered constructed curve of the average comparison to atomic time.

 

Note that all straight-line trends of any constant slope in the original data are filtered out, as desired.  Only the changing situation is plotted as the results.