UserX UserX 2 352 2001-08-13T01:36:00Z 2001-08-16T05:28:00Z 2001-08-16T05:28:00Z 1 218 1246 Work 10 2 1530 9.2720

Jan-Feb, 2003 Calculations



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. rN. 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 RN =  r1/d1,   (r2 - r1)/d2,   (r3 - r2)/d3,  . . . Where dN = Number of days (to at least several decimal places) between each measurement N.


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

CN =  (R2 - R1)/d2, (R3 - R2)/d3, . . . (RN - RN-1)/dN)


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


First Integral of average ACN or FIN = AC1*d1,  (AC1*d1+AC2*d2),  (AC1*d1+AC2*d2+ AC3*d3), . . . 


Integral of  FIN  or SIN= FI1*d1,  (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.