Mathematics – Logic
Scientific paper
May 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009dda....40.1801d&link_type=abstract
American Astronomical Society, DDA meeting #40, #18.01; Bulletin of the American Astronomical Society, Vol. 41, p.911
Mathematics
Logic
Scientific paper
The observed divergence between Ephemeris Time (ET) and Universal Time (UT1) comes from two main sources: (1) time dilation, a linear effect, and (2) tidal friction, a quadratic effect. [We retract from our 2007 paper that tidal friction exhibits a linear effect.] Time dilation is a larger effect until tidal friction dominates after about 200 years past an epoch. A recalculation of the tidal deceleration of Earth's orientation angle based on more paleontological records yields -5.6835E-7rad/yr2, or equivalently, -5.707E-22rad/s2 assuming 31556925.9747 ET seconds=1 tropical year. This is nearly Stephenson and Morrison's 1995 expectation of -6.20E-22rad/s2.
Time dilation was never applied to the ET definition that, in turn, was based on Newcomb's 1895 formula for the longitude of the fictitious mean Sun. In an earlier paper, we calculated that ET should have a 0.7787sec/yr lag on UT1 due to time dilation, comparable to the observed leap second insertion rate during 1958-1999.
The UT1 second has been slightly larger than the SI and ET seconds for over a century. Circa 2000, IERS adopted a different approach for computing UT1 using a formula that assumes the difference between the UT and SI second is negligible. This would suggest that the coefficient in the formula to convert Earth's orientation angle into UT1 is slightly incorrect by having eliminated time dilation.
Tidal friction still is not included in any model. If one eliminates time dilation, unmodeled tidal friction will cause a slower rate of divergence between UT1 and atomic time after 1999.
Current lunar models empirically use -26"/cy2 for the Moon's secular acceleration. Theoretical calculations show that if time dilation is not taken into account, one will get a value for the secular acceleration of -24.05"/cy2.
Deines Steve D.
Williams Carol A.
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