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Measurement of the Earth's rotation from 720 BC to AD 2015
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source: http://astro.ukho.gov.uk/nao/lvm/

Her Majesty's Nautical Almanac Office

This resource provides the results of the modern analysis of eclipse and occultation timings from ancient Babylonian, China, and the Arab and European worlds through early telescope observations to modern observations in the following paper:

Measurement of the Earth's rotation: 720 BC to AD 2015 (accepted 2016 November 4).

published in the Royal Society's Proceedings A, 472 by Stephenson, F.R., Morrison, L.V., and Hohenkerk, C.Y., and made freely available via Open Access.

The analysis provides an insight to the rotation of the Earth and allows formation of the change in the length of day (lod), relative to the standard day of 86400 SI seconds, and DT(t) = TT - UT1, via a spline fit using a weighted least-squares analysis of the data. For comparison with EOP series, we make them consistent with UT1 - TAI determined after 1958, adding to UT1 - TT the offset TT - TAI = 32.184s at the date 1958 January 1. So IERS EOP-PC provides DT'(t) = -DT(t) + 32.184 s.    

The values of DT should be used in conjunction with lunar ephemeris designated JPL DE430/LE430 in which the tidal acceleration of the Moon is -25.85"/cy2. 

This website allows users to extract the data from the spline fit, between -720 and 2016.0, and extrapolated values elsewhere.
DT = UT1 - T and LOD 


1) from -2000 to -800 :

The values tabulated in the DT and lod tables have been extrapolated backwards by integration using the long term lod function

lod = +1.78 t - 4 sin(2 pi t/15)

between the years -800 to -2000, where t is the number of centuries from +1825.0. 

2) from -720 to  1600 AD: mv ecl	

The spline (continuous-black curve) that has been fitted to the observations has been evaluated, from the start at -720, then the following century years, giving both DT and the lod.

DT is given to the nearest 10 seconds together with an estimate of the errors. 

3) from 1600 to 1800:

The spline (continuous-black curve) that has been fitted to the observations has been evaluated from 1600 to 1800 every 10 years, giving both DT and the lod.

DT is given to the nearest second and the lod to nearest 0.1 ms together with an estimate of their errors. 

4) from 1800 to 1850: 

The spline that has been fitted to the observations has been evaluated every year from 1800 to 1950.
DT is given to the nearest 0.1 seconds from 1800 to 1850 and to 0.01 seconds to 1950. The lod is tabulated to nearest 0.1 ms.

5) from 1950 to 2016: 

The most accurate results from 1962 onwards are those derived from VLBI and other high-accuracy observations. These are available from the International Earth Rotation and Reference System Service (IERS).

The less accurate DT and lod listed here are evaluated from a spline fit to the occultation observations, which has the effect of smoothing out the annual and sub-annual fluctuations in the raw data. The values are tabulated at half-yearly intervals to a precision of 0.01 seconds in DT and 0.1 ms in lod. They agree to within ±0.05 seconds with the IERS values of DT. Taken together with the occultation data before 1962, the results tabulated here show the long-term trends in these Earth's rotation parameters.