2009-01-18

Approximations of a sidereal time

A precision of computation of a sidereal time has been arouse curiosity of me during last days. So I experimented with formulas on the page Approximate Sidereal Time. I compared of computed GMST, the low GMST version ( GMST = 18.697… + 24.0657…D) and GAST with data by Horizons ephemeris. The enclosed graph represents of final results. The functions shows residuals of the computed sidereal times minus Horizons's ephemeris in time the interval from 2000 to 2050. For example, the red line represents of the difference: GAST - Horizon.

Comparison of sidereal time approximations. Click for SVG version.

As we can see that GAST is a perfect approximation for general purposes. But the GMST's approximations are also acceptable. The GMST is not corrected for a nutation with period of 18.6 year and one is nicely visualised by a big wave. A rapid wave superposed onto the nutation period is demonstration of annual orbit of Earth. Strangle breaks at 2006.0 and 2009.0 are effect of the adding of leap seconds. The low precision GMST approximation has visible differences, with respect to GMST, only at the end of the time interval.


Conclusions
  • To compute of sidereal time with low precision use of the low precision formula: GMST = 18.697374558 + 24.06570982441908 D, where 18.697… is sidereal time of the reference time 2000-01-01 at 0 UT, 24.0657… is a ratio of synodic and sidereal periods of Earth and D is days (and its fractions) since the reference time.
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