Function Accuracy

The two primary astronomical values that are calculated by The Sun API are  Declination and Equation of Time.  All the other values calculated by the program are derived from these two values.

Declination

For the period 1990-99 the Declination values returned by the sdxDecl function are within +/-29 seconds of arc of the values returned by the MICA package of the U.S. Naval Observatory.  The average absolute error is only +/- 7.4 seconds of arc.

Equation of Time

For the period 1990-99 the Equation of Time returned by the sdxEOT function returns values are within +/-274 milliseconds of the values returned by the MICA package.   The average absolute error is +/- 200 milliseconds.

In fact the following identity holds

    sdxEOT() - 0.200 seconds = MICA_EOT() +/- 0.078 seconds.

The origin of the 200 millisecond bias between the two programs is not known to the author. 

If we eliminate the 200 millisecond bias, then sdxEOT returns values within +/- 78 milliseconds of MICA.

Long Term Stability of Solar Values

The time base for the astronomical calculations made by The Sun API is Dynamical Time.  The calculations made in Dynamical Time have excellent long term stability so, the accuracy of solar values for the remote past and remote future is determined by the accuracy of conversion between UT and Dynamical Time carried out by the program.

Based on the maximum rate of change of Declination and Equation of Time per hour we can calculate that for every hour of uncertainty in the time base this gives uncertainty of:

• Declination values by +/-8 seconds of arc.
• Equation of Time values by +/-3 seconds

So - the following table shows the long term stability of the values returned by this program.