(34S) - Sunrise/Sunset

[Kiwi Geoff]

(02-15-2015 07:57 PM)Dieter Wrote:  I would like to ask a final question: the accuracy for 2015 is astonishing. But what about other years? I assume the program uses constants that are optimized for a certain period. How well does the program perform for e.g. 2000, 2050 or 2100? What is the range of years the used constants were optimized for?

Hello Dieter, interesting questions.

To try and help answer, I have made a comparison between the WP34s 'RS' algorithm and JPL DE200 ephemeris for each day from 1st Jan 2000 until 31 Dec 2019 (20 years OR 7,305 days).



If you wish to examine the data yourself, here is the difference data (in CSV format) for the 7,305 days.
  RS_DIFF.zip (Size: 41.27 KB / Downloads: 10)

Code:


Note on the graph how every 4 years, there is a larger difference,
that occurs during the Equinox (when the Sun is moving "fastest"
across the horizon each day). It's as if the extra day every 4 years
displaces the otherwise very good trig algorithm !

The Maximum Sunrise Delta = 47.8 seconds on the 17th March 2017.

2017-03-17    07:30:24.84   = WP34s Sunrise algorithm
2017-03-17    07:29:37.082  = JPL DE200 Ephemeris

Using the Nasa JPL ephemeris at

http://ssd.jpl.nasa.gov/horizons.cgi

Gives the sunrise as:

2017-Mar-17 07:29:38 = JPL DE431LE

Which agrees within 1 second of the DE200 value, so the 47.8 second difference is mainly in the WP34s algorithm.

However the "averaged sunrise error" over the 20 years, is less than 1 second !!

So I think the WP34s 'RS' algorithm is VERY useful (at least for a few more years) and a grand example of using a programmable calculator.

Regards, Kiwi Geoff.