gnomoni.ca

Layout

Separate Equation of Time and Solar Declination tables, with columns for each month (2 × 31 rows)

Single table with columns for Equation of Time and Solar Declination, one row per day (365|366 rows)

Equation of Time version

Traditional: the amount to be added for converting local solar (sundial) time to mean time

Inverted (that is, IAU style): the amount to be added for converting mean time to solar (sundial) time

Adjust to reflect clock time for the UTC-12:00 UTC-11:00 UTC-10:00 UTC-09:30 UTC-09:30 UTC-09:00 UTC-08:00 UTC-07:00 UTC-06:00 UTC-05:00 UTC-04:00 UTC-03:30 UTC-03:00 UTC-02:30 UTC-02:00 UTC-01:00 UTC+00:00 UTC+01:00 UTC+02:00 UTC+03:00 UTC+03:30 UTC+04:00 UTC+04:30 UTC+05:00 UTC+05:30 UTC+05:45 UTC+06:00 UTC+06:30 UTC+07:00 UTC+08:00 UTC+08:45 UTC+09:00 UTC+09:30 UTC+10:00 UTC+10:30 UTC+11:00 UTC+12:00 UTC+12:45 UTC+13:00 UTC+13:45 UTC+14:00 time zone

Equation of Time format

Minutes and seconds (mm:ss)

Decimal minutes (mm.m)

Seconds (sss)

Degrees of Hour Angle (dd.ddd)

Period

This year

Next year

Averaged from to

The results will include an entry for February 29 only if applicable; hence there are either 365 or 366 data depending on the selection made.

Other than that, the option is mostly insignificant: although the values vary over the Leap Year cycle as well as changing gradually over decades, there is only about 15 seconds of variation in the daily Equation of Time value over the period to 2099; the difference in Solar Declination is equally trivial. However, it is no extra effort for a computer to calculate any of the variants above so I decided to offer the choice, for the sake of doing it.

Place

My current location

Longitude (Decimal degrees; East positive)

This option is mostly insignificant: even in the worst case, there is only 15 seconds difference between a local Equation of Time value and the standard value (Greenwich); the difference in Solar Declination is equally trivial. However, it is no extra effort for a computer to calculate either of the variants above so I decided to offer the choice, for the sake of doing it.

This page calculates annual tables for the Equation of Time and Solar Declination using the methods described in Jean Meeus' book "Astronomical Algorithms".

Meeus' high accuracy refinements are not included. My understanding is that Meeus' standard precision Equation of Time method gives results that are close to both his higher accuracy results and those produced by the advanced models provided by JPL (about 15 seconds difference in the worst case). An equivalent minimal difference applies to the Solar Declination results.

During development of the page, I verified my results against NOAA's Solar Position Calculator and the Excel spreadsheet implmentation of Meeus' algorithms published by the Earth System Research Laboratories. However, if you suspect any remaining errors or discrepancies, please contact me. Clicking the envelope icon in the upper right corner of this page will reveal my email address.

Lastly, quite a few other sites show results to higher precision than I do (sometimes even to the millisecond!). I show the Equation of Time to the nearest second or 0.1 minutes, and Solar Declination to only 2 decimal places. There are 3 main reasons why I avoid the extra decimal places:

• First, as mentioned above, the results shown here (and on most of those other sites) differ by several seconds from the best calculations possible. There're no point showing sub-second precision if your calculations aren't that accurate. If you do need more decimal places, you probably want to use JPL Horizons.
• Second, even a well-aligned, well-made sundial can be only be read reliably to the nearest minute or so. High precision reference data is, quite simply, unimportant for sundialling purposes.
• Third, these are representative daily values, calculated using mean time's noon. In reality, the data change as the day progresses. Use the results at other times of day, and you are introducing additional inaccuracy.