A personal blog by George Gladfelter


Delta T


Astronomical calculations are commonly made using Terrestrial Time (TT), or if a specific location on the surface of the Earth is involved then both UT1 and TT are needed.  Also, it is desirable to tabulate the time using UTC, or the time in a local time zone linked to UTC.  Thus, it is desirable to know (for past events) DUT1 and DUTC, or for future events estimates of these quantities:

     DUT1 = TT - UT1

     DUTC = TT - UTC

The file deltat.txt lists year, month, day, DUT1, DUTC, UT1-UTC, and notes on the source for the first of the month at 0 hours TT from 1972 through the present on to four years in the future.  For the first year in the future the estimates are made by the International Earth Rotation Service (IERS) in Paris, France.  For years two through four, the numbers are basically a projection based on the rate of increase in DUT1 over the twelve months prior to the present and so these projections are increasingly uncertain the further they lie in the future.



Occultations of bright planets and stars (magnitude 3.3 or brighter) for 2020.

All dates and times are MST

Only events visible from western South Dakota are listed.

Times listed below are valid for observers at the Journey Museum in Rapid City.


Occultation of Acrab 2.56 by moon 28% illuminated at phase= 64 degrees

09/21/2020 18:26:19.7 Start Total, 19:22:55.6 End Total


Occultation of Venus -3.9 by moon 5% illuminated at phase= 335 degrees

This event occurs during daylight hours and may be visible using a telescope IF EXTREME CAUTION IS EXERCISED!

12/12/2020 14:24:27.3 Start Partial

12/12/2020 14:24:56.8 Start Total

12/12/2020 15:18:18.2 End Total

12/12/2020 15:18:45.3 End Partial


Notes about occultations:  The timing is very specific to your exact location.  Few clocks can be relied on to be accurate at the sub-second level, including the inexpensive radio-controlled clocks which are typically corrected once per day around midnight, also note that the clock display on a computer or phone is typically corrected infrequently.  The accuracy of a clock can be verified by time signals broadcast on shortwave frequencies, or by using a GPS receiver, or by accessing a network time server on the Internet if you have software specifically designed for this purpose. However, it is very difficult to visually determine the exact time when a star appears or disappears at the illuminated limb of the moon.  Photography, and a telescope, are therefore very helpful.


If you need data for your particular location, please send me an email with the latitude, longitude, and preferably also your altitude above mean sea level in meters or feet, for your observing location.  Please specify the units you use, such as degrees and meters and specify North or South, East or West for your coordinates.




High Precision Daily Polynomial Coefficients for Lunar Coordinates



The Astronomical Almanac lists the apparent right ascension, apparent declination, and true distance (light time not factored in) of the moon at zero hours Terrestrial Time for each day of the year.  The online web site at http://asa.usno.navy.mil/SecD/LunarPoly.html gives daily polynomials for apparent right ascension, apparent declination, and horizontal parallax for any desired time during the day listed.  However, there are a few points to consider: (1) the polynomials for years after 2018 are not posted, and the practice in the past was not to post beyond the current year.  (2) The coefficients for horizontal parallax have not had the required number of significant figures to match the distance listed in the Astronomical Almanac.


Posted here are text files giving the daily coefficients for apparent Right Ascension, apparent Declination, True Distance, and Horizontal Parallax,   The distance is the true distance in kilometers (light time not factored in).  The others are in degrees.  Each quantity is to be computed as:

                quantity = A0 + A1f + A2f2 + ... + A5f5

                where f = h/24, with h = time (TT) in hours

                so that  0.0  <=   f   <  1.0


The results for the angular coordinates should agree very closely with the apparent coordinates as listed in the Astronomical Almanac, section D, and the distance should agree within a few meters. The coefficients of the polynomials are computed so as to minimize any discontinuity in the calculation of any quantity at the boundary between one day and the next day.


The files available here are:

LMP01c.txt  330 KB for 2020-2021 (12/31/2019 - 01/02/2022)

LMP01p.txt  490 KB for 2017-2019 (12/31/2016 - 01/03/2020)

LMP01f.txt   4.8 MB for 2022-2050 (12/31/2021 - 12/31/2050)


If you have any questions, comments, or needs concerning these polynomials, please send an email to:   g e o r g e 0 7 @ r a p . m i d c o . n e t  (omit imbedded spaces).