A personal blog by George Gladfelter

About Lunar Eclipses and the May, 2022 eclipse in particular


The eclipse of May 15-16, 2022 ran on schedule (see Astronomical Almanac for the year 2022, page A86), but failed to show the bright red coloration that was expected.  Apparently, the dust from the Tonga volcano blocked so much light that the Moon was too dark during the total phase to make much of an impression.  Long-exposure photography did reveal the red coloration, but human eyes were not able to duplicate the photography.

For observers on Earth, of course, there will be more total Lunar Eclipses in the future.  Specifically in the western part of North America, the following total Lunar Eclipses will be visible this decade (dates and times are UTC - 7 hours for the total eclipse phase):
11/08/2022 03:16 to 04:42
03/13/2025 23:25 to 03/14/2025 00:32
03/03/2026 04:04 to 05:03
06/25/2029 19:31 (this is shortly before the Moon rises for those in western South Dakota) to 21:13

The following total Lunar eclipses will not be visible from South Dakota:


When did the June solstice occur? And when will the December solstice occur?

10/02/2021 (rev. 05/16/2022)

On June 21, 2021 (European and most of Asia time, June 20 in North and South America), a solstice of the Sun occurred - but when exactly?

As explained below, the official time was June 21 at 3:32:09.215 UTC (June 20 at 11:32:09 EDT) when the Sun's apparent ecliptic longitude was 90 degrees, but 3:21:57.496 UTC when the Sun's declination reached a stationary value of 23.43739 degrees north. 

On September 22, the equinox was at 19:21:04.806 UTC (apparent ecliptic longitude was 180 degrees), but it was at 19:20:32.941 that the Sun's declination was zero (i.e. the Sun was over Earth's equator). 

And, on December 21, the solstice was at 15:59:17.742 UTC while the time of maximum excursion of the declination (23.43747 degrees south) was 15:57:11.180.

All of the times above are based on calculations in Terrestrial Time and a value of DUTC (TT-UTC) of 69.184 seconds.  The calculations in TT are rather good, but the value of DUTC beyond 2022 is only an estimate, so the times of seasonal changes for future years in terms of UTC are less and less certain for the years farther into the future.  For 2022, the times (UTC) are: 03/20/2022 at 15:33:24, 06/21/2022 at 09:13:50, 09/23/2022 at 01:03:41, and 12/21/2022 at 21:48:12.

Subtract 5 hours from UTC for EST, or 4 hours for EDT.       For MST subtract 7 hours, or 6 hours for MDT .

More on the definitions.

In each calendar year, there are two solstices (times when the Sun's stops moving south in December, or stops moving North in June), and two equinoxes when the Sun crosses the Earth's equatorial plane (in March and September). But, at the time of a solstice, the Sun's declination is not changing, which means that the declination is then changing very little in a reasonable unit of time such as an hour or two; thus there is a problem with defining the seasons in terms of the Sun's declination.

However, the Sun's ecliptic longitude increases throughout the year at a nearly uniform rate. Therefore, the time of an equinox is defined by astronomers as the instant when the ecliptic longitude is zero degrees in March, or 180 degrees in September, and the solstices are defined as the times when the Sun's longitude is 90 degrees in June, or 270 degrees in December. The definition in terms of ecliptic longitude facilitates precision in the computation of the timing of each event.  Due to a number of factors, especially precession and nutation, (1) the time for an equinox does not tend to coincide with the time when the Sun's declination is exactly zero, and (2) the Sun's declination at the time of a solstice is not necessarily the time when the declination is at an extreme value, nor the same from one solstice to the next one a year later.

Another consideration about computing the times of the seasons is that solar system dynamics (such as Earth's orbital motion around the Sun) proceed according to dynamical time, and that time is independent from Earth's rotation around its axis (but UTC and UT1 are dependent on that rotation). Thus, predictions of the civil times of the seasons (UTC, EST, etc.) are dependent on an unpredictable offset between TT (Terrestrial Time) and UT1 (the time defined by the Earth's rotation around its axis) and thus also the offset between TT and Coordinated Universal Time (UTC). 


High Precision Daily Polynomials for Lunar Coordinates

Rev. 04/24/2021

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.hmnao.com/SecD/LunarPoly.html gives daily polynomials for apparent right ascension, apparent declination, and horizontal parallax so that these quantities may be computed for any desired time during the day listed.  However, there are a few points to consider:

(1) The coefficients for horizontal parallax did not have the required number of significant figures to match the distance listed in the Astronomical Almanac. 

(2) These polynomials appear to have been fitted so as to lower the maximum error with the result that the error at the start of the day, and at the end of a day is not minimized.  This means that the polynomial for 24 hours at the end of one day does not give the same value as the polynomial for the next day at zero hours.  While the discrepancies for right ascension and declination are not meaningful, for parallax they can be noticeable, and for algorithms in a computer discontinuities can cause difficult problems. The polynomials given below are computed so as to minimize the discontinuities between one day and the next - with the maximum errors elsewhere being slightly increased as a result.

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 given here are computed so as to minimize any discontinuity in the calculation of any quantity at the boundary between the end of one day and the start of the next day. 

The data from which the polynomials posted here were derived came from the program MICA, and the results using these polynomials agree with MICA data within the following limits: Right Ascension +/- 1 millisecond (0.016 arc-seconds), Declination +/- 0.01 arc-seconds, Distance +/- 1 meter. The MICA results, in turn, are in close agreement with the Astronomical Almanac for 2021 and at least several previous years.

The files available here are:

LMP01p.txt  5.1 MB for 1990-2020

LMP01c.txt  328 KB for 2021-2022

LMP01f.txt   4.6 MB for 2023-2050

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 embedded spaces).


"Scary" Eclipses and "Signs of the End"!


News sites love to attract readers with attention grabbers.  The Lunar eclipse of July 5, 2020 from 03:07:48 to 05:52:01, mid-eclipse at 04:30:02 (dates and times UTC) was barely detectable by humanity (it was a partial penumbral eclipse), and the actual start and end times were detectable only by observers at the right spots on the Moon's surface.  Nevertheless, reports in the popular press termed this a scary event. As Lunar eclipses go, this was very close to a non-event.  Also, eclipses of the Moon are quite common (usually two or three per year), and visible to all cloud-free areas of the planet that enjoy a view of the night sky at the time.  The existence of "scary" newspaper articles should cause publishers to hide in shame.



revised 01/10/2021

Occultations of bright planets and stars (magnitude 3.3 or brighter) for 2021.

All dates and times here are MST (UTC - 7h)

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 Nunki 2.05 by moon 99% illuminated at phase= 189 degrees

At the time this occultation ends, the Sun will be barely below the horizon and observation will be difficult, or impossible.

06/25/2021 03:09:32.5 Start Total

06/25/2021 04:01:14.8 End Total

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 only once per day near midnight, also note that the clock display on a computer or phone is typically corrected automatically, but only 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.

For a complete listing of occultations for the next few years click here.

(Added 05/25/2020:)  Your computer is also a "clock" displaying the current time.  Computers obtain the time from very accurate sources on the Internet called network-time-servers.  However, with billions of computers in the world, computers are programmed to query these servers infrequently, thus making their accuracy as clocks somewhat chancy.  By using a web browser on your computer to query https://time.gov you can get an accurate display of the time, and a measure of the error in your computer's clock.

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.




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 future 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 farther they lie in the future. The file linked to above is refreshed several times per year, and date stamped near the end of the file.