A personal blog by George Gladfelter


It Happens About Once in Twenty Years

12/23/2020 revised 01/10/2021

The planets Jupiter and Saturn are close together, as seen from Earth, about once every 20 years.  In 2020 they were 0.102 degrees apart at 18h UTC on December 21st.  On average Jupiter and Saturn draw close together every 19.86 years with minimum separation values (for 1600 to 2200) ranging from 0.086 (in 1623) to 1.215 degrees (in 2100).  Thus, to find a closer encounter of these two we have to go back to 1623, or forward to 2080 (0.100 degrees).  Thus, over the span of six centuries, 2020's conjunction is the third closest of 31 occurrences. 

On the night of December 21st at Rapid City, SD (2020-DEC-22 00:30 UTC) Jupiter (magnitude -2.0) and Saturn (mag. 0.6) did appear 9.7 degrees above the horizon and 0.1056 degrees apart.  Even for one with old, poor eyesight the two were visible as two separate objects, although the difference in brightness (2.6 magnitudes) could cause one to think the two had merged into one bright object.  This was not visually all that spectacular - but still, the third closest conjunction in a span of six centuries is noteworthy.


High Precision Daily Polynomials 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 formerly gave 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) No polynomials for years after 2018 were posted, and the practice in the past was not to post beyond the then current year.  

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

(3) The polynomials posted by USNO appeared 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 meant that the polynomial for 24 hours at the end of one day would not give the same value as the polynomial for the next day at zero hours.  The polynomials given here are computed so as to minimize the discontinuities between one day and the next - with the maximum error 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 one day and 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 files available here are:


LMP01a.txt  4.4 MB for 1990-2017 (01/01/1990 - 12/30/2016)

LMP01p.txt  492 KB for 2017-2020 (12/31/2016 - 12/31/2020)

LMP01c.txt  328 KB for 2021-2022 (01/01/2021 - 12/31/2022)

LMP01f.txt   4.8 MB for 2023-2050 (01/01/2023 - 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 embedded spaces).





If you have any interest in astronomy, you probably knew that the recent equinox occurred at 13:31 UTC (or thereabouts) on September 22, 2020. 

But, in the popular press, the time was often given as 13:30 UTC, or an equivalent local time such as 9:30 AM EDT, or 7:30 MDT. Also, the equinox was often explained to be the time when the Sun was directly over Earth's equator (i.e. zero declination). Both of these details are close to being correct, but not quite. 

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 season.  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 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 tied to that rotation). Thus, predictions of the civil times of the seasons (UTC, EST, etc.) are dependent on an unpredictable offset between Terrestrial (dynamical) Time (TT) and UT1 (the time defined by the Earth's rotation around its axis) and thus also between TT and Coordinated Universal Time (UTC).  

Perhaps I should also mention that since the publicized time of the recent equinox was commonly rounded to the nearest minute, and probably computed months ago when the value of (TT-UTC) for September 22 was only an educated guess. So now we can only guess about the process that led to a predicted time of 7:30 AM MDT rather than 7:31.  It's no wonder that the popular press has problems when announcing the time when a season starts, or attempts to explain exactly what the announced time signifies.



"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) were 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.  As Lunar eclipses go, this was very close to a non-event.  Also, eclipses of the Moon are quite common (commonly 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.


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 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.