A personal blog by George Gladfelter
About Lunar Eclipses and the May, 2022 eclipse in particular
09/25/2025
Eclipses occur fairly regularly, typically 2 or 3 lunar eclipses, and a total of 5 lunar and solar eclipses, per year. However, for any one specific location on Earth, visibility of Lunar eclipses is hit or miss, and Solar eclipses are rarely visible.
In the western part of
North America, the following total Lunar Eclipses will be visible in the
remainder of this decade
(dates and times are UTC - 7 hours for the total eclipse phase):
03/03/2026 04:04 to 05:03
06/25/2029 19:31
The following total Lunar eclipses will not be visible
from South Dakota:
09/07/2025
12/31/2028
11/20/2029
For the following Solar Eclipses, only one will be
visible from Rapid City, SD:
09/21/2025
02/17/2026
08/12/2026
02/06/2027
08/02/2027
01/26/2028
07/22/2028
01/14/2029 visible 08:33 - 11:31 MST
06/12/2029
07/11/2029
12/05/2029
When do the seasons change?
09/25/2025
In March of each year, the Sun, in the view of people on Earth, is moving steadily north and the line from center of the Sun to the center of the Earth crosses the Earth's equator at a specific time called the Equinox. In June, the Sun's northward movement ceases at a time called the Solstice, and becomes a southward movement resulting in another Equinox in September, and another Solstice in December.
However, the tradition among astronomers is to compute the angle called the Solar Ecliptic Longitude (the angle on the celestial sphere between the Sun at the March Equinox, and the Sun at the current time) and determine the times when that angle is 0, 90, 180, or 270 degrees for these events. There are other refinements also involved, so the whole concept of when the seasons change is somewhat flakey, but the major point is that the timing is not tied to any exact multiple of 24 hours, so not tied, year after year, to a specific day of the month.
Here are the traditional dates for 2025-2029 in the TT time scale.
Year
March
June
September December
2025 03/20 09:03
06/21 02:43 09/22 18:20 12/21 15:04
2026 03/20 14:47
06/21 08:26 09/23 00:06 12/21 20:51
2027 03/20 20:26
06/21 14:12 09/23 06:03 12/22 02:43
2028 03/20 02:18
06/20 20:03 09/22 11:46 12/21 08:21
2029 03/20 08:03
06/21 01:49 09/22 17:40 12/21 14:15
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 2021-2022LMP01f.txt 4.6 MB for 2023-2050If 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"!
09/14/2020
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.
Occultations
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
04/24/2021
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.