NOTES ON MOON PHASES AND LUNAR AND SOLAR ECLIPSES
April, 2019 edition.
Note: Any copies of old editions of files 1A or 1B should be discarded.
Click here for a note on the accuracy/inaccuracy of the times listed in these tables.
1A. Click here to see the table of eclipses, moon phases, equinoxes, and solstices, and other solar system phenomena.The table covers 2019 through 2022. April, 2019 edition. Click here for the same table, but keyed to the Journey Museum and Learning Center with date and time in MST (not MDT, but when MDT applies the time is flagged). April 20, 2019 edition.
Another file is available to provide details for solar eclipses. When a lunar eclipse is in progress it is visible to observers scattered over about half of our planet, if clouds do not intervene. In the case of a solar eclipse, however, at any one time there is only one point on earth that is geometrically the ideal place from which to view the eclipse, and from other locations the eclipse might be only partial, or not even be visible. Therefore, it is desirable to have the detailed data provided in this file if you plan to travel to an observing location.
1B. Click here for a listing with the following details concerning solar eclipses for 2019-2020. (N.B. this is a large file.) March, 2019 edition.
The items listed are described below:
Date and Time (UTC): The date and time are listed in Coordinated Universal Time. Add 7 hours to MST to obtain UTC, or 6 hours to MDT. UTC is disseminated by shortwave radio (WWV is available at 2.5, 5.0, 10.0, 15.0, and 20.0 MHz, WWVB at 60,000 Hz is used by radio-controlled clocks <so-called atomic clocks>, but these clocks typically reset only once per day and may display the time with an error on the order of one second. UTC can also be derived from GPS signals, but some GPS receivers may convert GPS Ephemeris time to UTC unreliably while still displaying location correctly. Computers use the internet to obtain the time, but may develop large inaccuracies due to infrequently fetching time checks (once per day or once per week).
DoW is the day of the week for the listed date.
UT1 is the time determined by the rotation angle of the Earth. See "DUT1" below.
TT is "Terrestrial" (Dynamical) Time. A bit of a misnomer. Although defined differently, it corresponds to Ephemeris Time and is independent of Earth's rotational angle which advances at a variable rate. TT and atomic time advance at the same rate in units of the SI second. This is (nearly) the time scale used in the calculation of phenomena beyond the Earth's atmosphere.
Solar Time HVO is the time defined by the apparent position of the Sun at the Hidden Valley Observatory. It is derived from UT1 with corrections for the longitude of HVO and the equation of time which arises from tilt of the Earth's rotational axis and the Earth's orbit being elliptical.
LV is a code for eclipses designating the type of eclipse seen by an observer at HVO. Se the boxed information below.
Sun elev. HVO is the elevation of the Sun in degrees above the horizon at HVO.
Moon elev. HVO is the elevation of the Moon in degrees above the horizon at HVO.
DUTC is the value of TT-UTC (in seconds) used in the computation of the listed event. See below.
DUT1 is the value of TT-UT1 (in seconds) used in the computation of the listed event. See below.
For listing 1B giving detailed data for Solar Eclipses, the following additional items are provided:
K is a code showing the eclipse stage: 0 = no eclipse, 1 = partial, 2 = annular, 3 = total.
Pct. is the percentage of the Sun's disk obscured by the Moon at the listed time for an observer at the listed position.
Obs. Lat. is the observer's latitude (at which the best view of the eclipse should be obtained).
Obs. Long. is the observer's longitude (at which the best view of the eclipse should be obtained).
Sh. Diam Narrow is the width of the Moon's shadow (in kilometers) on the surface of the Earth.
Sh. Diam Wide is the length of the Moon's shadow (in kilometers) on the surface of the Earth.
T/A start is the time in seconds, relative to the tabulated time, when the total or annular phase of the eclipse starts at the observer's location.
T/A end is the time in seconds, relative to the tabulated time, when the total or annular phase of the eclipse ends at the observer's location.
All of the tabulated data are computed in what used to be called Ephemeris Time (ET), but is now called Terrestrial Time (TT). The times denoted as UTC (Coordinated Universal Time) are derived by subtracting an adjustment from TT. After June 30, 2019, the adjustment is only my estimate (no official announcement for DUTC beyond that date has been issued yet).
In current practice (started in 1972) a second of time (UTC) exactly equals a second of time (SI and TT) and the difference (TT-UTC) is always 42.184 seconds plus the number of positive leap seconds since 1972-January-01 (minus the number of negative leap seconds, but so far there have been none, and none are likely). However, for all dates in the future, the value of DUT1 is a predicted value, and following 2018 the value of DUTC is also a predicted value based on the predicted value of DUT1. If the listed value in the table for Delta-T (DUTC = TT-UTC) proves to be wrong, it will be advisable to correct predicted UTC times accordingly.
The estimated value of DUT1 (DUT1 = TT-UT1) is listed in the detailed data, and to the extent it is in error affects the calculation of local solar time, eclipse paths, and apparent positions above the horizon. The values listed after September 1, 2018 for DUT1 are predictions subject to correction.
The column labeled "Solar Time" shows the apparent local solar time at the Hidden Valley Observatory. This is a function of date, time (UTC), DUTC, DUT1, and longitude.
To convert UTC to MST, subtract 7 hours. For
MDT, subtract 6 hours.
Example: May 26, 02:43 UTC = May 25, 19:43 MST = May 25, 20:43 MDT = 7:43 PM MST = 8:43 PM MDT.
The phase of the moon (0 degrees for a New Moon, 90 degrees for First Quarter, 180 degrees for a Full Moon, 270 degrees for Last Quarter) is defined as the difference in the longitude of the sun compared to the longitude of the moon measured along the ecliptic of date. The tabulated times are then derived by subtracting the time zone adjustment listed above so as to have the time on the UTC time scale. Note that New Moon does not usually correspond to minimum angle of separation (Sun - Moon), or 50% illumination for first quarter, and so on for the other lunar phases. The times for minimum illumination, 50 percent, and maximum are also listed.
About Planetary Phenomena:
For the inferior planets Mercury and Venus, the date and time when the planets appears at its greatest elongation (calculated as the geocentric angle of separation between the planet and the sun) is of interest since the closer the planet appears to be to the Sun, the less able we are to see it. However, the time of greatest elongation is not always the same as the time of maximum brightness, nor is it always the time that the planet is highest above the horizon at the time of twilight.
Although the times listed for greatest elongation are given to the nearest second, the normal practice for elongation times is to list only the hour. In addition, the calculated times of dichotomy (the times when the planet's apparent disk is 50% illuminated and the phase is 90 degrees) are listed; but, actual observations of this may be valuable although they may be difficult for several reasons.
For the superior planets Mars, Jupiter, Saturn, etc., the date and time of opposition (based on apparent ecliptic longitude) are listed. The planet should be an all-night object at, and near, this date. In addition, the date and time when the planet will appear to be closest to the Earth is listed (i.e. the fact that we see a planet not where it is, but rather where it was due to the finite speed of light, is taken into account). Note: Other sources usually list planetary distances as "geometric" or "actual" meaning that light-time is not taken into account when giving the distance, or the time of least distance; nevertheless these sources may list the spherical coordinates of the planet as "apparent" with the coordinates corrected for light-time. Note: heliocentric coordinates are not listed here, but in other sources when heliocentric coordinates are listed it is customary not to take light-times into account.
For some planetary events, the apparent size of the planet's disk is given in arc-seconds.
For the planets (Pluto not included) the times of perihelion (closest to the Sun) and aphelion (farthest) are listed. Formerly, these times listed only for the Earth.
For the bright planets (Mercury through Saturn), conjunctions of two planets are noted. But, the concept of "conjunction" is complicated. The traditional definition is the moment when the right ascensions are equal. This time is listed as "Conjunction (RA)". However, right ascension is measured in Earth's equatorial plane, and planetary orbits are closer to the ecliptic plane. The conjunction time when when ecliptic longitudes are equal is also listed, but without the "(RA)" designation. Finally, the time when the apparent angle of separation between the two planets is least is listed as "------ and ------ closest (x.xx deg.)" "NEAR SUN" is added if the conjunction is within five degrees of the sun, otherwise "NEAR SUN" is omitted.
Starting with the April, 2019 edition, Lunar Occultations of a bright planet, or a bright star, are noted along with the best observing point on the Earth at the time when the angle object-center to Earth-center to Moon-center is minimal.
A Lunar Eclipse occurs when the moon enters into the
earthís shadow, or a Solar Eclipse occurs when, as viewed from some spot on the surface of
the earth, the moon blocks the light from some portion of the sunís visible
disk. The time noted at "midpoint" in an eclipse is the time when the angle between the geocentric vector
from earth to the moon, and the geocentric vector from the earth to the sun is
It seems that some authorities use a definition of "maximum" for solar eclipses based strictly on right ascension. However, this seems to be mistaken. The times listed here for midpoint of the eclipse are in close agreement with the data published by Espernak and Meeus.
In the calculations on which these tables are based, the lunar coordinates have been corrected for a discrepancy between the moonís center of figure and center of mass.
In a Lunar Eclipse, when the moon enters the earthís penumbra there is no visible change in the moonís appearance. For the purpose of listing eclipses, therefore, the following criteria have been used.
Lunar Eclipse Phase Listed as:
The moon is:
Totally within the earthís umbra.
Partly, but not completely, within the earthís umbra.
Penumbral Lunar (faint)
Completely within the earth's penumbral shadow.
|Partial Penumbral (defines first and last contact in the supplied table)||Partly within the earth's penumbral shadow.|
Not eclipsed by the earth.
For solar eclipses, the following criteria are used.
Solar Eclipse Listed as:
The moonís shadow on the surface of the earth:
Completely blocks the view of the sun for observers at some point or area on the surface of the earth. None of the solar eclipses for 2013-2030, and well beyond, will be total as seen from Rapid City, but the August 21, 2017 eclipse was total for viewers as close as Alliance, NE and nearly total in Rapid City.
Blocks the central part of the sun's disk, but the moon is completely surrounded by a ring of sunlight because the sun's apparent size is greater than the moon's.
Blocks an off-center part of the sunís disk, but the criteria for a total or annular eclipse are not met.
No eclipse (i.e. prior to the start of an eclipse, or after the end of an eclipse)
The moon's shadow misses the surface of the earth. There is no solar eclipse.
The midpoint time of the eclipse is based on the Apparent Right Ascension and Apparent Declination of the sun and of the moon without allowance for atmospheric refraction. However, for lunar eclipses the earthís umbra is calculated using 1.015 times the earthís equatorial radius to account for the fact that the earthís atmosphere effectively blocks grazing sunlight. (Some other sources use a factor of 1.02.)
The elevation of the sun above the horizon at the time listed for an eclipse is for an observer at the HVO observatory.
The elevation of the moon above the horizon at the time listed for an eclipse is for an observer at the HVO observatory.
The values of delta-T used to compute the time on the UTC scale, and the UT1 scale, are listed in seconds.
1A. Click here to see the table of eclipses, moon phases, equinoxes, and solstices, and more.
File 1B provides details for solar eclipses. When a lunar eclipse is in progress it is visible to observers scattered over about half of our planet (if clouds do not intervene locally). In the case of a solar eclipse, however, at any one time there is only one point on earth that is geometrically the ideal place from which to view the eclipse, and from other locations the eclipse might be only partial, or not even be visible. Therefore, it is desirable to have the detailed data provided in this file if you plan to travel to an observing location.
1B. Click here for a listing with the following details concerning solar eclipses for 2019-2020. (N.B. this is a large file.) See NOTEs below.
Day of week
Time (TT, Terrestrial Time (formerly called Ephemeris Time, this clocks in step with Atomic Time)
Local Solar Time at the observer's location (as listed on the same line)
"K" = eclipse stage; 0 for no eclipse, 1 for partial eclipse, 2 for annular eclipse, 3 for total eclipse
Percent of sun's disk blocked by the moon for an observer at the specified location
The observer's ideal location (Latitude and Longitude, WGS84 coordinates)
Shadow width in kilometers (the shadow is approximately an oval on the Earth's surface, this is the width of the oval)
Shadow diameter in kilometers (this is the length of the oval)
Time in seconds when the total or annular phase started at the observer's location before the time in column two
Time in seconds when the total or annular phase
will end at the observer's location after the tabulated time
(The total duration is formed by subtracting the start time from the end time; e.g. for a start of -81.1 and an end at 80.9 the total duration would be 162.0 seconds.)
DUTC = TT - UTC (as estimated at the time of the calculations)
DUT1 = TT - UT1 (as estimated at the time of the calculations)
Note: Beyond the current year, the value of DUTC is a guess made after researching official past data and predictions. For all future dates, the value of DUT1 is a guess based on data for which the uncertainty is greater than for DUTC. The values for DUTC and DUT1 are listed so that if they prove to be wrong, you may adjust the tabulated data, or look for a more current source. For example, if on a given date DUTC turns out to be 69.184 rather than a listed value of 68.184 seconds, you would need to subtract 1 second from the tabulated UTC time. Note that DUTC is always an integer plus 0.184 seconds.
However, to the extent that the value of DUT1 is off, a correction will be needed in the longitude column. For example, if DUT1 turns out to be 68.987 seconds rather than the listed estimate of 68.639 seconds, the difference of +0.348 seconds will displace the eclipse track, in this example, to the east by 0.348 x 15/3600 degrees = 0.00145 degrees of longitude. A correction by a negative number of seconds would displace the shadow's location to the west.
The corrections concerning DUTC and DUT1 must be made separately.
A NOTE concerning editions after August 1, 2017: These tables, 1A and 1B, have been recalculated using the latest data for DUT1. The changes are rather small, and many items remained unchanged.
A NOTE concerning the May 8, 2017 edition: The estimates of DUT1 were revised using the latest data and predictions from IERS. Nevertheless, the error in DUT1 during the August solar eclipse may approach 60 milliseconds. Because DUTC is tied to the atomic clock system, DUTC will be exactly 69.184 seconds throughout the year 2017.
A NOTE concerning the April 10, 2017 edition: The estimates of DUT1 were revised using the latest data and predictions from IERS. Nevertheless, the error in DUT1 during the August solar eclipse may approach 100 milliseconds. Because DUTC is tied to the atomic clock system, DUTC is exactly 69.184 seconds throughout the year 2017.
A NOTE concerning the April 4, 2017 edition: The radius of the Moon and the radius of the Sun were updated, and the tables were then recomputed. This does not change the tables drastically, but the changes are detectable for eclipses..
A NOTE concerning the March 15 and 27, 2017 editions: The methodologies for using the coordinates of the center of the Moon's figure rather than the center of mass, and for computing the Moon's coordinates in 2017, were revised.
A NOTE concerning the 2/25/2017 edition: Revised values for the equatorial radius and diameter of the Moon are now being used, starting with this edition, in order to bring the calculated duration times of solar eclipses into closer agreement with the Astronomical Almanac. This has little effect with regard to starting and ending times, and none on times for maxima.
A NOTE concerning the1/30/2017 edition: The latest revisions to the calculation of DUT1 and DUTC have been used, and for the lunar ephemeris on August 21, 2017 interpolation of hourly data from JPL's Horizons system has been used to improve (I hope) the accuracy of the eclipse data on that date.
A NOTE concerning the 4/05/2016 edition: in order to calculate the time at which a distance is greatest, or least, it is necessary to be able to calculate the distance for a moment in time, and then search for the time when the distance is least or greatest. The search is rarely an efficient process. To prepare this edition, the mathematical approach to finding the time was improved in terms of efficiency and the accuracy improved to .08 seconds before tabulating the time to the nearest whole second. In general, this changed the results, in comparison to previous editions by 0, 1, or 2 seconds, and rarely by ten seconds or more. But please remember that the moment of reaching a greatest or least distance cannot, in general, be determined with precision by direct observation.
A NOTE concerning the 3/14/2016 edition: previous editions used an approximate formula to estimate the parallax effect on the apparent location in the sky of the moon when estimating the duration of totality. However, the approximation, when used without iteration, produces errors on the order of 0.001 degrees. Starting with the 3/14/2016 edition, a mathematically exact method of taking parallax into account is being used which results in revisions of perhaps two to four seconds in the computed duration of totality. The refined computation of the apparent coordinates of the moon and the sun has made some very slight changes in other tabulated items.
George Gladfelter, BHAS, 03/20/2019