This page of explanations was revised on 05/08/2017.

Note: The detailed listing 1A, and listing 1B, were revised on 05/08/2017 (see notes near the bottom of this page).  Any copies of editions before that date  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 more.   The table covers 2017 through 2020. Recalculated 8/01/2017

Note:  The columns marked "Solar Time", "LV" (Local View), "Sun elev.", and "Moon elev." give data unique to the location of the Hidden Valley Observatory (HVO).  The column "LV" is a recent addition giving information on the visibility of eclipse events as viewed at HVO. To find lunar and solar eclipses that can be seen locally, look for entries in this column.

For Lunar Eclipses you will see, h = hypothetical (the moon is partially inside the penumbra and completely outside the umbra - thus the effect may be difficult to detect), f = faint (the moon is inside the penumbra, but not inside the umbra), P = partial (the moon is partly inside the umbra), or T = total (the moon is completely inside the umbra). This column is blank when the moon is below the horizon at HVO during an eclipse.

For Solar Eclipses you may see, P = partial (the sun is partly blocked by the moon as seen at HVO), or A = Annular (the sun appears as a ring around the moon), or T = total (the sun is completely hidden by the moon). This column is blank if the moon is below the horizon at HVO, or if the sun may be eclipsed as seen elsewhere, but not as seen at HVO.

Starting in late November of 2016, the dichotomies of Mercury and Venus are listed. Click here for more information.

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 December 31, 2017, the adjustment is only my estimate (no official announcement for DUTC beyond that date has been issued).

The adjustment table used (as revised May 5, 2017) is:

Seconds subtracted from TT to derive UTC (DUTC):

(Values after 2017 are predictions)

Year (UTC)

As of January 1 (UTC)

As of July 1 (UTC)























































The above table was revised extensively on May 5, 2017.  

In current practice (started in 1972) a second of time (UTC) exactly equals a second of time (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 2017 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 the listed UTC time 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 May, 2017 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.

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 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, and Saturn, 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.

About eclipses:

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 minimal.
     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:

Total Lunar

Totally within the earthís umbra.

Partial Lunar

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 listed

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:

Total Solar

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 will be total for viewers as close as Alliance, NE and nearly total in Rapid City.

Annular Solar

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.

Partial Solar

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.  Recalculated 8/01/2017

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, provided 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 2017 and 2018. (N.B. this is a large file.)  See NOTEs below. Recalculated 8/01/2017

Note: Beyond 2017, the value of DUTC is a best guess 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 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 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 the August 1, 2017 edition: The tables, 1A and 1B, were recalculated using the latest data for DUT1.  The changes were 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: A revised value for the (equatorial) radius/diameter of the Moon is 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, 03/30/2017