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the astronomical year numbering system
for all years in all calendars which it supports.
Local time is your local clock time, offset from Greenwich Mean Time (GMT) by a certain number of hours (or in some cases hours and minutes).
The toggle between Greenwich and Local corresponds to an imaginary shift in location between where you are now and Greenwich (the location of the Royal Observatory, five miles west of Central London). In both cases the software reads the time from your system clock and assumes that this is correct local time. When Greenwich is selected the program assumes that the system time is GMT.
Initially local time is set to GMT. You should set the local time according to your timezone, e.g., GMT plus 3 hours. You can then switch back and forward between GMT and local time. This is useful because lunar phases and eclipse times in published sources usually give times as GMT, whereas you will also want to know the local times of these events.
Clicking on Now causes the software to read the date and time from your system clock, to display this date in the various calendars and to calculate and display the corresponding phase of the Moon.
Switching between GMT and local time does not change the appearance of the Moon, but may change the calendar dates displayed, since it corresponds to a change of timezone. For example, if your local time is GMT - 5 hours, and it is 22:00 local time on a Thursday the 10th (as read from your PC's clock) then switching to Greenwich (as if you were suddenly transported from New York to London) will cause the date and time to change to 03:00 on Friday the 11th.
Generally it is best to use local time except when comparing times with those given in GMT from other sources.
A dark moon occurs when the Sun and the Moon are astronomically conjunct (or more exactly, when either the Moon's center lies on the line joining the centers of the Earth and the Sun or the plane defined by the Sun, Earth and Moon is perpendicular to the Earth's orbital plane).
The term "new moon" is not used here, since it is ambiguous. It can mean either a dark moon or the phase of the Moon when a crescent is first visible (in which sense a month in the Muslim calendar begins at new moon).
A lunation is a passage of the Moon from one dark moon to the next. A lunation begins at the dark moon (astronomical conjunction of Sun and Moon), and the next dark moon marks the beginning of the next lunation.
The program displays a date and a time; this moment occurs within a particular lunation, and the number of that lunation is shown in square brackets []:
Lunations are numbered -1, 0, 1, 2, ... in temporal order. Lunation number 0 began with the dark moon at 18:13 GMT on 2000-01-06, following the numbering used by Jean Meeus (the lunation numbers LN are such that LN = Brown Lunation Number - 953 and LN = Goldstine Lunation Number - 37105).
The age of the Moon is the time since the previous dark moon. The percentage in parentheses gives the position of the Moon in the current lunation. Full moons usually do not occur at exactly halfway through the lunation, but usually somewhere between 48% and 52%. Dark moons, by definition, occur at exactly 0%.
The software converts among dates in the following calendars:
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Conversions may be made by entering a date in any of the calendars into the Date/time window and clicking on Convert. For dates other than astronomical and chronological Julian dates, a time may be included, as in "2003-12-31 CE 15:55". If no time is specified then 12:00 (local) is assumed.
Note that days in the Hermetic Lunar Week Calendar begin at approximately dawn, so that the time 00:00 in a HLW date/time corresponds to 06:00 in any of the other calendars.
Common Era and Julian dates are displayed (and must be entered) in ISO 8601 format, that is, year-month-day.
Note that the year-numbering system employed in date entry is the astronomical year-numbering system, in which years B.C. are represented by zero and negative integers: 1 BC = 0 CE, 2 BC = -1 CE, 3 BC = -2 CE, and so on. So the 31st of December 22 B.C. is -21-12-31 CE. For a fuller explanation see Astronomical Year Numbering.
Clicking on a date displayed on-screen (in yellow) will copy it to the Date/time window, along with the time as displayed (either GMT or local). You can then modify that date and click on Convert to obtain corresponding dates in the other calendars.
The software allows adding or subtracting a time period to or from a date in one of these calendars, either by using the Move forward/back facility or by using the Convert facility with a value specified for "days".
The display may be moved forward or backward by any of the following time periods:
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The Move button is used to move the displayed dates forward or backward by any of the above periods; it does not require any content in the Date/time window.
The Convert button is used (a) to convert a date in the Date/time window to dates in the other calendars or (b) to add or subtract a specified number of days (which may include a fractional part) given in the plus/minus window to or from a date in the Date/time window.
If you click on Convert with a value in the plus/minus window, but with the Date/time window empty, then the program will perform the addition or subtraction with the currently displayed date.
This program finds the next or previous:
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Another name for an umbral lunar eclipse is "partial lunar eclipse".
When an eclipse is found the time given for the eclipse is the time of the maximum eclipse. For lunar eclipses the maximum eclipse is visible at the stated time (GMT) over most of the hemisphere of the Earth which is facing the Moon. For solar eclipses the situation is different. The time given for the solar eclipse is the time of maximum eclipse (GMT) from a geocentric point of view (as if an observer were located at the center of the Earth). This is usually not the same as the time of maximum eclipse from the point of view of a person somewhere along the path traced by the shadow of the Sun along the surface of the Earth. For an observer located at the start of the eclipse track the eclipse will occur some hours before the time calculated by this software, and for an observer located at the end of the eclipse track the eclipse will occur some hours later.
The time of the maximum point of eclipse is usually not exactly the same as the time of the full moon or dark moon, although in the case of solar eclipses the time of the maximum and the time of the dark moon are usually only minutes apart.
The saros number is the number of the saros series (or family) containing the eclipse (saros numbers range from 1 through 223). A saros series lasts for about 1,300 years, so eclipses a millennium apart may have the same saros number. Two eclipses in the same saros series are separated by 223 lunations, i.e., 6585.32 days (this is called a saros period).
Examples will now be given involving a search for eclipses.
First, suppose one wishes to find the time of the first lunar eclipse visible in Jerusalem in the year 33 JC. The longitude of Jerusalem is about 35 degrees 24 minutes East, so true local time is GMT + 2.35 hours, i.e., GMT + 2:21. The closest local time setting allowed by the software is GMT + 2:30, so we set it to this.
Then one enters "33-01-01 JC" into the Date/time box:
Clicking on Convert produces:
One now tells the software that one wishes to search for the next lunar eclipse:
Clicking on Search produces:
From which we may conclude that an umbral lunar eclipse occurred on Friday the 3rd of April, 33 JC (April 1st, 33 CE), with the penumbral phase beginning at about 14:22 and lasting until about 19:54, and the umbral phase beginning at about 15:43 and lasting until about 18:33.
We can refine this slightly, since, as noted above, true local time at Jerusalem is not exactly GMT + 2:30. Since true local time is GMT + 2:21, the calculated times for the above eclipse should be adjusted by -9 minutes, giving: penumbral phase began at about 14:13 (true local time) and lasted until about 19:45, and the umbral phase began at about 15:34 and lasted until about 18:24. Thus the umbral phase would be ending at about the time the Moon appeared over the horizon.
It should also be noted that the value of delta T used by the software for 33 JC is subject to an uncertainty of a few minutes, so we should conclude only that the umbral phase ended in the period 18:20 to 18:28 true local time.
The dates resulting from the eight most recent operations with the software are kept in a "history" list. Any of these may be selected to restore the display to that date.
Operations are recorded in a log if Log results is checked. When the log is empty the View log button is disabled. If the results are not being logged then the last result can (usually) be added to the log by clicking on Log this result. This allows logging only of results that are found to be interesting.
| Search for next coincidence of 1sts of month. 2001-10-17 CE 12:00 (local = GMT) GLC=5-0540-10-01 MP=102-27-08-01 LLT=100-08-01-1 HLW=5001-08-1-1 AJD=2,452,200.0000 Crescent moon (waxing), illum. = 4.7%, lunat. and age = [22] 0 days, 16 hrs, 36 mins (2.3%). |
The text in the log window (or a selected part of it) may be copied into a text editor and printed from there.
Clicking on Set log preferences opens a window which allows inclusion or exclusion of various calendar dates in the log entries (see image at right).
The state of the software may be saved at any time. When quitting you are asked if you wished to save the state (unless it has already been saved). When the program starts up again it restores the last-saved state (if any).
As a second example of an eclipse search, consider the eclipse which occurred over Europe on 1999-08-11 CE. Set the time to GMT. Enter "1999-08-10 CE" (one day before) in the Date/time window and click on Convert. Then select next solar eclipse and click on Search to obtain:
| Search for next solar eclipse. 1999-08-11 CE 11:03 (local = GMT) 1999-07-29 JC (Wednesday, 5-0538-06-30 GLC, 102-25-06-01 MP, 098-05-01-1 LLT, 95-2-19-1 SLT, 4999-05-4-7 HLW, 2,451,402.4606 CJD, 2,451,401.9606 AJD Dark moon, illum. = 0.0%, lunat. and age = [-6] 29 days, 8 hrs, 39 mins (100.0%). Central total solar eclipse, lunation number = -5, saros number = 145.
Search for next dark moon. |
It is a characteristic of eclipses in a saros series that every third eclipse in the series has a similar latitude and longitude. Thus to find out when there will again be a similar eclipse over Europe we proceed as follows: First select Eclipse in same saros series then search forward to the third eclipse, to obtain:
Thus the eclipse of 1999-08-11 CE over Europe will be repeated on 2053-09-12 CE.
Here are some further examples of eclipse data produced by this software. First some solar eclipses:
| CE date + GMT | JC | AJD | Eclipse type | Saros number |
| 2001-06-21 12:04 | 2001-06-08 | 2,452,082.0028 | central total | 127 |
| 1505-02-14 06:24 | 1505-02-04 | 2,270,793.7668 | partial | 103 |
| 1000-10-06 11:11 | 1000-09-30 | 2,086,580.9661 | central annular | 108 |
| 500-02-16 09:32 | 500-02-15 | 1,903,727.8973 | central annular-total | 77 |
| CE date + GMT | JC | AJD | Eclipse type | Saros number |
| 2003-05-16 03:40 | 2003-05-03 | 2,452,775.6526 | total | 121 |
| 1502-10-25 23:05 | 1502-10-15 | 2,269,951.4618 | umbral | 128 |
| 1002-03-07 23:18 | 1002-03-01 | 2,087,098.4705 | total | 97 |
| 501-01-22 10:34 | 501-01-20 | 1,904,067.9405 | partial | 61 |
For a general discussion of Julian day numbers see Julian Day Numbers, and in particular the explanation of the difference between astronomical and chronological Julian day numbers given in Section 3 and in Section 4.
To put it briefly, astronomical Julian days correspond to 24-hour periods which begin at noon GMT, with 0 AJD beginning at noon on -4712-01-01 in the Julian Calendar, whereas chronological Julian days correspond to 24-hour periods which begin at midnight GMT at the start of -4712-01-01 Julian. (But see the exception discussed at the end of this section.) A Julian date is a Julian day number with a fractional component representing the time within the day. Thus the astronomical Julian date 1.25 AJD corresponds to 18:00 GMT on -4712-01-02 JC, whereas the chronological Julian date 1.25 CJD corresponds to 06:00 GMT on -4712-01-02 JC. Chronological Julian dates relative to the prime meridian (0 degrees longitude) are always 0.5 greater than the corresponding astronomical Julian dates (since 0.5 days = 12 hours).
An astronomical Julian date is independent of location on the Earth, since it is always relative to the prime meridian of zero degrees. A chronological Julian date, however, is longitude-dependent. A chronological Julian day begins at midnight local time, not midnight GMT. (However, when the concept is used without reference to any particular location then by default the prime meridian of zero degrees is assumed.)
In this software, when local time is set to GMT then CJD exceeds AJD by exactly 0.5 (corresponding to the 12-hour difference in the start of the day). In this case, switching between GMT and local time does not change CJD.
When local time differs from GMT then AJD and CJD will differ by 0.5 plus or minus some quantity (<= 0.5) which depends on the offset of local time from GMT. E.g., if local time is GMT plus six hours (0.25 days) then CJD will exceed AJD by 0.5 + 0.25 = 0.75. In this case, switching between GMT and local time changes CJD (and may change the dates displayed, as in the example of Thursday the 10th given above).
In a calendar whose days (nucthemerons) are divided into 24 hours and 60 minutes a chronological Julian day is the period from one 00:00 to the next. Normally 00:00 occurs at midnight local time (or midnight at some given meridian of longitude for a particular timezone). However in the Hermetic Lunar Week Calendar 00:00 occurs six hours after midnight, so a chronological Julian day in this calendar runs from approximately dawn to the next dawn. This means that chronological Julian dates, when used with respect to the Hermetic Lunar Week Calendar take their fractional component from the time elapsed from six hours after midnight, not midnight itself. So, for example, noon at Greenwich on 2007-01-01 is Julian date 2,454,102.5 for calendars whose days begin at midnight, but is 2,454,102.25 for the Hermetic Lunar Week Calendar. The display of the chronological Julian date in this software always assumes days beginning at midnight, even when the Date/time box shows a HLW date.
Both the astronomical and the chronological Julian dates reflect delta T, the difference between GMT and TDT (terrestrial dynamic time, a.k.a. ephemeris time). TDT is atomic time, and thus, unlike GMT, is independent of the rotation of the Earth. Thus the times displayed for astronomical phenomena (such as full moons and eclipses) should be close to the times observed (or, for past events, would have been observed).
Unless great accuracy is required, delta T is important only for dates in the moderately distant past or future. Currently it is about one minute. It does not reach five minutes until about 1400 CE. As regards the distant future, reliable estimates of delta T cannot be made because we do not know how the Earth's rate of rotation will change.
Delta T for years past has been calculated in two ways: (i) By reference to eclipse records. (ii) By mathematical formulae. The first method gives an estimate of delta T at specific dates which is as reliable as the historical records. The second method is needed when delta T must be calculated for any given year (as in this software) but this method is not as accurate as the first.
Delta T is calculated by this program as follows: For years 1915 and later the formula of Espenak, as given on Robert van Gent's informative webpage Delta T: Approximate algorithms for historical periods is used (since this gives the best results of all formulae from the mid-20th C. to the present). [Robert van Gent's page has been temporarily withdrawn for revision, but a copy may be found here.] For years prior to 1915 delta T is calculated as the average of all non-extreme values obtained from all formulae given on that webpage except for the IAU (1952) and the Borkowski (1988) formulae (where a value is non-extreme if it does not exceed three standard deviations from the mean).
This method may not produce values for delta T as accurate as that based on historical eclipse records, but it does come close. For example, the software calculates delta T for 33 JC as as 2 hours and 48 minutes, whereas the true value (based on historical eclipse records — see the tables given in Robert van Gent's web page) is probably 2 hours and 51 minutes.
For times in the distant past there is considerable uncertainty about the value of delta T. The uncertainty in the value of delta T outside the range -1000 CE through 2500 CE is too large for lunar phases and eclipse dates to be computed precisely, so Lunar Calendars and Eclipse Finder accepts dates only in the range -3200-01-01 CE through 6000-01-01 CE (or equivalents in other calendars).
To clarify, due to the uncertainty in delta T prior to -1000 CE the software computes dates and times accurately, but not precisely. Thus the time of an eclipse in the recent past may be computed with a precision of a few minutes, but the time of an eclipse in the distant past may have a precision of a few hours. The further back in the past, the less precise is the calculated time.
It is still possible, however, to compute the occurrence or non-occurrence of eclipses in the distant past, even if precise times are not possible. For example, eclipses are mentioned in the Indian epic the Mahabharata. Krishna and Mahabharata: Historical reality states that:
- The full moon and lunar eclipse at Krittika occurred on 29th September, 3067 B.C.
- The solar eclipse at Jyestha occurred on 14th October, 3067 B.C.
These are dates in the proleptic Julian Calendar. To check them using this software the year must be expressed in the astronomical system of year numbering: 3067 B.C. = -3066 CE.
Lunar Calendars and Eclipse Finder says that there was a partial lunar eclipse at -3066-09-29 JC 01:02 (using Indian timezone +5:30), which is 29th September, 3067 B.C. (Due to uncertainty in delta T, this eclipse might have occurred on 28th September.) The software also says that there was a total solar eclipse at -3066-10-14 JC 13:47, which is 14th October, 3067 B.C. Thus the software confirms both of the dates on that web page.
Acknowledgements: This software was developed by Peter Meyer in January/February 2002 and revised at various times up to September 2009. Support for the Hermetic Lunar Week Calendar was added in April/May 2006. The Goddess Lunar Calendar, the Liberalia Triday Calendar, the Hermetic Lunar Week Calendar and the Meyer-Palmen Solilunar Calendar were invented by Peter Meyer during 1994-2005 (the last in collaboration with Karl Palmen). The lunar phase and eclipse calculations are done using a translation into C of a FORTRAN routine originally written by astronomer Robert van Gent (based on Jean Meeus's Astronomical Algorithms, Willmann-Bell Inc., Richmond, 1991, pp. 319-324 & 349-358), who kindly gave permission for its use as the basis for the astronomical functions in this software. Thanks also to Karl Palmen for beta testing and to Simon Cassidy for helpful comments.
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