Reversing a Chart - Finding the Date, Time, and Place When Not Given Software Recipes Table of Contents Contributor: Rick Hutchison E-Mail Address: hutch.56gemini@juno.com Software Recipe Title: Reversing a Chart - Finding the Date, Time, and Place When Not Given Software Requirements: any Halloran Software calculation program   This article will show you how to deduce the date, time and place that a chart was calculated for when the data is not given; in other words when all you have is a chart. A worked example using the author's natal chart positions will be given. This process appears to be lengthy and time consuming, but it can easily be done in a few minutes! It is much harder to explain all this than it is to actually do it. This article is intended only as a brief introduction to this topic. The example given involves the tropical zodiac, geocentric planetary positions for a Gregorian Calendar date in the 20th Century, and the Koch house system. Tools required: Halloran Software's Astrology For Windows, AstrolDeluxe, or AstrolDeluxe Report Writer A midnight ephemeris. A calculator with trigonometry functions. (But no knowledge of trig is required!) A map (with latitude and longitude lines) of whatever area the chart is calculated for. A geographic data source such as THE AMERICAN ATLAS or THE INTERNATIONAL ATLAS or the software version ACS PC ATLAS which is now included with Halloran Software's AstrolDeluxe Report Writer. A table of houses. SYMBOLS USED MEANING UT Universal Time LST Local Sidereal Time GST Greenwich Sidereal Time RAMC Right Ascension of the MC Obliquity Obliquity of the Ecliptic MC Midheaven ASC Ascendant RA Right Ascension ET Ephemeris Time h  Hours of time m  Minutes of time s Seconds of time º Degrees ' Minutes of arc " Seconds of arc 0h Midnight 12h Noon A QUICK OVERVIEW OF HOW IT IS DONE - The outer planets are used to find the year, the Sun points to the month and day, the Moon yields the Universal Time, the MC reveals the geographic longitude, and the Ascendant gives the geographic latitude. Then a map and a geographic data source such as THE AMERICAN ATLAS is used to find what city or town is located at the coordinates that have been uncovered. The example given here will involve planet and cusp positions given to the nearest minute of arc. Charts with planet positions and house cusps given with degrees only (no minutes) are beyond the scope of this article. It will be assumed here that the house system of the chart is one that the MC is the cusp of the tenth house and the ASC is the cusp of the first house. This would include Alcabitius, Campanus, Koch, Placidus, Porphyry, Regiomontanus, and Topocentric.  This method will work with other house systems if the MC and Ascendant are indicated. House systems such as Equal (if the MC is not given), or Morinus (if the MC and ASC are not given) are beyond the scope of this article. It will be assumed here that the software used to calculate the Author's chart positions is not known. DATA FROM THE AUTHOR'S NATAL CHART FROM SWISS EPHEMERIS SUN 27 GEMINI 23         URANUS 00 LEO 27 MOON 06 SCORPIO 05       NEPTUNE 27 LIBRA 45 Rx MERCURY 05 GEMINI 00     PLUTO 26 LEO 31 VENUS 03 CANCER 00 Rx    NODE 08 GEMINI 07 MARS 08 PISCES 08        MC 21 GEMINI 29 JUPITER 26 LEO 46        ASCENDANT 22 VIRGO 37 SATURN 27 SCORPIO 30 Rx House Cusp II 22 LIBRA 07 House Cusp III 21 SCORPIO 17 House Cusp V 24 CAPRICORN 00 House Cusp VI 23 AQUARIUS 18 WORKED EXAMPLE USING THE ABOVE DATA STEP 1: FINDING THE YEAR, MONTH, AND DAY From the Sun's position at 27 Gemini 23 it is obvious that the chart is calculated for a day in June. Looking only at the position of Pluto, flip quickly through the ephemeris to find when it was around 26+ Leo, then find the year that it was at 26 Leo 31 on the same day the Sun was at 27+ Gemini. This can be done in seconds. Next be sure that all the other planet positions in the chart occurred on that day. This will insure that the chart was calculated for this day and not some other in the past or future. Even a 10,000 year ephemeris does not contain two instants where all planet positions match exactly. From the ephemeris it is evident that the chart date is 1956 June 18, according to Universal Time. What time zone was actually used in calculating the Chart and whether Daylight Saving Time was observed or not is irrelevant.  Universal Time will be used until the final step when the location is known and the time is converted to that in use at that time and place. The ephemeris used by the author gives the planet positions for each day at 0h Universal Time (for the purposes of this article the same as GMT). An ephemeris calculated for Ephemeris Time (ET) may also be used, and it makes no difference whether the positions listed are true or apparent. The 24 hour clock will be used here instead of A.M. and P.M. STEP 2: FINDING THE UNIVERSAL TIME The key to deducing the Universal Time that a chart is calculated for is the position of the Moon. The Moon's motion varies from about 11º 48' to 15º 14' per day. From this it is evident that the Moon takes roughly between 1m 34s and 2m 02s of clock time to move one minute of arc. Usually the Moon's position in a chart will be rounded to the nearest minute of arc, allowing the time to be found within 3 minutes in the worst case when dealing with 20th Century charts calculated with any reasonably accurate software. NOTE: The vast majority of charts give the geocentric (as seen from the center of the Earth) Moon position. The slight possibility exists that the topocentric (as seen from the location on the surface of the earth that the chart is calculated for) position may be given. The topocentric Moon is also referred to as the "Parallax Corrected Moon". The difference between the geocentric and topocentric Moon can be as much as one degree. The seldom used topocentric positions are beyond the scope of this article and here it will be assumed that the Moon's position is geocentric. The method used to find the time for which a chart is calculated is the same as that used to find the time of a Lunar Return. First find the Moon position in the ephemeris before the Chart Moon and the Moon position following that of the Chart. Moon position before chart Moon           1956  June 18  12h     03 SCORPIO 40' 33" Moon position in chart                                           06 SCORPIO 05' Moon position following chart Moon        1956  June 19  0h      09 SCORPIO 58' 03" (2-1) Find the Moon's motion from the position before the Chart Moon to the Chart Moon by subtracting the Moon position before the Chart Moon from the Chart Moon position: Moon's Position In Chart                                          06 SCORPIO 05' Moon's Position Before Chart Moon                              -  03 SCORPIO 40' 33" ------------------------------------------------------------------------------------ Motion From Prior Ephemeris Position To Chart Position     =          2º  24' 27" (2-2) Find the Moon's motion during the interval between the Moon's position before the Chart Moon and the Moon's position following the Chart Moon by subtracting the former from the latter: Moon's Position In Ephemeris Following Chart Moon                 09 SCORPIO 58' 03" Moon's Position In Ephemeris Before Chart Moon                 -  03 SCORPIO 40' 33" ------------------------------------------------------------------------------------ Moon's Motion During Interval Between Ephemeris Listings    =          6º 17' 30" (2-3) Find the fraction of the time interval between the Moon's position before the Chart Moon and the Moon's position following the Chart Moon by dividing the result of  (2-1) by the result of  (2-2): Movement From Ephemeris Position To Chart Position                     2º 24' 27" Moon's Movement During Interval (Divide)                               6º 17' 30" ------------------------------------------------------------------------------------ Fraction Of Interval Between Ephemeris Listings = .3826490066 (2-4) Find the interval elapsed between the time of the Moon's position before the Chart Moon and the Chart Moon by multiplying the result of  (2-3) by the time interval between ephemeris listings for the Moon. This ephemeris lists the Moon's position for 0h and 12h so in this case the time interval is 12h: Duration Of Interval Between Positions In Ephemeris                   12h Fraction Of Interval Elapsed At Time Of Chart                   X     .3826490066 ------------------------------------------------------------------------------------ Interval To Be Added To Time Of Moon Position Prior To Chart Moon  =  4h 35m 30.44s (2-5) Find the approximate time the Chart is calculated for by adding the result of  (2-4) to the time the Moon's position before the Chart Moon is given for: Time of Moon Position Prior To Chart Moon         1956 June 18       12h 00m 00s UT Interval To Be Added To Time Of  Moon Position Prior To Chart Moon +  4h 35m 30.44s ------------------------------------------------------------------------------------ Approximate Time Chart Is Calculated For        1956 June 18       = 16h 35m 30.44s UT Most charts are calculated for whole minutes of time, so it will be assumed that this was the case with the example chart. Since the Moon does not move at a constant rate the simple interpolation used here could possibly result in the approximate chart time being off by about 4 minutes of time.  It will be assumed that the Moon's position in the example chart is rounded to the nearest minute of arc. Since the Moon takes roughly 2 minutes of time to move one minute of arc there will probably be more than one time that matches the Moon's chart position. Keeping this in mind enter the approximate data rounded to the nearest minute of time into your Halloran astrology software program, with the time zone set to UT. The geographic longitude and latitude are irrelevant at this point because geocentric planetary positions at any given instant are the same anywhere in the world. The Moon's position for the approximate chart time of 16h 36m is found to be 06 SCORPIO 06. This time is apparently too late. Entering other possible times results in the following: Date                        UT             Moon 1956 June 18          16h 36m               06 SCORPIO 06 1956 June 18          16h 35m               06 SCORPIO 05 1956 June 18          16h 34m               06 SCORPIO 05 1956 June 18          16h 33m               06 SCORPIO 04 From this data it is evident that both 16h 34m and 16h 35m are possibilities. Select one time for use with the following, keeping in mind that the other time may actually be the correct one. The 16h 34m time will be used here. STEP 3: FINDING THE GEOGRAPHIC LONGITUDE In order to understand how to deduce the geographic longitude the Chart was calculated for it will help to review how the Greenwich Sidereal Time, Local Sidereal Time, geographic longitude, and MC are related and how they are used to construct a chart. All sidereal times are local. Greenwich Sidereal Time is just what the name implies - the Local Sidereal Time at the longitude of Greenwich (0º).  The Longitude Time Equivalent is the geographic longitude divided by 15 and expressed in hours, minutes, and seconds. The difference between the Local Sidereal Times for any two longitudes at any given instant is equal to the difference in the Longitude Time Equivalents of those longitudes. Therefore when the Greenwich Sidereal Time is known then it is a simple matter to arrive at the Local Sidereal Time for any other geographic longitude. In constructing a chart the Greenwich Sidereal Time is found by first converting the Universal Time to Sidereal Time and then adding the GST listed in the ephemeris for the previous 0h. Then the Local Sidereal Time of the chart is found by finding the difference between the GST and the Longitude Time Equivalent, subtracting for geographic longitudes west of Greenwich or adding for geographic longitudes east of Greenwich.  The LST multiplied by 15 gives the RAMC, which is the Right Ascension of the MC. Then the RAMC is converted to it's position in ecliptic coordinates, which is the MC of the chart. At any given instant the MC is the same for all geographic latitudes having the same geographic longitude. In reversing this the Greenwich Sidereal Time may be found using the UT of the chart, and the Local Sidereal Time may be found from the MC. The resulting Longitude Time Equivalent is used to find the geographic longitude that the Chart was calculated for. The Obliquity of the Ecliptic is the angle between the Equator and the Ecliptic. This value changes slowly over time. THE AMERICAN EPHEMERIS FOR THE 20TH CENTURY 1900 TO 2000 AT MIDNIGHT lists the obliquity for the first day of each month. For 20th and 21st Century charts 23.45º is close enough to use in formula  (3-3). (3-1) Find the interval between 0h before the approximate Chart UT and the approximate Chart UT expressed in  Sidereal Time. This is done by changing the approximate UT from Solar to Sidereal time. This is sometimes called "The acceleration on the interval" or "ten second correction" and amounts to  9.8565s per hour. The method is to multiply the approximate UT by 1.002737909: Approximate UT of Chart                            1956 June 18       16h 34m Solar to Sidereal Correction                                      X   1.002737909 ------------------------------------------------------------------------------------ Sidereal Time interval from 0h before Chart to approximate UT     =  16h 36m 43.29s The Greenwich Sidereal Time for the 0h before the approximate UT of the Chart must be found. This is simply the Sidereal Time given in the Midnight ephemeris. Greenwich Sidereal Time Listed In Ephem. for 1956 June 18 at 0h UT = 17h 44m 50s (3-2) Find the Greenwich Sidereal Time which corresponds to the approximate UT of the Chart by adding the result of  (3-1) to the Greenwich Sidereal Time of the 0h before the approximate Chart UT. If the result is greater or lesser than 24h then subtract or add 24h to bring the GST into the range 0-24 hours: Sidereal Time interval from 0h before Chart to approximate UT        16h 36m 43.29s Greenwich Sidereal Time Listed In Ephem. for 1956 June 18 at 0h UT + 17h 44m 50s ------------------------------------------------------------------------------------                                                                     = 34h 21m 33.29s Subtract 24h to bring GST into range 0-24 hours                   -  24h ------------------------------------------------------------------------------------ Approximate Greenwich Sidereal Time of  Chart                      = 10h 21m 33.29s     (3-3) With A Calculator Find the Right Ascension of the MC using the following: RAMC = arctan ( tan MC x cos Obliquity) RAMC = arctan (tan 81º 29' x cos 23.45º) RAMC of Chart = 80º 43' 45.74"   (3-4) Find the Local Sidereal Time by dividing the result of (3-3) by 15 to change from degrees to hours: RAMC  of Chart                                                  80º 43' 45.74" Change from Degrees To Hours             (Divide)               15 ------------------------------------------------------------------------------- Approximate LST of Chart                            =           5h 22m 55.05s (3-5) Find the Longitude Time Equivalent by subtracting the result of  (3-4)  from the result of  (3-2): Approximate Greenwich Sidereal Time of  Chart                     10h 21m 33.29s     Approximate LST of Chart                                      -    5h 22m 55.05s -------------------------------------------------------------------------------- Approximate Longitude Time Equivalent Of Chart                     4h 58m 38.24s (3-6) Find the geographic longitude from the Longitude Time Equivalent using the following rules: If the Longitude Time Equivalent is positive AND less than 12h then multiply by 15 to obtain longitude west of Greenwich. If the Longitude Time Equivalent is negative AND between -12h and 0h then multiply by 15 to obtain longitude east of Greenwich. If Longitude Time Equivalent is not between -12h and +12h then it must be adjusted as follows: If LTE is greater than 12h then subtract 24h. The result will be negative, multiply by 15 to obtain longitude east of Greenwich. (Example: If LTE is 17h then subtract 24h which is -7h. -7h is equal to 105 degrees east, which is the same as going 255 degrees (17 x 15) west from Greenwich) If LTE is less than -12h then add 24h. The result will be positive, multiply by 15 to obtain longitude west of  Greenwich. Longitude Time Equivalent                                        4h 58m 38.14s Multiply by 15 Because LTE Is Positive And Less Than 12h          X   15 -------------------------------------------------------------------------------- Approximate geographic longitude of Chart                    =   74 w 39' 33.6" With the Halloran astrology software set to the date and one of the approximate times found in Section 2, 1956 June 18 at 16h 34m UT, entering the nearest longitudes gives the following results: Longitude         MC 74w41       21 GEMINI 28 74w40       21 GEMINI 29 74w39       21 GEMINI 29 74w38       21 GEMINI 30 From this it is evident that the geographic longitude that the chart was calculated for may be either 74w39 or 74w40, if the chart was calculated using whole minutes of longitude. Because astrology software programs using the ACS Atlas data, which includes version 6 of AstrolDeluxe ReportWriter, usually calculate charts using seconds of latitude and longitude it would not be wise to assume that whole minutes were used. Another fact to keep in mind is that some astrology software programs use apparent Local Sidereal Time to calculate the house cusps while others use mean Local Sidereal Time. The difference amounts at most to about 1.2 seconds of time. As a result the MC as calculated by two different software programs may differ by as much as roughly 19" of arc, which could easily cause the MC displayed to the nearest minute of arc to differ by 1'. From the above information it is evident that the geographic longitude that the example Chart was calculated for may be either 74w38, 74w39, 74w40, or 74w41, and it is also very possible that the location may lie between those whole minute values. STEP 4: FINDING THE GEOGRAPHIC LATITUDE A formula could be used to find the approximate latitude that the chart was calculated for, but it is much quicker and easier to use a table of houses. Open a table of houses to the LST nearest to the approximate Chart LST found in (3-4) to find a whole degree of latitude which roughly corresponds to the Chart Ascendant. Then enter the latitude into the Halloran software to see how close the resulting Ascendant is to the Chart Ascendant. In this case the nearest LST to the approximate Chart LST of 5h 22m 55s given in the table of houses used by the Author is 5h 24m, and 37º North looks like a good starting point since the Ascendant given for that latitude is 22 Virgo 37, the same as the Chart Ascendant. With the Halloran software set to 1956 June 18 at 16h 34m UT and geographic longitude 74w39, entering 37n00 latitude gives the Ascendant as 22 VIRGO 24. The Ascendant moves backwards in the zodiac as geographic latitude increases when the LST is between 6h and 18h, forward otherwise. This rule is valid for the Southern Hemisphere if latitudes south of the Equator are regarded as negative values, for instance 40º South =  -40º. For example when the LST is 12h 00m 00s the Ascendant for latitude 40º North is 11 SAGITTARIUS 32 and the Ascendant for 41º North is 10 SAGITTARIUS 55, and when the LST is 22h 00m 00s the Ascendant for latitude 40º North is 21 GEMINI 48 and the Ascendant for 41º North is 22 GEMINI 35. In the Southern Hemisphere when the LST is 12h 00m 00s the Ascendant for 40º South is 18 CAPRICORN 18 and the Ascendant  for 41º South is 19 CAPRICORN 05, and when the LST is 22h 00m 00s the Ascendant for 40º South is 17 TAURUS 32 and the Ascendant for 41º South is 17 TAURUS 06. LST 12h 00m Ascendant              LST 22h 00m Ascendant Latitude 41n   10 SAGITTARIUS 55   Latitude 41n    22 GEMINI 35 Latitude 40n   11 SAGITTARIUS 32   Latitude 40n    21 GEMINI 48 Latitude 40s   18 CAPRICORN 18     Latitude 40s    17 TAURUS 32 Latitude 41s   19 CAPRICORN 05     Latitude 41s    17 TAURUS 06 From this information it is evident that the latitude that the Chart was calculated for is greater than 37º. Entering 38º and 39º both also yield Ascendants that are well over 1' of arc from the Chart Ascendant, but the Ascendant for 40º is 22 VIRGO 36, which is within 1' of the Chart Ascendant 22 VIRGO 37 and therefore a possibility. Trial and error entry of latitudes would lead to the following:    Latitude         ASC 39n53 to 40n06  22 VIRGO 36 40n07 to 40n21  22 VIRGO 37 40n22 to 40n35  22 VIRGO 38 To avoid all this trial and error entry and at the same time narrow the possible range latitude the intermediate house cusps are used. In order to do this the house system used must be found if it is not indicated. Entering the latitude in the middle of the 22 VIRGO 37 Ascendant range, 40n14, with the Halloran software set to the default Placidus house system it is seen that the second house is 18 LIBRA 07 which is nowhere near the Chart's second house cusp at 22 LIBRA 07. It is evident that the Chart is calculated using a house system other than Placidus. After switching the Halloran software to Koch the house cusps all match within 1', so that is evidently the house system used. Trial and error latitude entry finds the range of latitudes yielding chart cusps that match the Chart within 1' to be between 40n14 and 40n32. STEP 7: FINDING THE TOWN OR CITY AND LOCAL TIME OBSERVED Remember from Section 2 that 16h 35m UT was also a possible Chart time. So far only 16h 34m has been considered.  Since this time is one minute LATER than the time just looked into 15' must be ADDED to the geographic longitudes at the beginning and ending longitude range. If the other possible chart time had been one minute EARLIER, then 15' would have to be SUBTRACTED. The latitude range will be the same. Therefore the Chart has been found to be calculated for somewhere within the following range of latitude and longitude: Latitude: Between 40n14 and 40n32 Longitude: Between either 74w38 and 74w41 OR 74w53 and 74w56 From the range of possible longitudes and latitudes the Chart was evidently calculated for a location in New Jersey. Looking at a map of that state it appears that Princeton has the largest population in the possible areas. The coordinates for Princeton according to THE AMERICAN ATLAS (5th Edition) and the ACS PC ATLAS are 40n20'55", 74w39'34". But it is by no means certain that this is indeed the correct location. Anyplace within the specified boundaries is a possibility. The distance covered by one minute of latitude varies slightly according to the latitude, but is equal to roughly 1.15 miles or 1.85 km at latitude 40º north (or south). The distance covered by one minute of longitude varies greatly according to the latitude, and is equal to roughly .88 miles or 1.42 km at latitude 40º north (or south). There are therefore two possible areas each covering about 2.64 miles (4.26 km) from east to west and about 20.7 miles (33.3 km) from north to south. Eastern Daylight Time was observed in this area at the time, so the chart time is either 12:34 P.M. or 12: 35 P.M.  (assuming whole minutes were used, which is probable but not a certainty). CONCLUSION OF WORKED EXAMPLE The example chart was calculated using the coordinates for Princeton, NJ that were listed in THE AMERICAN ATLAS (Third Edition), 40n21 and 74w39. The author learned to calculate his natal chart using these coordinates and saw no reason to change when a later edition listed the latitude and longitude including seconds of arc. Here is the complete data used: 1956 June 18 12:34 P.M. EDT (16h 34m UT) Princeton, NJ 40n21   74w39

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