ACCURACY OF DIRECT & Rx TIMES AND INGRESSES
IN ASTROLOGY SOFTWARE
Copyright © 2006 All Rights Reserved
by David Cochrane
Different programs give different values for the time that a planet turns Rx or Direct. The reason for this is that the planet has essentially no movement for a very long time, and extremely accurate calculations are needed to determine the time that the planet turns Rx or Direct.
For example, someone sent me the time that Mercury turns Rx on July 23, 2005 according to several sources. The times vary by up to 6 minutes. In order to determine when Mercury turns Rx, the accuracy of calculations must be less than 1 second of arc. On July 23 Mercury stays within 1 second of arc from about 2:53 AM to 3:07 AM GMT.
ACCURACY OF DIRECT & Rx TIMES:
Kepler 7 gives a time of 3:00 AM GMT on July 23, 2005 for the time that Mercury turns Rx. To determine how accurate this time is, I stopped Kepler to view the positions to more than 1" of accuracy.The positions that Kepler calculates from 2:58 to 3:01 AM are shown below:2:58 AM: 140.46986417
2:59 AM: 140.46986423
3:00 AM: 140.46986423
3:01 AM: 140.46986422
This shows that Mercury turned Rx at either 2:59 AM or 3 AM, showing that Kepler is as accurate as is possible given the technology available today. Kepler uses the Swiss Ephemeris calculations, and these are highly regarded as the most accurate calculations available on a desktop computer. The positions listed above are as accurate as is possible today.
Someone sent me these values obtained from various sources for the Mercury station:A popular computer program: July 23, 2:55 AM GMT
The American Ephemeris 2001-2010: July 23, 3:01 AM UT
The American Ephemeris for the 21st Century 2001-2050: July 23, 2:55 AM UT
The Mountain Astrologer magazine, June/July 2005, page 99: July 23, 2:55 AM GMT
Celestial Influenes Calendar: July 23, 3:00 AM GMT
Of these sources, only the Celestial Influences Calendar and Kepler 7 produced the result of July 23, 3:00 AM GMT, and have the hightest accuracy possible today for the purposes of astrologers.
ACCURACY OF INGRESS CALCULATIONS:
A customer noticed that for the Sun Ingress into Cancer for Los Angeles, California, Kepler gives a time of 5:25:52 AM PDT. He ran several other programs, with times varying from 5:23 to 5:26 AM. House cusps move about 1 minute in 4 seconds of time so a difference of a half minute, for example, would affect house cusp positions by 7 to 8 minutes on average, and sometimes more.
The Sun moves about 1 degree per day, which is equal to about 2 1/2 minutes of arc per hour, or 1 second of arc per 24 seconds of time. In other words, the Sun takes about 24 seconds of time to travel 1 second of arc. By trying different times I found that Kepler calculates the Sun to be at 0 degrees, 0 minutes, and 0 seconds of Cancer from 5:25:39 AM to 5:26:03 AM, which is 25 seconds, which is a reasonable value to expect. At a time about halfway through these 25 seconds, the Sun ingresses into Cancer. As one of the programmers of Kepler, I can stop the program during calculations, and by doing so I confirmed that the Sun entered Cancer between 5:25:51 AM and 5:25:52 AM, exactly the time that Kepler calculated. Therefore, Kepler's calculation is precisely accurate!
The only factor that could affect Kepler's accuracy is the accuracy of the calculation of the Sun's position. Like most astrology programs, Kepler uses the Swiss Ephemeris calculations, which are accepted as the most accurate available for astrology software. Therefore, the accuracy is the highest possible at this time. Interestingly, Kepler is the only program of the programs tested by this customer that calculated precisely the correct time of the Sun ingress into Cancer.
If you are a Kepler user, note that you can select Ingress charts and also eclipse charts and some other charts by selecting the "Get a Group" button in the data entry screen.
A FINAL TECHNICAL NOTE:
Kepler is using the assumptions that astrologers use, which is to take into account the time it takes for light to reach the Earth, not use refraction of light, etc., whereas astronomical calculations are sometimes, but not always, based on a different set of assumptions than what astrologers use.
There may be other factors that account for the discrepancy in times given by different programs that I am not aware of, but based on the above analysis, I believe that Kepler 7 produces a time for the stations of planets that is as accurate as is possible.
AUTHOR: David Cochrane