Wednesday, March 08, 2017

The Accuracy of Historical Solar Returns

©2017 J. Lee Lehman, PhD

In Classical Solar Returns, I discussed accuracy issues with respect to the accuracy of the calculation of solar returns, even as recently as several hundred years ago.1 This critique was based on wok that has been done on the accuracy issues facing ancient astronomy and its attempts to create accurate orbital equations within the geocentric system of circular orbits that were how these orbits were computed prior to Johannes Kepler.2 The conclusion of Morelon was that there was a genuine question of the accuracy of such returns.

Recently I began perusing Abraham ibn Ezra’s work on solar returns, and was stunned to discover that the very first paragraph in the work gives the method for computation which, examined carefully, gives a method for computation which turns out to not be as inaccurate as I had been led to believe.3 The method was simple, but definitely not what I learned myself when doing by-hand computations, lo! So many decades ago. In ibn Ezra’s method, the calculation was done by adding 365 days, plus 5 hours and 49 minutes to the time of birth for the next year after birth, and then repeating the computation as many times as necessary to arrive at the desired age of solar return. By contrast, our modern method was to interpolate between the time (noon or midnight) in the ephemeris for the day before the solar return to the day after, to arrive at the precise degree of the Sun, preferably expressed to complete minutes and seconds.

The figure 365 days plus 5 hours and 49 minutes is ibn Ezra’s figure for the length of the mean solar day. In other words, the solar return calculation is by definition, the time between the occurrence of the Sun at a particular degree and minutes, and the next time the Sun returns to that point is the solar day. My question was: how accurate is this? Ah, the internet is our friend, and so I found a very helpful page detailing modern ideas about this.4 It turns out the modern figure is 365 days + 5 hours plus 48.75 minutes: just 0.25 minutes less than ibn Ezra’s! This told me immediately that, while ancient figures would nt completely agree with modern ones, they would be fairly close.

To assess this concept in practices, I did the first few solar returns for Julie Andrews, whose chart I just so happened to have up in Sirius at the time. Here are the results.

Solar Return Year
Time computed in Sirius
Ascendant degree
Time computed by ibn Ezra method
Equivalent Ascendant degree
27 Sc 43
26 Sc 52
02 Pi 51
02 Pi 40
14 Cn 27
15 Cn 23
18 Vi 16
17 Vi 43
19 Sc 40
19 Sc 08

Natal data (B): 1 October 1935, 6:00 am, Walton-on-Thames, England.

As you can see, these are not huge differences: all amounting to less than a degree on the Ascendant.

1 Lehman, J. Lee. Classical Solar Returns. Atglen, PA: Schiffer Press, 2012, p. 19.
2 Morelon, Régis, “Eastern Arabic Astronomy between the eighth and eleventh centuries,” pp 20-57 in Rashid, Roshdi, and Régis Morelon, Encyclopedia of the History of Arabic Science. London ; New York: Routledge, 1996.
3 Ibn Ezra, Abraham, and Shlomo Sela. Abraham Ibn Ezra on Nativities and Continuous Horoscopy : A Parallel Hebrew-English Critical Edition of the Book of Nativities and the Book of Revolution. 2013, p. 373.

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