©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 byhand 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

09/30/1936

11:53:43

27 Sc 43

11:49

26 Sc 52

09/30/1937

17:38:21

02 Pi 51

17:38

02 Pi 40

09/30/1938

23:22:15

14 Cn 27

23:27

15 Cn 23

10/01/1939

05:19:09

18 Vi 16

05:16

17 Vi 43

09/30/1940

11:09:16

19 Sc 40

11:05

19 Sc 08

Natal data (B): 1 October 1935, 6:00 am, WaltononThames, England.
As you can see, these are not huge differences: all amounting to less
than a degree on the Ascendant.
2
Morelon,
Régis, “Eastern Arabic Astronomy between the eighth and eleventh
centuries,” pp 2057 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
HebrewEnglish Critical Edition of the Book of Nativities and the
Book of Revolution.
2013, p. 373.