How to Calculate a Solar Return by Hand

A recent question at Altair Astrology has motivated me to show how the solar return can be calculated by hand. Now that we have the convenience of a computer to do the calculations for us, there is also a danger that the ‘how’ – that is the calculations the computer is doing for us – are forgotten. Many of the younger generation, who have grown up with computers, may never have calculated a chart by hand and may not really know what calculations the computer is really doing, as it takes only a few seconds between a choice of a menu item and the results presented on the computer screen.

With a solar return one is searching for the time that the Sun reaches its radix position. (radix = root or birth position). Three things are known:

• the birth position
• the position at midnight (or noon depending on which ephemerides you use) for the day before the Sun reaches its radix position
• the position at midnight (or noon depending on which ephemerides you use) for the day after the Sun reaches its radix position

We are looking for an unknown; the time of the birth position. So we have the ingredients for a simple proportional relation:

daily movement of the Sun (a) : movement from previous midnight (noon) to radix position (b) = 24 hours :  unknown time (x)

simply put:

a:b = 24 : x

or

x = 24 (b/a)

Now an example. Let us say someone has the Sun at 29 Pisces 00. We want to calculate the solar return chart for 2009.

– Sun position on March 20th, 2009     29 Pisces 30 49
– Sun position on March 19th, 2009      28 Pisces 31  10 (I am using an ephemeris with midnight positions)

daily movement of the Sun (a) =  59m 39s

– radix position of the Sun                       29 Pisces 00 00
– Sun position previous midnight          28 Pisces 31  10

Suns’ movement to radix position (b) = 28m 50s

Now to use the above formula:

x = 24 (b/a)   =

24 (28m 50s/ 59m39s) =

24 (1730 seconds/3579 seconds) =

11 hours 36 minutes and 4 seconds

since we are using a midnight ephemeris the Sun reaches 29 Pisces 00 at 11:36 am GMT on the 19th of March, 2009. Now all that has to be done is decide to calculate the chart for the birthplace or if we use Morin’s method, for the place where the person is on their birthday.