Hi Martin - these differences may well be due to perturbations that need to be accounted for by calculations of solar, lunar and planetary returns. Michael Erlewine's Manual of Computer Programming for Astrologers, which forms the basis of much astrological programming today, mentions the need for calculation routines to take account of perturbations in orbit.

Erlewine says of the solar and lunar return routine in his book "This program makes use of a program originally submitted to MATRIX Magazine by Robert Hand. This program includes a good number of the major solar and lunar perturbations - which is why the rather good accuracy." (p. 103-104)

The solar and lunar perturbations are due to a wide range of factors.

https://en.wikipedia.org/wiki/Perturbat ... tronomy%29

Mitton (1991, 1993) in her Dictionary of Astronomy defines 'perturbation' as "a temporary or localised gravitational disturbance in the otherwise uniform motion of a body under a stable gravitational force." Essentially, each body in the solar system is subject to a range of gravitational forces which impact on its own motion and these need to be accounted for in the calculation of return positions.

Astralwanderer's answer is correct! Also, this section of the March Equinox wikipedia article is quite elucidative: the major perturbations seems to be nutation (Earth's nutation, maybe?) and other perturbations directly on the sun.

I've done the following figure which shows the solar year length compared to an average solar year of 365.2425 days (in minutes). It considers the "distance" between successive occurrences of spring equinox and shows, if I haven't commited any error, that the differences can achieve more than 25 minutes from peak to peak.
Our solar system is a quite complex clock!


Jo?o Ventura

Aha! That must be it. Thank you both very much!

Hi Martin and Jo?o

The following is from Jeff Mayo's The Astrologer's Astronomical Handbook (1976, 3rd ed.): "We can see gravity as a controlling force, keeping planets and satellites in their orbits with regard to a central body, yet it is also a disturbing influence. If it were not for the gravitational attraction of the other planets, the Earth would constantly describe the same orbit round the Sun. We call the continual disturbing effects of the other planets perturbations of the Earth's orbit." (p. 76)

This is a classic little volume that is very helpful with many astronomical concepts relevant to astrology.

The following, from wikipedia, is of course very suggestive from an astrological point of view: "On-going mutual perturbations of the planets cause long-term quasi-periodic variations in their orbital elements, most apparent when two planets' orbital periods are nearly in sync. For instance, five orbits of Jupiter (59.31 years) is nearly equal to two of Saturn (58.91 years). This causes large perturbations of both, with a period of 918 years, the time required for the small difference in their positions at conjunction to make one complete circle, first discovered by Laplace."

You can review the full paragraph at https://en.wikipedia.org/wiki/Perturbat ... tronomy%29.

One wonders about this concept of perturbations in terms of astrological 'effects': is there a system within the human body sensitive enough to register the impact of planetary perturbations on the Earth. It has seemed to me for some time that it is one of the most likely explanations for a human attunement to the solar system. Perhaps it is some part of the limbic system.

Ed

Just to keep a reference for whoever finds this thread in the future.

The source code to generate the graphics I left on my previous posts can be found at:

- Leap years to "reset" the calendar: https://github.com/flatangle/flatlib/bl ... apyears.py
- Length of solar years over time: https://github.com/flatangle/flatlib/bl ... aryears.py

It uses Flatlib and matplotlib libraries, and may be useful for someone..


Jo?o Ventura