Spherical Astrology
Copyright © 2006 by Lance Carlyle Carter

   See the tables below for a comparison between spherical angles and longitude only angles as well as a table with a comparison between spherical angles and right ascension alone.
   Spherical astrology uses spherical trigonometry to determine the three-dimensional relationships between the celestial bodies, including the Sun, Moon, planets, asteroids and stars. The astrological influences of the celestial bodies are intensified when specific angles are formed between two or more celestial bodies. These angles must be computed with the use of spherical trigonometry to be totally accurate.
   Traditionally, astrologers make computations of angles between celestial bodies based on their longitudinal position on the ecliptic, which is the apparent path of the Sun. The Sun is always 0 degrees latitude. Because we work with a two-dimensional horoscope, the angle computations aren’t always correct from a spherical point of view.
   Astrological interpretation has favored the use of conjunctions, oppositions and squares in transit analysis. These are the three aspects whose computed times are approximately the same whether using spherical trigonometry or the conventional method of subtracting longitudes. An astrologer using a trine, sextile or minor aspect for a prediction may interpret it accurately but compute the wrong time and miss on the exact timing of the prediction.
   Some knowledge of the principles of spherical trigonometry can help, even if exact spherical calculations are not made. At least the astrologer can know where his calculations are likely to be inaccurate. One would estimate the spherical distance between planets to figure if those planets are in the orb of an aspect. Note that celestial latitudes are used in judging spherical angles, not declinations. Celestial latitude adds a third dimension to an astrological chart.
   Although spherical calculations can be done using declinations, working with latitudes is easier because you can simply look at the latitudes and quickly determine if a difference in latitudes affects the orb of an aspect.
   New guidelines for aspect orbs need to be formulated for the spherical orbs for transits, progressions, and natal charts, etc. Planetary patterns in natal analysis have usually allowed wide aspect orbs, but what is permissible spherically? Should we stick to the orbs we use now but apply them to true spherical angles? Some angles that are in orb by finding the longitude difference will be way out of orb when looked at spherically, but other aspects may come into orb. We may have to give up the wider orbs for major aspects and make room for the minor aspects. The analysis of minor aspects is a new frontier for astrologers.
   Astrologers get good results from the conjunction since the timing is accurate. Consider the case of the conjunction of celestial bodies at the same degree of longitude such as occurs at the New Moon when the Sun and the Moon are in conjunction. The angular difference between those bodies computed by the spherical system shows that the difference in latitudes of the two bodies involved is the distance from an exact conjunction.
   For instance, if both planets are at the same degree of longitude but one planet is 5 degrees north latitude and another planet is 5 degrees south latitude, the spherical orb of the conjunction is 10 degrees. One can gauge the intensity of a longitudinal conjunction by measuring the latitude difference between planets.
   An exact opposition occurs when one planet is opposite another planet from a spherical perspective. Those planets must be in the opposite longitude at the opposite latitude. For instance, if a planet were at 10 degrees Pisces, 3 degrees north, the point exactly opposite would be 10 degrees Virgo, 3 degrees south. The intensity of a spherical opposition may be gauged by its deviation from the exact opposition.
   In the square aspect, the time calculated by both systems is usually very close, except in cases where the natal planet is at extremely far out latitudes, such as Pluto at 17 degrees north. If one planet is on the ecliptic, the exact square angle calculated by both systems is almost identical, no matter what the latitude of the second planet. In most cases it is adequate to calculate squares by longitude difference alone.
   The minor aspects, however, can sometimes present a major difference when comparing the longitudinal difference and spherical methods of calculating angles. Spherical trigonometry calculations must be made to determine minor angles between celestial bodies that lie north or south of the ecliptic, or tables may be consulted to get a close approximation of the angle distance between the bodies.
   Being able to make exact calculations regarding the timing of transits, etc. in regard to trines, sextiles and the minor aspects opens up a wider spectrum to the astrological analyst. More information about everyday and work activities might balance out the intense focusing, uncomfortable balancing acts and forceful turning points sometimes characteristic of major aspects.
   Dramatic events or significant trends characteristic of the major aspects might be more balanced with ordinary minor angles that allow a day-to-day and week-to-week interpretation of more mundane energies in life. Minor transits may take on more significance when the spherical system is applied.

Table 1: Using celestial Longitude and Latitude to calculate spherical angles.

  The table below shows how much or little the spherical angles between planets are in my horoscope. This table uses celestial longitude and latitude to calculate the spherical and longitudinal angles. The declination and right ascension calculations are presented below the first table.

SPHERICAL  ANGLES  CALCULATOR  © 2006 Lance Carlyle Carter  "A New Degree of Precision"