Joined: 04 Feb 2009
|Posted: Sat Jul 18, 2009 1:02 pm Post subject: Placidus' Polar Horoscopes
|In the Regiomontanus and Placidus thread http://skyscript.co.uk/forums/viewtopic.php?t=3048&postdays=0&postorder=asc&start=0 the articles of Michael Wackford about polar horoscopes are mentioned. http://www.skyscript.co.uk/polar1.html In the articles he offers a method for the use of Placidus' mundane positioning system.
Although he explicitly says that the system is not to be used as a system in the usual sense of house cusps depicted in the ecliptic, one still might be curious how it would look like. I calculated a table to illustrate the use of a polar projection of Placidus on the ecliptic at 70°North latitude.
One thing I'd like to mention is that I may be biased against this method. I strongly dislike the system because it goes against my sense of geometry (e.g. I don't accept this 'kink' in the curves). However I won't further mention this and I will only show some features that occur when used in the usual way of houses. After all Michael Wackford recognizes and faces the problems of polar horoscopes.
Explanation of the table:
The positions were calculated for ecliptic longitudinal positions with latitude 0°. The chosen latitude on Earth was 70° North (Lapland, Northern Canada and Northern Siberia.). The obliquity of the ecliptic I used was 23.43' or 23°25.8'.
Instead of a usual house table with cusp positions for every four minutes of Sidereal time, this table looks at the house positions of the ecliptic degrees from 0° - 180° (i.e. 0°Aries - 0° Libra) in steps of 10°. These points can be seen as places where planets could be situated. Just imagine the pictures of horoscopes which depict the houses always as equal parts of 30° instead of the 'squeezed and stretched' unequal parts in the ecliptic. The table mentions the positions in the first depiction with the ecliptic positions expressed in 'house degrees'. Since the most remarkable issues occur between 16:00 and 20:00 Sidereal Time, the table is limited to this span of time with also an added list of positions at 20:40, when the issues are 'normal'. The positions are calculated in steps of 40 minutes of Sidereal Time or 10° in Right Ascension.
Eclpt.| House Position according to Sidereal Time / Right Ascension
Deg. | 16:00/240° _16:40/250° _17:20/260° _18:00/270°
__0° | _0° ______II 20° ______I 10° ______I 0° _______I
_10° | _2°08.7 __II 20°45.5 __I _9°22.3 __I 28°25.4 XII
_20° | _4°54.1 __II 21°38.2 __I _8°22.2 __I 27°02.3 XII
_30° | _5°23.5 __II 22°30.6 __I _6°28.4 __I 25°40.1 XII
_40° | 13°33.2 __II 22°49.4 __I _2°05.6 __I 24°04.6 XII
_50° | 20°44.3 __II 19°11.1 __I 27°40.3 XII 21°43.8 XII
_60° | 28°54.6 _XII 23°54.6 XII 18°54.6 XII 13°54.6 XII
_70° | _4°10.9 _VII 29°10.9 XII 24°10.9 XII 19°10.9 XII
_80° | _9°33.7 _VII _4°33.7 VII 29°33.7 XII 24°33.7 XII
_90° | 15° _____VII 10° ____VII _5° ____VII _0° (I) / VII
100° | 20°26.3 _VII 15°26.3 VII 10°26.3 VII _5°26.3 VII
110° | 25°49.1 _VII 20°49.1 VII 15°49.1 VII 10°49.1 VII
120° | _1°05.4 VIII 26°05.4 VII 21°05.4 VII 16°05.4 VII
130° | 26°05.7 _VII 20°09.2 VII 14°12.7 VII _8°16.2 VII
140° | 25°41.5 _VII 19°06.2 VII 12°30.8 VII _5°55.4 VII
150° | 26°07.7 _VII 18°51.8 VII 11°35.9 VII _4°19.9 VII
160° | 27°02.1 _VII 19°00.6 VII 10°59.1 VII _2°57.7 VII
170° | 28°19.2 _VII 19°24.4 VII 10°29.5 VII _1°34.7 VII
180° | _0° ____VIII 20° ____ VII 10° ___VII 0° ______VII
Eclpt.| House Position according to Sidereal Time / Right Ascension
Deg. | 18:40/280° __19:20/290° _20:00/300° 20:40/310°
__0° | 20° _____XII 10° ____XII _0° ____XII 20° _____XI
_10° | 19°30.5 _XII 10°35.6 XII _1°40.8 XII 22°45.9 _XI
_20° | 19°00.9 _XII 10°59.4 XII _2°57.9 XII 24°56.5 _XI
_30° | 18°24.1 _XII 11°08.2 XII _3°52.3 XII 26°36.4 _XI
_40° | 17°29.2 _XII 10°53.8 XII _4°18.5 XII 27°43.1 _XI
_50° | 15°47.3 _XII _9°50.8 XII _3°54.3 XII 27°57.8 _XI
_60° | _8°54.6 _XII _3°54.6 XII 28°54.6 _XI 23°54.6 _XI
_70° | 14°10.9 _XII _9°10.9 XII _4°10.9 XII 29°10.9 _XI
_80° | 19°33.7 _XII 14°33.7 XII _9°33.7 XII _4°33.7 XII
_90° | 25° _____XII 20° ____XII 15° ____XII 10° ____XII
100° | _0°26.3 _VII 25°26.3 XII 20°26.3 XII 15°26.3 XII
110° | _5°49.1 _VII _0°49.1 VII 25°49.1 XII 20°49.1 XII
120° | 11°05.4 _VII _6°05.4 VII _1°05.4 VII 26°05.4 XII
130° | 02°19.7' _VII 10°48.9' _VI _9°15.7' _V 07°42.4' IV
140° | 27°54.4 '__VI 07°10.6' _VI 16°26.8' _V 25°43.1' IV
150° | 23°31.6' __VI 07°29.4' _VI 24°36.5' _V 05°25.2' _V
160° | 21°37.8' __VI 08°21.8' _VI 25°05.9' _V 11°49.9' _V
170° | 20°37.7' __VI 09°14.5' _VI 27°51.3' _V 16°28.1' _V
180° | 20° ______VI 10°_____VI _0°_____VI 20° _____V
Some notable features:
- Looking up to down ('forwards' thruogh the ecliptic) in the list at 16:40 ST one sees that the house position first increases then decreases at 40°Ecl and increases at 70°. In every ST list except the last one this is seen. This means that an object that never is retrograde in the ecliptic (Sun, Moon) can be retrograde in the houses.
- As the Ascendant is defined where on the ecliptic House I follows house XII, at 18:00 ST for example there will be two positions that meet the requirement of this definition. 0° Aries, 0°Cancer and 0°Capricorn are at those positions. At the same time 0°Cancer, 0°Libra and 0°Capricorn are Descendant. Such a thing is constantly the case during 4 hours between 16:00 and 20:00 ST.
- As the circumpolar houses above the horizon are from VII to XII which meet in the line from the north celestial pole to the north point on the horizon, one could wonder if the (usual) inbetween houses I to VI shouldn't be defined as existant but infinitely small. If this isn't the case then there can be no MC and IC while there are three Ascendants and three Descendants in the four hour span.
- In this 4 hour period the ecliptic rises in reversed order, 0° Taurus rises earlier than 0° Aries which rises earlier than 0° Pisces.
- At the beginning and ending of this period or more exactly at the moments 15:57:20 and 20:02:40 ST, there is a MC and an IC but these are in exact conjunction with Ascendant and Descendant. There will be no houses I, II, III and VII, VIII, IX or IV, V, VI and X, XI, XII or these should be defined as infinitely small.
- If Primary Directions are used (with zodiac latitude set at 0°) then for example the point on the ecliptic at 60° (0° Gemini) which is found at 28°54.6' XII at birth time of 16:00 ST can be conjuncted by two different points on the ecliptic at the same time. At 17:20 for example the 50° and the 80° point on the ecliptic are close to the same house position of the first point.
- Finally in some cases there will be no existing cusps houses II, III, IV, V and VIII, IX, X, XI. No place on the ecliptic will be in these houses. Furthermore Cusp VI and XII will never be touched (by the ecliptic). This will raise problems for systems that depends on planetary strengths accordin to house cusps in combination with sign rulers.
As a concluding remark it can be said that the proposed method perhaps might better not be used in an ecliptical sense. Whether it should be used in a mundane sense, I'll leave that an open question.
(edit: since the software doesn't seem to read the 'space' key the table got difficult to read. I therefore used the 'underscore' _ key to make the table look more pleasant to read. There also were parts missing, hopefully the table is fully correct now.)
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