Testing PV Paran calculations - new Meridian Longitude formula

[Jim Eshelman]

I have a new spreadsheet that calculates Meridian Longitude by the formula

TAN ml = 1 / (TAN alt / SIN ha)
where ha is horizon angle (= planet azimuth minus 90°), alt is planet's altitude.

This is one of three variations of PVPs. I have no other calculating source to test again so at least I want to test it exhaustively against my earlier estimated calculations in SMA. So far, it seems the aspects are confirmed but the orbs are far smaller. - All I'm going to do is search each chapter of SMA for the text "PVP" and check any chart that has one that is horizon-to-PV.

[Jim Eshelman]

DESTRUCTION OF 2nd TEMPLE (Liblunar)
The problem I'm encountering (a quadrant error on my part?) is that planets on the horizon aren't showing as square but as conjunct. All of these are "3rd house" placements showing as conjunctions. Besides the Mars-Pluto conjunction and Saturn-Neptune opposition, I had previously calculated Neptune-Pluto 0°21', Mars-Neptune 1°38', and Saturn-Pluto 2°38'. Here I get:

Mar 27°31'
Sat 29°33'
Nep 29°54'
Plu 29°44'

Thus, Neptune-Pluto 0°10', Saturn-Pluto 0°11', Mars-Neptune 2°23' (larger than before), and possibly an existing Mars-Saturn 2°02' that I missed before (estimations had the orb to large).

SIEGE OF CONSTANTINOPLE (Capsolar)
I cited a Jupiter-Uranus opposition PVP square rising Mercury. Indeed the positions give these aspects except, again, they all appear as conjunctions/oppositions:

Jup 9H 29°44'
Ura 4H 0°19'
Mer 4H 1°15'

Same event (Cansolar)
I cite Jupiter PVP square Uranus (2°06') and Pluto (1°24'). ML positions are:

Jup 9H 29°32'
Ura 4H 0°17'
Plu 4H 1°38'

Aspects are confirmed but with different orbs: Jupiter-Pluto 2°06', Jupiter-Uranus 0°45'.

BTW, I might be seeing why these all appear as conjunctions-opposition. The 'vertical' axis of the ML calculations is Antivertex-Vertex, the 'horizontal' axis is Northpoint-Southpoint. Even though Asc-Dsc planets are on the horizon (and so I expected them to appear along the SP-NP axis), the Asc-Dsc placements seem aligned in azimuth closer to the 'vertical.' If this remains true throughout, I'm not sure how to distinguish which group for computer calculation of the aspects.

D-DAY (Capsolar)
I cited a Pluto PVP square to setting Saturn. This is confirmed. However, I don't know how to sort it from other aspects that seem to exist also. Half the planets appear within about 3° of the central axis. Are these all really in aspect?

Ven 3H 27°16'
Plu 3H 28°51'
Sat 4H 0°08'
Sun 4H 3°13'
Mer 4H 3°19'

How to distinguish these? Saturn is closely foreground, 0°17' from Dsc. Venus is more widely foreground, 5°35' from Asc. The filtering rule I've used takes out Sun and Mercury which, in azimuth, are 8° and 18° from the PV, so we have an easy screen. It's possible that the Venus-Pluto square (which surely fits the events) should have been caught in my estimation or, any case, could be limited by applying, ay, a 3° boundary on Asc-Dsc contacts as well.

VE DAY in ENGLAND (Arisolar(
I cite Venus PVP square the rising Moon and Uranus. New calculation gives the following. (Again Sun and Mercury were within 3° ML but easily filtered because they are far from PV in azimuth.)

Ven 3H 28°50'
Ura 10H 0°08'
Mon 10H 1°22'

KOREAN WAR BEGAN (Liblunar)
Venus on AV was PVP Uranus 1°48' per prior estimation. The new calculations also capture Sun that was not in my estimations but was closely foreground. (The Liblunar occurred almost the minute of sunrise, which was the minute the invasion began.) - Sun 0°48' above horizon, Uranus 1°00' below, Venus 2°56' before Av in azimuth, and the orbs squeeze to produce the following:

Sun 10 0 21
Ven 10 1 22
Ura 9 29 33

KOREAN WAR ARMISTICE (Caplunar)
Sun PVP square the setting Venus-Jupiter. New calculation of ML shows many planets within close contact of the middle axis, but we can rule out Moon, Mercury, and Uranus by the 3° rule. There is an added Mars contact I did catch by the estimation process (thought the orb was much to large). However, applying the two planets within 3° of PV in azimuth to the two that are in the setting foreground gives:

Sun 3H 28°05'
Jup 4H 0°20'
Ven 4H 0°42'
Mar 4H 1°42'

The Sun-Mars is too wide (over 5° is azimuth), but to Sun-Jupiter 2°15' and Sun-Venus 2°37', we can add the previously undetected (and less fitting but probably valid) Mars-Jupiter 1°22' and Venu-Mars 1°00'.

[TO BE CONTINUED WITH THE YOM KIPPUR WAR]

[Jim Eshelman]

The May 6 Canlunar appears to have Moon in PVP square with Neptune on IC and Mercury setting. (The chart also has Jupiter and Mars widely straddling IC.)

Mercury-Neptune is easy: In PV longitude, Neptune is 0°11' past IC, Mercury is 2°48' past Dsc, their mundane square is 2°37'.

Moon is azimuth 272°46', or 2°46' past Vertex. The Moon-Neptune aspect is easy, since (PV to meridian) it's just a square in azimuth with an orb of 2°35'. Bug how about Moon-Mercury?

Using my estimation method, with Moon and Mercury both past their angles, Moon's PV amplitude is 2°06', Mercury's altitude is 2°21', the orb is 0°15'. Does this test out?

The spreadsheet calculates the following:. It suggests (like a couple of other examples) that I've been flipping one of the plus-minus values the wrong way in estimation calculations (probably PV amp). I've included Pluto which almost makes the arbitrary azimuth cut at 3°01' from Antivertex.

Mon 4H 2°19'
Mer 3H 28°45'
Plu 9H 27°21'

This says the Moon-Mercury square is too wide at 3°34' (too wide for what I've been allowing, or seeing work with other aspects). It does, however, show a close Mercury-Pluto PVP square, orb 1°24'.

The math is probably right on the spreadsheet. The Pluto would have been missed with a sharp 3° cut-off, and we might just live with that border behavior. This is another of several cases that looks like I flipped a PV amplitude value on plus-minus, leading to misleading (wrong) results during estimation.