Celestial Latitude: Correction of Astrological

Charts with the Package Software Phoebius

M. Giannuzzi*, P. E. Zuco

September 26th, 2021

Abstract

Most astrological applications do not consider the latitude of planets,possibly leading to wrong identification of their aspects and positions inthe houses. In this context, Phoebius provides a helpful tool to adjusthoroscopes cast with other software.

The software is available at phoebius.altervista.org

1 Introduction

Why does not an eclipse always occur at every conjunction between the Sun andthe Moon? The doubt arises because astrologers represent the horoscopes asdiscs (2D, like geographic maps) rather than spheres (3D, like globes). Indeed,it is common to establish the position of a planet only by its angular distancemeasured along the ecliptic from the vernal equinox, γ, i.e., in terms of celestiallongitude, λ (which is the value commonly reported on ephemerides). Consid-ering only this coordinate, it is as if the bodies in the sky were all on the sameplane, but this is not so. As was already assumed by Ptolemaic astronomy[1],they may lie above or below the ecliptic, at a distance from it known as celes-tial latitude, β. To better understand these definitions, refer to Fig. 1, wherethe ecliptic coordinates are illustrated together with the equatorial coordinates(i.e., right ascension, α, and declination, δ). In this way, the planets describeperpetual undulatory motions, lying at alternate times to the north or south ofthe ecliptic.

Ancient astrologers considered both the longitude and latitude of the plan-ets in their calculations (with the help of astrolabes and armillary spheres),so they cast ‘real’ astral charts[2]. Although some influential authors (includ-ing the Italians Federico Capone[3], Fulvio Mocco[4], Ciro Discepolo[5], LuciaBellizia[6] and Claudio Crespina[7]) have called for reflection on the subject,most astrologers currently neglect ecliptic latitude, unaware of the effects thiscan have on their analyses.

The paper aims to demonstrate the importance of this variable using the soft-ware package Phoebius, which allows making more accurate astrological maps(birth charts, event charts, horary charts, solar returns, etc.) drawn with otherapplications.

*Correspondence e-mail: m dot giannuzzi at protonmail dot com.

1

N

S

Body

δ

α

β

λ

γ

Ecliptic

CelestialEquator

Figure 1: Orthogonal coordinates.

2 Astrological meaning of latitude

Before describing the usefulness of celestial latitude in identifying aspects be-tween planets and their positions in the houses, it is interesting to examine itsintrinsic significance in classical astrology[8]:

� Planets with north latitude (especially if they are moving north) are re-lated to the idea of growth, expansion, greater visibility; hence they aredignified. Conversely, planets with south latitude (especially if they aremoving south) are related to the concepts of decrease and lowering, so theyare debilitated. Some modern astrologers also take this meaning into ac-count. For example, Dane Rudhyar recognises in psychological astrology astructural difference between the Moon with north and south latitude[9].

� The effects described above manifest themselves most strongly if the planetis at its maximum latitude, known as the boreal peak for north latitude orthe austral peak for south latitude. Tab. 1 shows the absolute maximumdistances that planets can reach from the ecliptic[6]. However, note thata celestial body does not all times achieve these latitudes. Therefore, thepeak is considered the maximum distance from the ecliptic that a planetreaches during a specific cycle. Considering that the zodiacal belt extends8°30’ north and 8°30’ south of the ecliptic, all the planets fall within itsboundaries. The only exception is Pluto, whose maximum latitude exceeds16° both to the north and to the south, so in some times it goes outside thezodiacal band, for a measure equal to twice its extension. For this reason,some modern astrologers question the influence of this planet when itslatitude is too high[10]. The same applies to fixed stars and asteroids,some of which have latitudes greater than 60°.

� Planets in their node (latitude 0) represent a turning point, a sharp change.

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Table 1: Maximum latitudes of the Planets.

Planet Boreal peak Austral peakMoon 5°18’ 5°18’

Mercury 3°52’ 4°44’Venus 8°35’ 8°49’Mars 4°38’ 6°53’

Jupiter 1°49’ 1°49’Saturn 2°53’ 2°53’Uranus 0°48’ 0°48’

Neptune 1°45’ 1°50’Pluto 16°15’ 16°30’

Table 2: Medietas orbs.

Planet OrbSun 7°30’

Moon 6°00’Saturn 4°30’Jupiter 4°30’Mars 4°00’Venus 3°30’

Mercury 3°30’

At a node, the planet’s effects are weaker but more rapid.

3 Real zodiacal aspects (3D aspects)

The most familiar form of astrological contact is the zodiacal aspect, i.e., theangular relationship between two planets lying in mutually configured signs.A clarification is necessary: aspects in the Zodiac are calculated only betweenplanets; it does not make sense to consider zodiacal contacts (except conjunc-tions, which are not aspects[11]) of planets with the cusps, lots or fixed starssince these points have no proper motion along the Zodiac[12].

The influence of the aspect between two planets is significant when the an-gular distance between them is within a tolerance limit known as orb. Modernastrologers define this value according to the type of aspect[13], while classicalastrologers define it according to the planets involved in the contact. For exam-ple, Tab. 2 shows the orbs most widely documented in the tradition (medietasor moiety)[14].

Consider a practical case. Computing with astro.com the birth chart fora person born in Rome (Italy) on March 15th, 2017, at 7.40 pm (CET), thelongitudinal positions for Mercury and Venus are 3°44’ and 10°27’ in Aries,respectively (Fig. 2). The website indicates that there is a conjunction betweenthese two planets: the difference between their longitudes is 6°43’ (i.e., 6.72°),which is less than the sum of the medietas orbs of the two planets (3°30’ + 3°30’= 7°00’). However, astro.com and many other applications (web and desktop)in calculating the orb of an aspect, assume that the celestial bodies lie in a

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I

IV

VII

X

Figure 2: Natal chart calculated by astro.com for a person born in Rome, Italy(41°N54’, 12°E29’), on March 15th 2017 at 7.40 pm (CET). Geocentric, Tropical,Placidus, True Node.

two-dimensional space, but in reality, they occupy a three-dimensional spacedefined by curved lines. Therefore, the actual distance between two planets (Aand B), characterised by their latitudes (βA and βB) and longitudes (λA andλB)1, is the spherical distance (r)[15]:

r = arccos(sinβA sinβB + cosβA cosβB cos |λA − λB |). (1)

This trigonometric equation is valid both for body contacts (conjunction) andcontacts by the rays or figures (opposition, trine, square, sextile, ...). How-ever, latitudes have a significant effect only on conjunctions and oppositions,while they vary the longitudinal distance very slightly in trines, squares andsextiles[16].

According to astro.com, for the date and time previously considered, Mer-cury and Venus had latitudes 0°33’S (i.e., -0.55°) and 8°2’N (i.e., 8.33°), respec-

1It is necessary to convert relative longitudes into absolute longitudes. For example, if theMoon is in Scorpio at 1.77°, its absolute longitude is 211.77° (i.e., 1.77° + 210°).

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PLANET 1: MERCURY

- Longitude (λ)

sign: Aries

degrees (0-29): 3

minutes (0-59): 44

- Latitude (β)

direction (N/S): S

degrees (0-90): 0

minutes (0-59): 33

PLANET 2: VENUS

- Longitude (λ)

sign: Aries

degrees (0-29): 10

minutes (0-59): 27

- Latitude (β)

direction (N/S): N

degrees (0-90): 8

minutes (0-59): 20

===

MERCURY - VENUS

Δλ = 6.72°

Δβ = 8.88°

r = 11.12°

Orb = 11.12°

Figure 3: Phoebius printout for the calculation of the spherical distance betweenMercury and Venus in the examined birth chart.

tively. Therefore, applying equation 1:

r = arccos(sin(−0.55◦) sin(8.33◦) + cos(−0.55◦) cos(8.33◦) cos(6.72◦)) = 11.12◦.

This value is the actual distance between Mercury and Venus. Since it is aconjunction, the spherical distance between the two planets corresponds to theorb, which is greater than the sum of their respective medietas orbs (7°00’).Therefore, in reality, there is no conjunction.

In the case of an opposition, the orb of the aspect is 180◦ − r; for a trine, itis 120◦ − r; for a square, it is 90◦ − r; for a sextile, it is 60◦ − r.

The above calculations for determining the spherical distance between twoplanets can be performed automatically by simply entering their ecliptic coor-dinates into Phoebius. Fig. 3 shows the ticket printed by the software for thecase examined in this paragraph. Fig. 4 provides a complete comparison be-tween the Ptolemaic aspects characterising the considered birth chart, takinginto account (a) or not (b) the latitude of the planets.

4 Real position of the planets in the houses

Before proceeding further, it is necessary to explain some astronomical conceptsfor defining horary distances of the planets in an astral chart[6]. To make thefollowing easier to understand, refer to Fig. 5.

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(a) 2D aspects (b) 3D aspects

Figure 4: Aspectarians of the examined birth chart before (a) and after (b)applying Phoebius corrections.

As is well known, the planets move clockwise around the Earth (an imag-inary movement called diurnal motion), along a parallel of declination, i.e., acircle parallel to the celestial equator. When this parallel intersects the celestialhorizon (the extension on the celestial sphere of the plane perpendicular to theobserver’s vertical on Earth) in the east, the planet rises (A) and becomes visi-ble. It then proceeds southwards, where it culminates (B), then declines againto the west, where it sets (C ), to become invisible again to the north, where itanticulminates (D). Therefore, the planet’s declination parallel consists of twoparts: one above the horizon, visible, called diurnal arc (ABC

_), and one below

the horizon, not visible, called nocturnal arc (CDA_

).The diurnal arc of the equator is equal to the nocturnal one and measures

12 h: therefore, each hour on the equator is equivalent to 15° (15° × 12 = 180°).On the other hand, away from the equator, an hour (temporal hour) is greaterthan 15° if the planet is to the north (positive declination δ), less if it is to thesouth (negative declination δ). In particular, the diurnal temporal hour of aplanet is:

Htd = 15◦ +1

6AD, if δ > 0◦, (2)

or

Htd = 15◦ − 1

6AD, if δ < 0◦, (3)

and the nocturnal temporal hour of a planet is:

Htn = 30◦ −Htd. (4)

In 2 and 3, AD (expressed in degrees) is the ascensional difference, i.e., thedifference, measured on the equator, between the right ascension of the planetand the arc of the equator intercepted between the vernal equinox and theequator point rising at the considered time (oblique ascension). It depends onthe declination δ of the planet and the terrestrial latitude ϕ of the observer,according to the following formula[17]:

sinAD = tan δ · tanϕ. (5)

6

Zenit

Nadir

Planet

N

S

Horizon

Equator

Parallel ofdeclinationA

B

C

D

Figure 5: Diurnal motion of a planet.

In addition to the temporal hour, another fundamental element for calcu-lating the horary distance of a celestial body is its right distance, RD, i.e., itsdistance from the celestial meridian, measured on the equator. The calculationof this variable depends on the planet’s position in the astral chart[12] (refer toFig. 6 for the numbering of the quadrants). In particular, for a celestial bodylocated in the east relative to the Midheaven (i.e., in the I quadrant), its rightdistance is:

RD = αP − αMC , (6)

where αP is the right ascension of the planet, and αMC is the right ascension ofMidheaven2. On the other hand, if the planet is in the west of the Midheaven(i.e., in the II quadrant):

RD = αMC − αP , (7)

For a planet that lies to the west of the Imum Coeli (i.e., in the III quadrant):

RD = αP − αIC , (8)

where αIC is the right ascension of the Imum Coeli, which is equal to αMC±180◦

(subtract when the sum exceeds 180°). On the other hand, if the planet is inthe east of the Imum Coeli (i.e., in the IV quadrant):

RD = αIC − αP . (9)

If the result of 6, 7, 8 or 9 is negative, add 360°.Knowing the temporal hour and the right distance, it is finally possible to

calculate the horary distance of the planet from the Midheaven or the Imum

2Both of these values can be found, for example, by entering the desired date, timeand place on the Astro-seek website at https://horoscopes.astro-seek.com/birth-time-

rectification-calculator-primary-directions (then selecting the Speculum tab).

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I II

IV III

MC

IC

AC DC

Horizon

Mer

idia

n

Figure 6: Quadrants of an astrological chart.

Coeli. In particular, if the planet is above the horizon (i.e., in quadrant I or II):

HD =RD

HTd(10)

Otherwise, if it is below the horizon (i.e., in quadrant III or IV):

HD =RD

HTn(11)

Looking at an astral chart erected with the Placidus system, the houses allmight have different widths, but this is not so: it is a perspective matter. Inparticular, the ecliptic is oblique to the celestial equator, so in an astrologicalmap, the projected houses are some larger and some smaller, but in reality, theyall have the same temporal amplitude, which is 2 h. With this in mind, it ispossible to determine the exact position of a planet within a house by knowingits horary distance3. Fig. 7 illustrates the horary distances of the cusps fromthe meridian. For example, a planet that is in the second quadrant with HD =3 h from the superior meridian will be positioned precisely in the middle of theeighth house; on the other hand, if a planet is in the third quadrant with HD =4 h from the inferior meridian, it will be precisely conjunct to the cusp of thesixth house.

Consider the birth chart in Fig. 2 again. According to the scheme obtainedwith astro.com, Venus is in the sixth house. Inserting in Phoebius the observer’slatitude, the right ascension of the Midheaven, the right ascension of the planetand its declination, the software finds that the horary distance of Venus fromthe Imum Coeli is 6.08 h. It means that the celestial body is actually in the

3This approach is only feasible for charts with houses defined in terms of time, not space.Therefore, it is applicable with temporal systems (e.g. Placidus), but not with spatial systems(e.g. Regiomontanus, Campanus).

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MC

IC

AC DC

0

2

4

6

4

20

2

4

6

4

2

I VI

II VIII IV

XII VIIXI VIII

X IX

Figure 7: Horary distances between the cusps and the meridian in Placidussystem.

seventh house, at 0.08 h (about 5’) from the descendant. Therefore, neglectingthe declination (and thus the latitude) of Venus, it would be positioned in thewrong house. Fig. 8 shows the ticket printed by Phoebius for the case examinedin this paragraph. The probability that a planet is in the wrong house increaseswith its latitude and proximity to a house cusp[12]. For this reason, erroneousplacements occur mainly for the Moon, Venus and Pluto, which are the threeplanets that can reach the highest latitudes (Tab. 1). In fact, in the consideredexample, Venus has a very high latitude (8°20’N). For a three-dimensional viewof the actual arrangement of the planets in the chart, refer to Fig. 9.

As regards forecasting methods[3], in the primary directions, the influenceof latitude is already well known, while in the transits, few know that it canshift the times when transiting planets are on the house cusps of the radicalchart (except bodies that are almost exactly on the Midheaven or Imum Coeli,which, even in a birth chart, are not disturbed by latitude). This matter isirrelevant for fast planets like the Moon, but even for Venus or Mars, therecould be a difference of a few days. The issue is especially significant for Pluto:as mentioned earlier, this planet can have a very high latitude, and it can shifta transit on the Ascendant by several years compared to a purely longitudinalone.

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- Terrestrial Latitude (φ)direction (N/S): Ndegrees (0-90): 41minutes (0-59): 54

- MC Right Ascension (α_MC)degrees (0-359): 106minutes (0-59): 4

===α_IC = 286.07°

Number of planets (1-10): 10

PLANET 1: SUN PLANET 2: MOON PLANET 3: MERCURY- Quadrant (1-4): 3 - Quadrant (1-4): 4 - Quadrant (1-4): 3- Right Ascension (α) - Right Ascension (α) - Right Ascension (α)

degrees (0-359): 355 degrees (0-359): 211 degrees (0-359): 3minutes (0-59): 44 minutes (0-59): 10 minutes (0-59): 39

- Declination (δ) - Declination (δ) - Declination (δ)direction (N/S): S direction (N/S): S direction (N/S): Ndegrees (0-90): 1 degrees (0-90): 7 degrees (0-90): 0minutes (0-59): 50 minutes (0-59): 53 minutes (0-59): 58

PLANET 4: VENUS PLANET 5: MARS PLANET 6: JUPITER- Quadrant (1-4): 3 - Quadrant (1-4): 2 - Quadrant (1-4): 4- Right Ascension (α) - Right Ascension (α) - Right Ascension (α)

degrees (0-359): 6 degrees (0-359): 31 degrees (0-359): 200minutes (0-59): 17 minutes (0-59): 49 minutes (0-59): 1

- Declination (δ) - Declination (δ) - Declination (δ)direction (N/S): N direction (N/S): N direction (N/S): Sdegrees (0-90): 11 degrees (0-90): 13 degrees (0-90): 6minutes (0-59): 48 minutes (0-59): 5 minutes (0-59): 45

PLANET 7: SATURN PLANET 8: URANUS PLANET 9: NEPTUNE- Quadrant (1-4): 4 - Quadrant (1-4): 2 - Quadrant (1-4): 3- Right Ascension (α) - Right Ascension (α) - Right Ascension (α)

degrees (0-359): 267 degrees (0-359): 21 degrees (0-359): 343minutes (0-59): 12 minutes (0-59): 19 minutes (0-59): 56

- Declination (δ) - Declination (δ) - Declination (δ)direction (N/S): S direction (N/S): N direction (N/S): Sdegrees (0-90): 22 degrees (0-90): 8 degrees (0-90): 7minutes (0-59): 5 minutes (0-59): 20 minutes (0-59): 45

PLANET 10: PLUTO- Quadrant (1-4): 3- Right Ascension (α)

degrees (0-359): 290minutes (0-59): 31

- Declination (δ)direction (N/S): Sdegrees (0-90): 21minutes (0-59): 10

AD (°) Htd (°) Htn (°) RD (°) HD (h)----------------------------------------------SUN -1.65 14.73 15.27 69.67 4.56MOON -7.14 13.81 16.19 74.90 4.63MERCURY 0.87 15.14 14.86 77.58 5.22VENUS 10.81 16.80 13.20 80.22 6.08MARS 12.04 17.01 12.99 74.25 4.37JUPITER -6.10 13.98 16.02 86.05 5.37SATURN -21.36 11.44 18.56 18.87 1.02URANUS 7.56 16.26 13.74 84.75 5.21NEPTUNE -7.02 13.83 16.17 57.87 3.58PLUTO -20.34 11.61 18.39 4.45 0.24

Figure 8: Phoebius printout for the calculation of horary distances in the exam-ined birth chart.

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Figure 9: 3D representation of the birth chart in Fig. 2, obtained by Astrolog7.30 [18]. Legend: black graduated circle = celestial horizon; green graduatedcircle = celestial meridian; grey graduated circle = celestial equator; blue grad-uated circle = ecliptic.

5 In mundo aspects

In addition to zodiacal aspects, many classical astrologers (especially the Ital-ian ones of the Cielo e Terra association) also consider in mundo aspects[6],sometimes called horary aspects, since they depend on the position of the plan-ets in the houses and their mutual horary distance4. Unlike zodiacal aspects,in mundo aspects last much less (a few minutes, due to the diurnal motion ofthe planets) and change according to the place on Earth considered. Anotherdifference to angular aspects is that planets form in mundo aspects not only toeach other but also to the cusps, lots and fixed stars[12]. Aspects in the celestialsphere indicate a potential effect, while those in the local sphere act to realise

4A particular type of in mundo aspect is paran[8], i.e., potent connections that occur whentwo planets are on angular points on the chart. For example, if the Moon rises (i.e., is on theAscendant) while Mars culminates (i.e., is on the Midheaven), the two planets form a square,regardless of whether or not there is a zodiacal aspect between them.

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that effect[6]. For example, if two planets are in zodiacal aspect to each otherbut not related through an in mundo aspect, the influence of the zodiacal aspectwill not manifest or will manifest in a different or lesser way.

After positioning the planets according to their horary distances (as de-scribed in the previous paragraph), it is possible to determine the in mundoaspects between them. Each of the five Ptolemaic aspects corresponds to acertain number of hours: 0 h (conjunction); 4 h (sextile); 6 h (square); 8 h(trine); 12 h (opposition). Due to the rapidity with which these aspects formand dissolve, the orbs considered are very narrow[6]:

� 28’ (0.467 h) if the Sun and the Moon relate to each other;

� 24’ (0.40 h) if the Sun or the Moon relates to a planet;

� 20’ (0.334 h) if two planets relate to each other.

Software that allows automatic determination of in mundo aspects are few.Two of the most promising of these are Sphæra[19] (developed by the Italianassociation Almugea) and Prometheus[20] (developed by Capricorn AstrologySoftware). In any case, as already mentioned in the last paragraph, Phoebiuscan determine the horary distance of a planet, and this enables the identificationof the aspects it can form with the other planets in the local sphere.

According to Fig. 2, there is a zodiacal square between the Sun (25°21’Pisces, 0°0’N) and Saturn (27°24’ Sagittarius, 1°19’N): is there also an in mundoaspect? Phoebius calculates that the Sun and Saturn are distant from ImumCoeli at 4.56 h and 1.02 h, respectively (Fig. 8). Therefore, the horary distancebetween the two planets is 5.58 h, with a deviation of 0.42 h from the perfectsquare (6 h). This value is higher than the maximum allowed orb (0.40 h), sothere is no in mundo contact between the two planets: the zodiacal aspect isthus incomplete.

As a further example, the chart shows a zodiacal opposition between theMoon (1°46’ Scorpio, 4°28’N) and Mars (4°8’ Taurus, 0°12’N). According toPhoebius’ calculation (Fig. 8), the Moon is 4.63 h away from the Imum Coeli,while Mars is 4.37 h away from the Midheaven. Therefore, the horary distancebetween the two planets is 12.26 h (4.63 h + 6 h + 1.63 h), with a deviation of0.26 h from the perfect opposition (12 h). This value is less than the maximumpermitted orb (0.40 h), so there is an in mundo aspect between the Moon andMars, which completes the relevant zodiacal contact.

6 Conclusions

Apart from its intrinsic astrological significance, the celestial latitude can in-fluence the horoscopic scheme in two ways: by invalidating zodiacal aspects(also due to the absence of pertinent in mundo aspects) and by changing thehouse position of the planets (Placidus system) determined only from celestiallongitudes. Without forcing users to discard their usual astrological software,Phoebius complements it by providing valuable support for latitudinal horoscopeadjustments (by calculating spherical and horary distances).

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