John Pazmino
 NYSkies Astronomy Inc
 2008 September 7 
    My article 'Astrology for astronomers' generated a LOT of comment, 
much of it, uh, deprecative. However, many readers took a fancy to the 
fact that there is much in astrological calculation of good value for 
astronomers. On the other hand I sure did not win over any 'converts' 
to regulation astrology. If you missed that piece, it's in the 
articles section of '' under John Pazmino. 
    To fully visualize how astrological calculation can assist the 
astronomer, I include HERE a classical 'wheel' chart done up for 0h 
EST on 24 December 2007 in New York. That's the night before the 2007 
Mars opposition. It turns out that, by happy chance!, this night has 
major significance for astrologers. For us as astronomers, it presents 
a most curious and interesting arrangement of planets in the sky that 
can enhance our skywatching. 
    The astrologer plots the planets on a circular chart, commonly 
called a wheel for its obvious shape with rim, hub, and spokes. The 
one we'll explore was generated by ZET, a standard astrology computer 
program that has some really handy features for astronomers. 
    I do not here discuss the workings of this program but merely 
explain this particular output from it. If you're interested, ZET is a 
free download. It's large for a dialup Internet connection, 11Mb. 
    Please note that I in this article give only brief descriptions of 
the astrological concepts. You really better read 'Astrology for 
Equatorial chart 
    If you recall the equatorial chart usually shown in astronomy 
magazines, that's a big, really big, head start in understanding the 
wheel. In that diagram the equator and ecliptic are unrolled from the 
sky and spread out flat. east is on the left; west, right. In southern 
hemisphere magazines, this chart is inverted to better match the stars 
in the local sky. 
    The seam is usually at the vernal equinox, but a close second 
choice is to put it at the Sun. That way the entire night sky, from 
dusk to dawn, in in one piece. In this method, a new base map is 
prepared for each magazine issue. 
    The equator is the horizontal centerline of the chart and the 
ecliptic is the 'sine wave' trending left to right. It is rare to see 
this chart aligned with the ecliptic with a sinuous equator. Stars, to 
some modest depth of magnitude, are sprinkled over the map field. The 
declination width is about +/- 40 degrees north and south to make sure 
all the planet motions are contained within it. 
    Planets are plotted for the instant or coming month by symbols or 
icons, including the Sun and Moon. The Moon may be plotted for her 
cardinal phases. A quickly moving planet may be plotted for the 1st 
and last days of the month. No other solar system bodies are marked, 
like asteroids or comets. Other parts of the magazine deal with them. 
    This equatorial chart can be elaborated by fancy art with a 
daylight glowball around the Sun, phase discs of the Moon, tinted 
stars, air brushed Milky Way, and so on. To some astronomers, the more 
jazzed up is the chart, the harder, not easier, it is to read. In the 
old days, such charts were simple black-&-white maps with hand-drawn 
dots and labels for the planets. 
    The chart presents at a glance the locations of the planets 
relative to the Sun and stars by which you then assess their 
visibility in your local sky. You have to mentally sketch in the local 
horizon for the instant hour or refer to a regular allsky map. I do 
see, once in a long while, an accompanying template to copy and cut 
out. Placed over the chart, lined up with certain index marks, it 
masks off the part of sky below the horizon. 
Wheel chart
    HERE is the astrologer's version of the equatorial chart. It is 
not unrolled, left circular, and centered on the Earth at its hub. You 
can compare this to the equatorial chart curled around, taped at the 
seam, and somehow squashed flat into a broad circular band. The wide-
screen view becomes a cyclorama of the ecliptic zone of the sky. 
    To be a bit more careful, this is a natal chart, one cut for a 
person's moment of birth. For the record, according to one astrologer 
I know, the moment of birth is NOT, as commonly thought, that of 
seeing the light. 
    It's when the child first interacts independently with the 
cosmos. This is signaled by its first cry, completing its first breath 
by which it ingests the mix of celestial inducements at the instant.  
These inducements imprint the child with the general qualities of life 
it will live thru.  
    There's an other chart, the horary chart, compiled for a moment 
within a person's life. Such may be for buying a house, moving out of 
town, getting divorced, &c. The mechanics of generating a horary chart 
are the same as for the natal chart, only the processing of the 
information in the chart differs. 
    By skipping the astrology function of the chart, you may use 
either type. Most astrology computer programs cut a natal chart in the 
lack of other instruction. Hence, you can create a 'natal' chart for 
any moment you want, like I did here for the Mars opposition.. 
    Everything is predicated on the geocentric solar system, which, of 
course, is invalid for dynamical and physical astronomy. However, for 
us staying on Earth and looking into space, the geocentric model is 
quite handy and adequate. Just don't push its envelope too far. No, I 
have no idea how astrologers deal with the planets and zodiac as seen 
from other places in the solar system. 
    The horizontal line thru Earth in the center (smothered by 
overlying lines in this chart) is your horizon. The left side is at 
the rising point of the ecliptic; right, setting. Because of the 
obliquity of the ecliptic against the equator, the rise and set points 
are generally NOT at the east and west points of the horizon. 
    The rising point of the ecliptic is the ascendent, 'Asc' on the 
chart. Where the ecliptic sets is the descendent, 'Dsc'. The tow are 
always exactly six zodiac signs, 180 degrees, apart. Both words are 
also spelled with '-dant' from a French derivation. The astronomer 
prefers the Latin base with '-dent'. 'Ascendere' is a 3rd conjugation 
verb; feel better now? 
    The rim is the circles of the zodiac and of the houses. The signs 
are labeled by their traditional symbols and the houses are labeled by 
Roman numerals. Houses have fanciful names but most astrologers prefer 
the numbers. Both houses and signs progress eastward, Aries thru 
Pisces and house #1 thru house #12. 
    Near the top of the chart is the medium coeli, 'MC', where the 
ecliptic crosses the upper meridian. This point is the astrologer's 
equivalent of the astronomer's sidereal time. Near the bottom is the 
imum coeli, 'IC', the crossing of ecliptic and lower meridian. 
    The planets are plotted by their symbols at their places in the 
zodiac. The little numbers next to them are the degree within the sign 
where they sit. In this particular chart some locations are given to 
the degree, others to the degree and minute. In the text here I round 
all angles to the degree. 
    In the belly of the chart are various alignments among the planets 
and points. For the most part these can be ignored but I set the 
programs for the major alignments, or aspects, as handy ways to 
appreciate the cyclorama of planets around the sky. The lines join the 
associated planets with symbols on them for the aspect. 
    That's really all there is to it! What at first looks like a 
mysterious cosmic diagram left behind by flying-saucer creatures, is 
nothing more than a stylized chart of the zodiac for a given moment. 
If you understand the initial description in this section, you're home 
free for the following details. 
Initial parameters
    At the top left are the place, date, hour for this chart. They are 
like the setting for a planetarium program. The location in ZET is 
selected from a humongous list of towns around the world. I stumbled 
on a wicked glitch. I looked up 'Brooklyn'. There it was among the 
towns in New York! I selected it and proceded to explore the program. 
    The horizon was too far north; the timezone offset was too far 
west. The 'Brooklyn' in the list is NOT the fourth largest city in the 
United States! It's a hamlet on Lake Ontario in upstate New York! I 
changed to 'Manhattan', the correct Manhattan in New York City. 
    Under these are other settings: 
        Tropical - this chart uses the traditional sequence of signs, 
    starting with Aries at the vernal equinox. This is far and away 
    the preferred method. The alternative is 'Sidereal' which uses the 
    current alignment of signs with the zodiac constellations. This 
    method will cause gross confusion for both astrologers and 
    astronomers. Stick with the classical signs! 
        Ecliptic - the rim is the very ecliptic. The alternative is 
    'equator' but this can cause distortion in the angular relations 
    between planets and be a hindrance in spotting them in the sky. 
    Stay with the ecliptic. 
        Topocentric - the positions are computed for the observer's 
    location on Earth. The alternative is 'geocentric', which is quite 
    adequate for all the planets except the Moon. 
        Meridian - The houses are those of the 'meridian' scheme, 
    where the cusps are placed at 2-hour intervals of hour angle 
    eastward from the upper meridian. There are some 20 other methods 
    of delineating the house cusps, but only one other has any sense 
    for astronomy. That is the 'horizontal' system where the cusps are 
    at 30-deg intervals of azimuth eastward from the upper meridian. 
    I use these settings as defaults but can change them at will for 
special purposes. Like astronomy programs, astrology programs can save 
a set of default parameters that load at each run. In astrology, 
however, each case may have its own location (birthplace) so the 
settings are altered far more frequently than in astronomy. 
    The wheel is a snapshot, like a planisphere set to a given moment. 
ZET, and many other astrology programs, have animation that rotates 
the sky. The wheel turns around the Earth hub and the planets are 
carried round with it. If you run the animation for many days, the 
planet enter and leave alignments, the aspects. Lines delineating the 
aspects turn on and off. It can look like a kaleidoscope on the 
computer screen! 
The zodiac
    I find it easiest to picture the chart as a special planisphere 
view based on the ecliptic rather than the equator. The observer is in 
the middle, looking south. Medium coeli is near the top of the chart, 
in the 'front' of the sky while looking south. Imum coeli is behind 
and below you. 
    Some astrologers call these points zenith and nadir. The real 
zenith and nadir are not shown at all in the wheel chart because, 
except in the tropic latitudes, the ecliptic never reaches them. 
    The zodiac above the horizon extends from the descendent in the 
western sky, up thru the medium coeli, down to the ascendent in the 
eastern sky. The rest of the ecliptic, ascendent thru imum coeli to 
descendent, is below the horizon and not visible at the instant. 
    Probably the biggest obstacle to a clear reading of the chart for 
astronomy is the dispersion of the zodiac signs and constellations. 
Astrology of today is founded on the works of Ptolemaeus, some 2,000 
years ago. The names of the signs at that time did line up more or 
less with the constellations. 
    By now they are one step west, relative to the stars, due to 
precession. The slippage is about 28 degrees, not quite a full sign. 
Hence, it is really not feasible to rename the signs to better match 
the stars. It may have been wise in early times to letter the signs, 
like alpha thru mu. This would have avoided the contention about 
precession among astronomers and astrologers. 
    Never the less, by mentally indexing the signs you can visualize 
where among the stars the planets sit. This tactic can be only 
approximate because the constellations are of various lengths along 
the ecliptic while the signs are zones of 30 degrees each. 
The houses
    Unlike the universal acceptance of the signs there is massive 
dispute about the houses. The idea is to build a set of 12 divisions 
of the zodiac based on the observer's location to complement those 
based on the celestial sphere. No general consensus was so far 
reached, despite centuries of debate, on the proper construction of 
the house divisions. 
    The runaway most prevalent scheme is the Placidus system, because 
thruout most of the 20th century there were cheap, widely-available, 
tables for only this system. Tabulations for other schemes were too 
costly and hard to find.. 
    For astronomy I find, of the 20 and more house methods out there, 
only two of use. Astrology computer programs, recognizing the lack of 
agreement on a house method, let you select the method you want. I set 
ZET for the meridian houses, spaced at 2-hour intervals of hour angle 
from the upper meridian. Where these hour circles cut the ecliptic are 
the cusps of the houses. 
    The other useful scheme is the horizontal house, set up as 30-
degree intervals of azimuth from the upper meridian. The house cusps 
are where the azimuth circles cut the ecliptic. 
    The houses circles stay still on the horizon while the signs, 
planets, points roll behind them in diurnal motion. The cusps slide 
north and south along the circles, according as the declination of the 
ecliptic at each intersection. The medium coeli, by definition in the 
meridian system, is the cusp of the 10th house. Imum coeli is the cusp 
of house #4. 
    Houses are numbered eastward from #10 at medium coeli, thru 12, 
then 1, and continuing back to 10. House #1 is in the eastern sky 
while #7 is in the western sky. In many charts, the labels for the 4th 
and 10th house is omitted because they are the imum and medium coeli. 
    The meridian houses show what point of the ecliptic is on the 
meridian at 2-hour increments thruout the day. For example, in the 
chart the medium coeli, 10th house, is the 4th degree of Cancer 
(Cancer 4) 
    Two hours ago, at 22:00 on December 23rd. it was the 6th degree of 
Gemini (Gemini 6). This point now at 0h is at the cusp of the 9th 
house. The cusp of the 11th house will be on the meridian in two 
hours, at 02:00 on the 24th, and is the 2nd degree of Leo (Leo 2). 
    To help you over the hurdle of sign versus constellation, the 
medium coeli at chart time is in the beginning, front, cusp, of 
constellation Gemini. In two hours it'll be the front of Cancer. Two 
hours ago it was the front of Taurus. 
Ascending node 
    Astrology tracks many fake planets, most of which are of no value 
for astronomy. A couple are, believe it or not, of good value. At the 
cusp of Pisces you see a squiggly symbol which you may recognize from 
orbital mechanics. It's the ascending node symbol. In particular, it's 
the ascending node of the Moon's orbit. The descending node is usually 
not marked but it is opposite, 6 signs away. When marked, it uses the 
up-side-down squiggly symbol. 
    When the Moon, the white crescent symbol near medium coeli, is 
near either node, she is close to the ecliptic, with latitude near 0 
degree. When she is 90 deg east of the ascending node, she is near her 
maximum north latitude of +5.5 degrees. 90 deg west of the ascending 
node puts the Moon near her maximum south latitude, -5.5 deg. 
    Thus, the ascending node helps assess the Moon's latitude for 
possible star and planet occultations and for eclipses of Sun or Moon. 
    Lilith is a strange point for having either of two meanings. 
Lilith for astronomy  should be set to be the apogee of the Moon's 
orbit, like for this article. The other sense is the second, empty, 
focus of the Moon's orbit. Astrology programs allow the selection. 
    In the middle of Scorpius (which astrologers call Scorpio) you see 
a black crescent with a plus sign under it. This is the astrological 
symbol for Lilith for both meanings. The opposite point, usually not 
marked, is the perigee of the Moon's orbit. 
    When the Moon is near Lilith, she moves at her minimum angular 
speed thru the stars, about 11-1/2 degree/day. Her angular speed 
increases with elongation from Lilith until the maximum, about 14-1/2 
degree/day, at the perigee, 6 signs away. Lilith helps visualize the 
speed of the Moon for indexing her position during the night. The 
planets, in contrast, move so slowly that you may leave them fixed 
during the night where they are at chart time. 
The Planets
    Astrologers include all nine (yes, nine) planets and a bunch of 
asteroids in their basic chart construction. Astrology programs let 
you turn off the unwanted ones, like I did here to leave only the 
classical planets from Mercury thru Saturn. 
    Asteroids on the chart will be in very misleading places. They 
wander so far from the ecliptic that they can not be properly plotted 
to match their places in the sky. I just don't use them at all. 
    The classical planet symbols are those used widely by astronomers 
until the mid 20th century. Even today, they are handy for note taking 
or other quick writing. 
    Scanning from west to east, we see no planets in [the signs of] 
Aries, Taurus, Gemini, up to medium coeli. Thus, the entire western 
sky is bare of planets. 
    Crossing into Cancer we got two planets, Moon and Mars. Moon is in 
Cancer 4 and Mars is in Cancer 3. Medium coeli is Cancer 4, so the 
Moon and Mars are also on the meridian. This you already figured out 
because Mars is at opposition, being then on the meridian at local 
midnight, which is chart time. 
    That the Moon is also near the meridian and near Mars is pura 
mente an accident. Note that the Moon is also opposite the Sun, so she 
is in her full phase. Yes, on the night before opposition, Mars is 
overshined by the full Moon! 
    Continuing east, we find Saturn in Virgo 9. Venus is in Scorpius 
22, near conjunction with Lilith. This aspect has no significance at 
all in astronomy. 
    We come round to imum coeli to find Sun, Mercury, and Jupiter 
clustered near the cusp of Capricornus (the astrologer's Capricorn). 
Sun is in Capricornus 2; Mercury, Capricornus 6; Jupiter, Capricornus 
1. All three are in mutual conjunction a are in mutual opposition to 
Moon and Mars! 
    Moving onward thru Aquarius and Pisces we find no more planets. 
This completes the circuit of the zodiac for 24 December 2007 at 0h in 
New York. We got three planets up in the night sky (Moon, Mars, 
Saturn) and four down (Venus, Sun, Mercury, Jupiter). 
    The retrograde motion of a planet is very important for both 
astronomy and astrology, yet few astronomy programs tell you directly 
when a planet is in retrograde. You have to step the planet a day to 
and fro and see how its longitude changes. Astrology programs make this 
motion clear in their output. When in retrograde, a planet's longitude 
decreases with time. 
    On the chart, see the little 'R' next to Mars and Saturn? This  
indicates that these planets are in retrograde. All the other planets, 
with no 'R' on them, are in prograde. 
    Mercury is in progade. This means that he is in a superior, not 
inferior, conjunction. Mercury continues his direct movement to cross 
from morning to evening apparition. If there was a 'R' against 
Mercury, the motion would be retrograde and the conjunction would be 
an inferior one. Mercury would be scooting westward to get from 
evening to morning sky. 
    Do not confuse retrograde motion with a decrease of elongation 
from the Sun! Mercury can lag the Sun's pace so the Sun catches up to 
him and form the conjunction. It's only in the final days before 
inferior conjunction that Mercury reverses tracks into retrograde. 
    Here's what Mercury does in late 2007-early 2008, taken from an 
astronomy program: 
        date         event
        -----------  ---------------------------
        2007 Sep 29  greatest eastern elongation
        2007 Oct 12  enter retrograde loop 
        2007 Oct 23  inferior conjunction 
        2007 Nov  1  leave retrograde loop 
        2007 Nov  8  greatest western elongation 
        2007 Dec 17  superior conjunction 
        2008 Jan 22  greatest eastern elongation 
        2008 Jan 28  enter retrograde loop 
        2008 Feb  6  inferior conjunction 
        2008 Feb 17  leave retrograde loop 
    In the morning sky, the decrease of elongation, as Mercury heads 
toward superior conjunction, must be direct. It is, in fact, faster 
than the Sun's pace to catch up to him. 
    A similar train of reasoning applies to Venus. At chart time Venus 
happens to be prograde as a morning star during western elongation. 
    The Moon's ascending node is always retrograde. This particular 
chart doesn't flag it. Some other programs plot the chart with the 'R' 
next to the ascending node so you can't miss it.. 
Part of Fortune 
    This is a fake planet of no use for astronomy that I can figure 
out. I include it here only in answer inquiries from my article 
'Astrology for astronomers?'. I turned it off for the chart here. 
    The explanation in astrology tends to read like dreamy feminist 
tracts from the 1970s. I spare you the particulars and note here only 
the calculation of Part of Fortune. This is for curiosity, you know? 
    The longitude of the ascendent and of the Moon are added, then 
that of the Sun is subtracted. From data in the chart, the PoF is at: 
        longitude of ascendent     Libra 03 = 183 
        longitude of Moon         Cancer 04 =  94 
        -----------------         ---------   ---
        sum                           ---     277 
        longitude of Sun     Capricornus 02 = 272 
        ----------------     --------------   ---
        difference                            005 
        longitude of PoF           Aries 05 <-/
    If I had PoF turned on, it would be plotted in the beginning of 
Aries with its symbol, looking like a railroad crossing sign. It is in 
a square aspect with Moon-Mars and with Sun-Jupiter-Mercury, in 
conjunction with descendent, and in opposition with ascendent. 
    If you look carefully at the medium coeli, it is not exactly the 
midpoint between ascendent and descendent. It is close ONLY by chance 
for the instant hour. In general MC is severely offset from the 
midpoint because of the ecliptic obliquity. 
    The ecliptic can rise to the left or right of the east point. 
Think of the displacement of the Sun's rising point with the seasons. 
He rises to the left of east in summer; right of east in winter. 
    The setting point of the ecliptic, the descendent, is opposite the 
ascendent, and is displaced to the same amount from the west point. 
Think of the full Moon settings. In summer she sets left of west. The 
winter full Moon sets right of west. 
    When the ascendent is to the left of east, there is a larger arc 
of ecliptic from it to the meridian than from meridian to descendent. 
Because the wheel chart shows the ecliptic, the MC is right of the 
what looks like an asymmetry in the sky. 
    When the ascendent is right of east, the lesser arc lies between 
it and MC; the greater, MC and descendent. MC is then left of the 
midpoint on the chart. 
    The astrology chart shows clearly the ascendent displacement 
relative to due east. When the cusp of house #1 is above the ascendent 
on the chart, above the horizon in the sky, the ascendent is left of 
due east. When the cusp of house #1 is below the ascendent, below the 
horizon, the ascendent is right of due east. 
    I must emphasize that this applies to the houses of the meridian 
system. It is not a general rule for any wheel chart. For the Placidus 
houses, the cusp of house $1 is fixed at the ascendent. You can still 
appreciate the shift by the MC. when it is left of the midpoint of the 
chart, the ascendent is right of east and vice versa. 
    Elongations in astronomy are almost exclusively banked off of the 
Sun. To find the elongation between two other planets you must 
manually subtract their solar elongations. Astrology computes 
elongations between all pairs of planets! This is z trivial chore for 
a computer program but those for astronomy don't include this faculty. 
    In astronomy certain elongations are specially noted, like 
opposition (elongation 180 deg) and conjunction (elongation 0 deg). 
Others used from time to time are quadrature (90 deg), greatest 
elongation (27 deg for Mercury, 47 deg for Venus), and stations at the 
vertices of retrograde loops. 
    Astrology recognizes most of the astronomy special elongations, 
called aspects, and adds several more.
       aspect               | elon | equivalent 
        conjunct            |   0  | conjunction 
        sextile (SEKS-till) |  60  | (not common) 
        square (SKWAIR)     |  90  | quadrature 
        trine (TREEN)       | 120  | (not common) 
        opposite            | 180  | conjunction 
    These are the 'major' aspects, promulgated by Ptolemaeus. Over the 
ages many other elongations were examined but none achieved general 
    Astrology programs offer a wide selection of these plus the 
ability to enter a custom aspect. I set ZET to show only the major 
aspects, otherwise the chart would be criss-crossed with aspect lines 
to the point of illegibility. 
    In astronomy the sense of the elongation is vital, whether it is 
to the east or west of the home body. Astrologers generally ignore the 
sense and work only with the absolute value of elongation. You have to 
manually take the sense from the wheel chart. 
    Aspects are calculated on the fly by ZET and laid out in the chart 
by lines joining the associated planets. On the line is the symbol for 
the aspect, a triangle for trine, a square for square (none in this 
chart), and a 6-point aster for sextile. Conjunction and opposition 
are usually not labeled, perhaps because they are so obvious. When 
described in text their symbols are the same as for astronomy. 
Lots of aspects
    On 24 December 2007 there are lots of aspects! Sun. Mercury, 
Jupiter are in conjunction. Mars and Moon are in conjunction. The 
first three are in opposition to the second two. Astrology treats EACH 
pair as its own aspect, so we have Sun opposite Mars and Sun opposite 
Moon. Then Mercury opposite Mars and Mercury opposite Mars, and so on. 
For the conjunction, we got Sun-Mercury, Sun-Jupiter, Mercury-Jupiter. 
    The lines joining each pair overwrite in the center of the wheel, 
looking like ropes tying Moon-Mars to Sun-Mercury-Jupiter. They in 
this case obscure the earth at the wheel hub. 
    There is in Scorpius a conjunction of Lilith and Venus, tho not so 
tight as the other conjunctions. 
    There are trines between Saturn and Sun-Mercury-Jupiter and 
between ascending node and Moon-Mars. Sextile stands between Moon-Mars 
and Saturn and between ascending node and Sun-Mercury-Jupiter. 
    Now hold the chart away a bit and relax the eyes. See the huge 
rectangle in the sky? The corners are Sun-Mercury-Jupiter, Saturn, 
Moon-Mars, and ascending node. Sides are 120, 60, 120, 60 degrees. The 
alignments are not precise, but pretty close. One corner is a fake 
planet, ascending node, invisible. Never the less, this night of the 
Mars opposition presents very interesting alignments of many planets 
thruout the zodiac. 
    This configuration is destroyed late on the 24th and is vanished 
by nightfall because the Moon moves along, out of aspect with the 
other planets. In the sky, on the night of the 24th, Moon is a dozen 
degrees east of Mars and almost a day past full.. 
    Altho the astrological chart is a snapshot for a single given 
moment, there is some kinetics we can extract from it. We saw this in 
the use of meridian houses to tell what's on the meridian at steps of 
two hours in the day, With these houses we can estimate culmination of 
the planets. 
    When does Saturn reach the meridian?
    Saturn sits about 1/5 of the way into house #12. The cusp of house 
#12 comes to medium coeli (same as culmination) four hours after the 
instant medium coeli at the cusp of house #10. 1/5 of two hours after 
that, Saturn comes to the meridian. So, Saturn culminates at 
    (culm) = (chart hour) + (full houses) + (part of next house) 
           = (00:00) + ((2) * (2h)) + ((1/5) * (2h)) 
           = 00:00 + 4h + 24m 
           = 04:24
This agrees within a couple minutes with astronomy programs. 
    This trick works well for culmination but fails badly for rising 
and setting. This is a consequence of the ecliptic obliquity. To 
better appreciate the kinetics of the wheel, you may cut charts at, 
say, one hour intervals during a night. Or run the program's 
animation, if available. 
    While astronomers may have little regard for the tenets of 
astrology, there are features of value. The construction, via an 
astrology computer program, of the wheel can give an easy-to-read 
diagram of the zodiac with planets deployed along it for any given 
moment and location. The information in this chart is valid for 
astronomy with reasonable interpretation. You may end up using it in 
parallel with the conventional equatorial chart.