OPERATION OF THE ASTROLABE
------------------------
John Pazmino
www.nyskies.org
nyskies@nyskies.org
2009 August 13 initial
2022 June 3 current
Introduction
----------
These instructions for the function and operation of the astrolabe
are specific to the particular model distributed at the 2009 August 17
NYSkies Astronomy Seminar.That model was taken Daniel Rislove's
website.
Without much error it can be used within any standard time, zone,
ignoring daylight savings time. Except for the movement of the Moon,
the celestial bodies shift position too slowly within a given day to
notice on the size of this model.
Because astrolabes are similar across designs these instructions
apply to most other models with reasonably obvious modifications.]
Climata
-----
Climata for this model are from N 15 degree thru N 65 degree in 5-
degree steps. The clima for N 40 degree is omitted because it is close
to New York City's horizon and isalready inscribed on the mater.
A clima ideally shows the entire sky over you, with a full set of
alt-az cutves. Some astrolabes have retes that cut off at the winter
solstice pont, not all the way to the southern limit of the horizon.
In such instruemnts the clima for some latitudes will be truncated in
the low south.
An early instruction rells how to set the astrolabe to a given
latitude by attaching the clima for that latitude.
Foreign rete
----------
Please kow well that 'rete' is a Latin word pronounced 'REH-teh'.
It is NOT 'REET', REE-tee', a couple really common goofs.
The rete in this specific model is from Keith Powell's website,
scaled to fit Rislove's mater. I labeled a few more stars and cleaned
up some clutter. I also labeled the zodiac signs at both ends to
help count degrees of ecliptic longitude.
This rete has a scale for the mean Sun around its edge, where the
right ascension scale would be in a typical instrument.HOME The line
OF the vernal equinox on the rete to the mater's midnight point for
reading right ascension or plotting new targets. This zero line is
also useful for indicating hours around the mater for time
differences, freeing the regula for other functions.
To use right ascension fon the homed rete, read from the mater's
hour scale. Count the hours CCW from 0h.
Because of the strong stretching of radial distance far from the
north celestial pole in the typical astrolabe, the rete may not extend
to the southern horizon. It usually is cut off at the winter solstice.
This feature can hold the instrument to a convenient physical size
Target
----
A target is a point in the celestial sphere. It may be a star,
meteor shower radiant, galactic center, deepsky feature, &c. Targets
typicly are cataloged with their RA and DE. The lack of a true RA
scale on this rete is sorely felt. A planet, other solar ssytem body,
is catalogued by either RA-DE or ecliptic lat-lon. The latter are
easier to note or plot along the ecliptic on the rete.
If the planet's latitude is only a few degrees from the ecliptic,
it is usual to ignore the latitude and place the planet on the
ecliptic according to its longitude.
Some basic tasks
--------------
To pin, tie, fix, attach parts together means to hold them with a
paperclip while taking care to let the remaining parts turn freely.
The joined parts mover as a unit and are stated together, like 'mater-
alidade' or 'rete-regula'.
To set parameters means to manipulate the astrolabe to present the
parameter on scales or pointers or marks. The process is deailed in a
prior instruction.
To get a aprameter means to seek it in an external source, not the
astrolabe, and note it for use in the instant instruction.
To mark points or lines means to draw them on the rete with an
erasable medium. Or deaw them on clear plastic tissue placed on the
rete. .
To read, note, take a parameter means to keep it in mind, or
written down, for further use in the instruction.
SOme instructions ctell to take, measure, capture, altitudes.
These are included for an astrolabe built from substantial rigid
material and the regula or alidade has sighting vanes.
The model ssumed here is made of paper or thin card, too flimsy
and flexible for taking altitudes.
Mean vs apparent solar time
-------------------------
/ For most skywatching it doesn't matter much which time is used.
The greatest dispersion between them is about 16 minutes.
As a general rule if you're dealing with activitiess at night, you
may use mean time. This is given by the scale on the rete.
To set the mean date, lay the regula over the date on the rete
and pin it there. Rotate the rete-regula to the hour on the mater. The
astrolabe is set to the date and hour.
In this mode the astrolabe works like a planisphere, star-finder,
star-wheel.
For events in daytime you can use apparent time. This is found by
the scales on the dorsum. Noote the ecliptic longitude of the Sun
against the date. Then lay the regula over that longitude on the rete
and tie it there. Rotate the rete-regula to the hour on the mater.
The astrolabe is set to the date and hour.
Setting the time both ways gives a discrepancy of several
minutes. This offset is the equation of time for the given date. A
better methodfor equation of time is one of the instructions.
Set the latitude
--------------
Select a clima nearest to the given latitude, from N 15 to N 65
degrees.
Unbolt the model and remove the regula and rete.
Place the clima onto the mater so its north coincides with north
on the mater. Attach them together with a couple paperclips.
Place the rete and regula over the clima and bolt the model
together.
The astrolabe is now set for the given latitude.
Set the sidereal time
-------------------
On the hour scale of the mater count hours CW from SOUTH to the
given sidereal time. Ignore the numerical labels and count the hour
marks.
Rotate the rete to place its zero line against the given sidereal
time on the mater.
The astrolabe now set for the given sidereal time. The right
ascension on the meridian is the very sidereal time.
Rotating the regula over the mean date scale on the rete and the
hour scale on the mater gives combinations of date and time that yield
the given sidereal time.To view the sky at the given sidereal time,
look on any of the date-hour combinations.
Set the date by apparent solar time
---------------------------------
From the dorsum read the Sun's longitude against the given date.
Place the regula over this longitude on the te te's ecliptic and
pin it there. The regula and ecliptic cross at the place of the
apparent Sun.
The astrolabe is set for the date by apparent solar time.
Set the date by mean solar time
-----------------------------
Place the regula over the given date in the limb of the rete and
tie it there. The crossing of regula and ecliptic is the place of the
mean Sun, not the real Sun.
The astrolabe is set for the date by mean solar time.
Set the hour of the day
---------------------
Place the regula over the hour of the day on the mater and pin it
there.
The astrolabe is now set for the hour.
Note the longitude of the Sun where the regula and ecliptic cross.
Turning the rete under the regula slides the Sun thru the days.
The Sun wanders in altitude and azimuth thruout the year at the
given hour of the day.
Set both date and hour
--------------------
Set the date by mean or apparent solar time. Pin the regula to
the rete.
Rotate the rete-regula so the regula points to the hour on the
mater. Pin the rete-regula to the mater.
The astrolabe is set for the date and hour.
Plot a new target on the rete
---------------------------
Home the rete on the mater and pin it there.
Olace the regula on the target's right ascension by counting hours
CCW from north and fix it there.
Mark the target against the declination along the regula. attached
to the rete in the area of the target.
The target is now plotted on the rete. This method works for a
rete made from a transparent sheet, not an open scrollwork.
Plot a target's diametricly opposite point - method I
---------------------------------------------------
Place the regula over the target and note its declination.
Turn the regula end-for-end and again place it over the target.
This maneuver is necessary because the regula has the declination
scale on only one arm, not both.
Mark the point against the declination of OPPOSITE SIGNUM but
EQUAL VALUE as the target's.
The diametricly opposite point is now plotted on the rete.
This function is trivial for the Sun or other body in the
ecliptic. The regula placed over the Sun also sits on the ecliptic
diametricly opposite from the Sun.
This function is restricted by the southern extent of the rete, in
this model -23.4 degrees. You are limited to targets within 23.4
degrees of the equator. A rete reaching farther south allows a
corresponding larger range of declination for opposite points.
Plot a target's diametricly opposite point - method II
----------------------------------------------------
Rotate the rete to place the target on the horizon, either east or
west.
Place the regula over the target.
Mark the point where the regula crosses the horizon opposite from
the target.
The diametricly opposite point is plotted on the rete.
Because in this model the horizon is sliced off in the southern
sky, the range of declination is more restricted than for method I.
For New York, +40.75 deg latitude, the usable zone is within 20
degrees from the equator.
An other restriction is that north of declination +49.25 degree,
in New York's latitude, a target can not reach the horizon. It is
semperpatent. This doesn't matter because its opposite point is in the
semperlatent zone around the south pole.
Plot a planet on the rete
-----------------------
If the planet's RA and DE are gicen, procede like for plotting a
new target.
If the planet's ecliptic lat-lon are givend, place the regula over
the longitude along the ecliptic and tie it there.
Mark the planet at the intersect of regula and ecliptic
Usually the latitude is ignored. The planet is assumed to sit on
the ecliptic.
Mark the planet at this place.
The planet is now plotted on the rete.
To account for latitude, count along the regula, as an offest from
the ecliptic. degrees from the ecliptic to the planet. This is
approximate because the declination and latitude coords are inclined.
The greatest error is near the equinoxes; least, solstices.
Plot a planet's aspects
---------------------
An aspect is a certain angular displacement, elongation, of the
planet from an other body, Usually, but not always, the Sun.
Set the date.
Note the longitude of the Sun as sign-degree, like 'Gemini 15',
rather than '75 degree'.
The common aspects of a planet are, relative to Sun:
-----------------------------------------------------
inf/sup conjunction 0 degree coincident with Sun
greatest elongation (varies due to excentric orbits)
sextile 60 degree 2 signs
square/quartile 90 degree 3 signs
trine 120 degree 4 signs
station (varies due to excentric orbits)
opposition 180 degree opposite from the Sun
--------------------------------------------------------------
The elongation is either east or west of the Sun according as the
location of the planet in the zodiac. Latitude is ignored. The planet
is on the ecliptic.
Count whole signs by stepping to the SAME DEGREE of each as that
of the Sun. For the greatest elongations and stations, finish the
count with the leftover extra degrees.
Mark a point on the ecliptic at the aspect elongation. The
planet's aspect is now plotted on the rete.
Plot the Moon on the rete - method I
----------------------------------
Get the hour of moonrise next before the given hour and the
moonset next after the hour., both for your location and timezone.
Set the date and hour for moonrise.
Mark the intersect of the ecliptic and east horizon. This is the
place of the Moon at moonrise.
Set the date and hour for moonset.
Mark the intersect of the ecliptic and west horizon. This is the
place of the Moon at moonset.
Mark the eclipiic halfway between the first two marks. This is the
approximate place of the Moon for its culmination, which should be
close enough for the given hour. The Moob's longitude is read at this
mark.
Erase the fmoonrisemoonset marks.
Set the date and given hour.
This method is approximate because the Moon moves rapidly thru the
zodiac and wanders north and south of the ecliptic.
Plot the Moon on the rete - method II
-----------------------------------
Get the dates of the cardinal phase next before the given date and
the one next after that date, both for your location and timezone.
The cardinal phases of the Moon are:
-------------------------------------
New 0 deg, coincident with Sun
1st Qtr 90 deg, 3 signs east from Sun
Full 180 deg, opposite from Sun
3rd Qtr, 90 deg, 3 signs west from Sun
--------------------------------------
From the dorsum against the first date read the longitude of the
Sun and mark it on the ecliptic of the rete.
Mark the ecliptic at the elongation of the first cardinal phase.
Call this point 'bef'.
Repear this procedure for the second crdinal phase and call the
point 'aft'.
The angular interval of ecliptic between the 'bef' and 'aft'
points is equal to the time interval between the two phases. This is
usually seven or eight days.
By eye divide this ecipitc span into these seven or eight equal
parts.
Eyeball the point between 'bef' and 'aft' for the location of the
given date. mark the ecliptic at this point and call it 'now'
This 'now' point is the approximate place of the Moon for the
given date.
Erase the Sun's, 'bef', and 'aft' points, leaving just the 'now'
point.
Set the given date .
This method is approximate because a phase can occur at any time
within its listed date and the Moon wanders north and south of the
ecliptic.
The longitude of the Moon is read at the 'now' mark.
Plot a rapidly moving target on the rete
--------------------------------------
The Moon and typicly a comet shift location drasticly day by day,
requiring a new plot for each.
Procede like for plotting a new target, placing marks for each
day. Label the marks with their dates.
Use the proper mark for each day of astrolabe setting.
FInd the sidereal time
--------------------
Set the date and hour.
The zero line of the rete points to the sidereal time on the
mater. Ignore the enumber labels and count CW from SOUTH, not north.
The right ascension now on the meridian is the very sidereal time.
Measure the altitude of a target other than the Sun.
-------------------------------------------------
This instruction is for an astrolabe made of sturdy material like
thick plastic, metal, wood. It can not be applied for one made of
paper or card. The instrument is too light and fflexible.
Face the target and hold the astrolabe by its suspebsion cord to
let it hang freely.
Hold it high enough to sight the target along the alidade. If the
alidade has sighting vanes, use them.
Gently rotate the alidade, keeping the mater straight and
vertical, until the target is squarely lined up with the alidade. When
When the target is properly lined up tie the alidade to the mater.
Take down the astrolabe and read the target's altitude where the
alidade sits in the mater..
Measure the altitude of the Sun - method I
----------------------------------------
This instruction is for an astrolabe made of sturdy material like
thick plastic, metal, wood. It can not be applied for one made of
paper or card. The instrument is too light and flexible.
Stand sideways against the Sun with your shadow to one side.
Hold the astrolabe by its suspenseion cord to let it hang freely
in front of you.
Gently rotate the alidade,keeping the mater straight and vertical,
until the shadow of the upper end or vane falls squarely onto the
lower one.
DO NOT LOOK AT THE SUN ALONG THE ALIDADE! Serious and perhaps
permanent eye damage can result.
When the Sun is properly lined up tie the alidade to the mater.
Take down the astrolabe and read the altitude of the target where
the alidade sits in the mater.
Measure the altitude of the Sun - method II
-----------------------------------------
Get a vertical pole on level ground in sunlight. A vertical corner
of a building will do as well.
Place a mark on the pole at a convenient known height on it so it
shows in the pole's shadow. This mark is the 'top' of the pole.
Measure the height of the pole and length of its shadow.
Get the ratio (pole height)/(shadow length) and reduce it to a
fraction of 12ths.
On the dorsum rotate the alidade to lay over this ratio on the
altimeter scale. Be sure the 'rise' (height) and 'run' (length) are
right way round.
The alidade points to the Sun's altitude on the mater.
If the shadow is greater than the pole, the Sun altitude is less
than 45 degree; less, greater.
It is easier on the math if the measures are in units of 12ths
This only because this particular model has a scale divided into
12ths. A modern astrolabe has decimal scales.
Find the equation of time for a given date
-----------------------------------------
Read the longitude of the Sun on the dorsum against the given
date.
Rotate the rete to place this longitude on the south meridian and
tie it to the mater. The apparent solar time is 12:00.
Place the regula over the given date on the rete's mean date
scale.
Read the hour from the mater against the given date. In general it
will differ from 12:00.
Subtract algebraicly 12:00 from this mean hour. The difference
is the equation of time for the given date. It is the value
a;gebraicly added to a sundial reading, apparent time, to obtain the
clock hour , mean Sun.
Find the coordinates of a target on the rete
------------------------------------------
Home the rete on the mater and tie it there.
Lay the regula over the target and tie it to the rete.
Read the declination of the target along the scale on the regula.
The regula points to the right ascension on the mater's hour
scale. Ignore the number labels and count CCW from north.
Find the hour of sunrise or sunset
--------------------------------
Set the date..
Rotate the rete-regula to put the Sun on the east horizon for
sunrise; west, sunset.
The regula points to the hour on the mater for sunrise.sunset.
Find rise and set hour for a target
---------------------------------
Set the date.
Rotate the rete-regula to place the target on the east horizon for
risingl west, setting.
The regula points to the hour on the mater for the target's
rising/setting.
Find when a target culminates
---------------------------
Set the date.
Rotate the rete-regula to place the target on the south meridian.
The regula points to the hour on the mater for the culmination.
Some targets may culminate north of the zenith. Place them on the
meridian between the north pole and the zenith.
Semperpatent stars have two culminations, above and below the
north pole. The function works for both in turn by placing the target
on the meridian above and then below the pole..
Find when the Sun culminates
--------------------------
Read the longitude of the Sun on the dorsum against the given
date.
Rotate the rete to place this longitude on the south meridian.
The hour by apparent solar time is 12:00.
Place the regula over the given date on the rete's mean date
scale.
Read the hour from the mater against the given date. This is the
mean hour, on a clock, when the Sun culminates on the given date.
BThis mean hour is in general not 12:00, the sunrise and sunset,
in mean ime, ae assymetic avout apparent solar 12:00.
Find the hour angle of a target
-----------------------------
Set the date and time and then tie the rete to the mater.
Place the regula over the target.
The regula points to the hour angle on the mater. Ignore the
number labels and Count hours clCWe from SOUTH, not north.
Sometimes the hour angle is counted westward thru +12h; eastward
thru -12h. The latter is the hours UNTIL culmination of the target;
former, hours SINCE.
Find the longitude of the Moon or planet in the sky
-------------------------------------------------
Set the date and hour.
Note which side of the sky the Moon or planet sits in, east or
west.
Measure the altitude of the body.
Note where the measured altitude crosses the ecliptic on the
proper side of the sky.
The longitude at this point is the spptoximate longitude of the
bodyt. It ignores ecliptic latitude, which can be substantial.
Find the elongation and age of the Moon in the sky
------------------------------------------------
From the dorsum read the longitude of the Sun for the given date
and hour.
Find the longitude of the Moon in the sky for this date and hour.
Subtract the Sun's longitude from the Moon's, minding a rollover
thru the vernal equinox.
The difference is the rast elongation of the Moon from the Sun.
Divide this elongation by 12.2deg/day. The result is the Moon's
age in days since the previous new Moon.
Slyho rvlipyiv latitude is neglected, the result is surprisingly
good.
Find when a target touches a given altitude
-----------------------------------------
Set the date.
Rotate the rete-regula to place the target at the given altitude.
In general this happens twice during the day, on the east side of the
sky and on the west. Select the proper instance.
The regula points to the hour on the mater when the target touches
the given altitude.
Find when a target touches a given azimuth
----------------------------------------
Set the date .
Rotate the rete-regula to place the target at the given azimuth.
The regula points to the hour on the mater when the target touches
the given azimuth.
Find when the Sun shines on a vertical wall
-----------------------------------------
Get the azimuth alignment of the wall and its outward-facing
direction.
Note on the clima the azimuth alignment and outward side of the
wall.
Set the date of the year.
Slowly rotate the rete-regula from sunrise thru sunset. The regula
rides over the hours on the mater.
When the sun first shines on the wall, by sunrise or touching the
azimuth, note the hour pn the mater.
When the sun last shines on the wall, by suset or touching the
azimuth, note the hour pn the mater.
Depending on the alignment, season, latitude, there could be TWO
periods of sunshine during the day.
Find the interval between two events
----------------------------------
Set the date and hour for the first event.
Mark the rete on its rim against the 0h point on the mater.
The regula is occupied by the first event and may be needed for the
second one.
Set the date and hour for the second event.
Note the hour on the mater against the mark for the first event.
This is the interval between the two events.
Find the ascension or descension of a aodiac sign
-------------------------------------------------
The ascension of a sign is the interval between the rising of its
west and east boundary. The descension is the duration between the
settings of these two boundriess.
Place the west boundary of the sign on the east horizon.
Place the regula on the mater's 0h point and tie it to the rete..
Totate the rete-regula to place the sign's east boundary on the
east horizon.
Note the hour on the mater against the regula. This is the
duration of the sign's ascension.
Repeat this procedure for the setting on the west horizon. This is
the duration of the sign's descension.
This exercise shows that, unlike equal spans of the celestial
equator, equal spans of the ecliptic, or of any great circle inclined
against the equator, do not rise and set in equal intervals.
Find the angular separation of two targets - method I
---------------------------------------------------
This is a cut-&-try exercise requiring a swop of climata.
Rotate the rete to place the targets together on the SAME great
circle on the clima. suitable great circles are the horizon and an
azimuth.
If the targets are on the horizon, note their azimuths along the
horizon.
If the targets are on the same azimuth meridian, note their
altitudes on that meridian.
The difference in azimuths or altitudes is the angular separation
of the targets.
If no good fit is possible with a one clima, try an other. It may
be necessary to interpolate between two climata's best, not good
enough, fits.
With the limited set of climata in this model there may be NO good
fit of the targets.
Find the angular separation of two targets - method II
----------------------------------------------------
For ONE of the targets plot its diametricly opposite point.
Procede like for method I with this opposite point and the other
target.
Subtract the separation for these two points from 180 degrees.
The result is the angular separation of the two targets.
Like for method I you may find NO good fit.
Plot a great circle thru two targets
-------------------------------------
This is similar to the angular separation function, being a cut-&-
try exercise. There may be no solution with the climata in this model.
Rotate the rete to place the two targets on either the horizon or
an azimuth. You may have to swop climata to find a good fit.
When the targets are properly placed, mark the arc between them
exactly over the horizon or meridian.
The arc is the great circle between the two targets.
Plot a great circle around a target - method I
--------------------------------------------
The target is a pole of the great circle, 90 deg away.
Rotate the rete to place the target on the horizon and pin it.
Note the azimuth 90 degrees left and right of the target.
Mark the arc over the azimuth from the left 90-deg point, thru
zenith, to the right 90-deg point.
Compete the great circle by repeating this procedure with the
taget placed on the opposite horizon.
This arc is the great circle whose pole is the target.
Plot a great circle around a target - method II
---------------------------------------------
Because of the confined southern extent of the rete, the target may
not reach the horizon or one azimuth of the great circle is
interrupted.
Plot the diametricly opposite point from the target.
This point is the opposite pole of the great circle around he
target.
Rotate the rete to place this opposite point on the horizon and
pin it to the mater..
Procede with method I on this opposite point. The resulting are is
the great circle around the target.
Plot a great circle around a target - method III
----------------------------------------------
Rotate the rete to place the target on the south meridian and tie
it to the mater. For a semperpatent target, place it on the meridian
above the north pole.
Note the altitude of the target.
Mark along the meridian the altitude 90 degrees away, eiter above
or below the target,
Mark the points where the equator crosses the horizon in both east
and west.
The three points sit on the great circle around the target.
Procede as for finding the great circle thru two targets, pairing
the points and marking the arc between them.
It could be simpler to construct by geometry the circle passing
thru the three points.
Find the observer's latitude by day
---------------------------------
This is intended for a latitude not among the climata with the
astrolabe. Place any clima near the unknown latitude on the mater and
tie it there.
Set the date.
Rotate the rete-regula to put the Sun on the south meridian.
Note the altitude of the Sun.
Wait until 12:00 apparent solar time when the Sun culminates.
At the culmination hour, measure the altitude of the Sun.
Subtract algebraicly the measured altitude from the displayed altitude.
Add algebraicly the difference to the clima's latitude.
The sum is the latitude of the observer's latitude.
To trap math mistakes repeat this procedure, keeping the measured
solar altitude, with a clima of an other nearby latitude.
Find the observer's latitude by night
-----------------------------------
This is intended for a latitude not among the climata with the
astrolabe. Place any clima near the unknown latitude on the mater and
tie it there.
Set the date and hour..
Note a target on the rete which is approaching its culmination.
Find the hour of the target's culmination.
At the culmination hour, measure the altitude of the target.
Subtract algebraicly the measured altitude from the displayed
altitude.
Add algebraicly the difference to the clima's latitude.
The sum is the latitude of the observer's latitude.
To trap math mistakes repeat this procedure, keeping the measured
solar altitudfe, with a clima of an other nearby latitude.
Find the observer's longitude
---------------------------
Get the predicted times for the stages of the next lunar eclipse.
The longitude of these predictions is the home longitude. Often, but
not always, this is 0 deg.
A lunar eclipse is best for this method because its aspect in the
sky is independent of the observer's longitude. A lunar eclipse also
has several, up to four, stages available to capture data within the
one night.
Set the date for the first stage of the eclipse.
During the eclipse, at each stage, take and record the altitude
of a target on the rete. Choose one in the east sky so it has greater
chance of being visible for the whole eclipse. A west target may set
during the eclipse.
After the eclipse find the hour, in local mean solar time, from
the target altitudes.
For each stage algebraicly subtract the home home hour from the
observed hour. Mind any rollover across midnight. A negative result
means that your longitude is west from the home longitude positive,
east.
Take the average of these differences They should be the equal
within a minute.
Convert this average difference to angle at 15 deg/hr and 1/4
deg/min. In special cases the time difference is the final result with
no angle conversion.
The result is your longitude relative to the home location.
Find the hour of the day by the Sun
---------------------------------
Set the date .
Note which side of the sky the Sun is in, east or west.
Measure the altitude of the Sun.
Rotate the rete-regula to place the Sun at the measured altitude
on the proper side of the sky.
The regula points to the hour of the day on the mater.
Find the hour of the day by night
---------------------------
Set the date of the year.
Rotate the rete-regula so the rete displays as closely as
practical the view of the sky. This is best assessed with stars near
the horizon.
The regula points to the hour of the day on the mater.
FInd the hours of twilight
------------------------
Set the date.
Rotate the rete-reegula to place the Sun at the first crepuscular
circles in the west, alt -6 deg.
The regula points to the hour on the mater.
This is the end of civil twilight.
Repeat for the 2nd and 3rd crepuscular circle, alt -12 anad-18 deg
These are the ends of nautical and astronomical twilight.
A symmetrical procedure applies to the morning twilights.
Find when the Sun srises/ets in a given azimuth
---------------------------------------
Rotate the rete to place the ecliptic on the east/westhorizon at
the given azimuth. In general there are two instances when this can
occur.
Read the Sun's longitude at the intersect of horizon and ecliptic.
From the dorsum read the date for this longitude.
Repeat for the second instance.
These dates are when the Sun rises/sets in the given azimuth.
There is no occurrence if the azimuth is too far right or left
(nortof the due east/west point on the horizon. The Sun can not
rise/set in the given azimuth.
Find the compass directions by day
--------------------------------
Set the date and hour. The regula sits over the Sun.
Fix the mater, regula, and rete together.
Squarely face the Sun by lining up with your shadow. Or sqarely
face your shadow and do an about-face.
Hold the astrolabe upright in front of you.
Rotate the whole astrolabe in its own plane, like a wheel, so the
regula points straight up, aiming at the Sun in the sky.
Tilt the whole astrolabe back, away from you, face-up, into a
horizontal position like on a level surface.
Do not alrer its oreientation. The rgula must point straight
forward in front of you.
The degrees in the mater now line up with the compass the ground.
0 degrees is north; 90, east; 190, south; 270, west.
Find the compass directions at night
----------------------------------
Set the date and hour.
Fix the mater and rete together.
Select a visible target in the sky that is on the rete.
Place the regula over this target on the rete. Pin ithe regula,
rete, and mater together..
Squarely face the target in the sky as best as you can.
Hold the astrolabe upright in front of you.
Rotate the whole astrolabe in its own plane, like a wheel, so the
regula points straight up, aiming at the target in the sky.
Tilt the whole astrolabe back, away from you, face-up, into a
horizontal position like on a level surface.
Do not alter its orientation. The regula must now point straight
forward n front of you.
The degrees in the mater now line up with the compass the ground.
0 degrees is north; 90, east; 190, south; 270, west.
Find the sun-gap of a target
--------------------------
Rotate the rete to place the target at setting in the west.
Note the longitude where the ecliptic intersects the -18 deg
crepuscular circle in the west, -18d altitude.
From the dorsum read the date against this longitude.
This is the start of the sun-gap, when the target is last visible
in a ull night sky due to approach of the Sun.
Repeat for the target rising on the east horizon.
This is the end of the sun-gap, when the target is first visible
in a full night sky due to reproach of the Sun.
Find the semperpatent latitude of a target
----------------------------------------
Lay the regula over the target.
Read the declination of the target along the regula.
Subtract this declination from 90 degrees.
The result is the semperpatent latitude for the target.
This function applies to targets of northern declination.
Find the semperlatent latitude of a target on the rete
----------------------------------------------------
Lay the regula over the target.
Read the declination of the target along the regula.
Add this declination to 90 degrees.
The result is the semperlatent latitude for the target.
This function applies to targets of southern delination. It also
has limited range in this astrolabe necause the rete cuts off at the
winter solstice, decl -23-1/2 deg.
Find the dates of the white night season
--------------------------------------
Rotate the rete to place the ecliptic on the lowest crepus ular
altitude, -18 deg, in the north, 0 deg azimuth. There are in general
two instances for this situation.
Note the ecliptic longitude for each instance.
From the dorsum read the dates against thiese longitudes.
The dates are the start and endd of the white night season.
If the latitude is less than +49 degrees there is no White Night
season. Thr Sun around midnight is below -18 deg altitude, making
full night.
Find the approxiaaqte date of a target's heliacal rising/setting
-------------------------------------------------------------
Rotate the rete to place the target on the east horizon
Note the longitude of the ecliptic sitting on the first
crepuscular circle, -6 deg alti in the east.
From the dorsum against this longitude, read the date.
This is the date of the target's heliacal rising.
On following days the visibility period lengthens as the Sun moves
farther east in the ecliptic.
A symmetrical procedure applies to heliacal setting. Place the
target on the west horizon and note the longitude of the ecliptic
sitting on the first crepuscular circle in th west. The date of this
situation is that of the target's heliacal setting.
The heliacal rising/setting is a precise event. It relies on the
actual sighting of the target under a complex of factors, most
impeding visibility of the target near the expected heliabal date..
Find a target's heliometric rising and setting
------------------------------------------
There are four heliometric cases for a target:
* Cosmic or mundane rising - target rises at sunris
* Cosmic oe mundane setting - target sets at sunrise
* Acronychal or temporal rising - target rises at sunset
* Acronychal or temporal setting - target setss at sunset
None of these is observable due to daylight at sunrise or sunset.
The mathod for all four is similar. Rotate the rete to place
the target on the appropriate horizon.
Read the longitude of the ecliptic sitting on its appropriate
horizon.
Read the associated date from the dorsum against this longitude.
Find the coordinates of a new unknown target in the sky
-----------------------------------------------------
Set the date and hour.
Tie rete and mater together.
Note which side of the sky the target is in, east or west.
Measure the altitude of the target.
On the rete mark the altitude circle of the target on the proper
side of the sky. Make thiws arc generously long. Interpolate between
the altitude circles and make your arc concentric with them.
Wait a few hours and Set the astrolabe to the new hour.
Tie the rete and regula together.
take a newe altitude of the target.
Mark on the rete the new altitude arc. Only a short arc is needed
near the first arc.
Where the two arcs intersect is the location of the target.
Home the rete and mater and pin them.
Place the regula over the intersect of arcs to read the
declination.
The regula points to the RA on the mater. Ignore the number labels
and Count CCW the RA from north.
Find the height of a point of known distance away on the ground
--------------------------------------------------------------
Assume the ground is level.
Measure the altitude of the point like for a target in the sky.
Fix the alidade to the dorsum.
Measure the distance from you to the point along the ground.
On the dorsum read where the alidade crosses the altimeter scale
for the 'rise' and 'run'. On this astrolabe the ratio is in twelfths.
Solve
height = rise * distance / run
The result is the height of the point above the observer's eye.
Find the distance to a point of known height above the ground
-----------------------------------------------------------
Assume the ground is level.
Measure the altitude of the point like for a target in the sky.
Tie the alidade to the dorsum.
On the dorsum read where the alidade crosses the altimeter scales
for the 'rise' and 'run'. The scale is in 12th parts.
Solve
distance = height * rn /(rise
The result is the distance of the point.
Find the trigonometric functions of an angle
------------------------------------------
The dorsum's altimeter gives approximate values for the six
trigonometric functions.
Place the alidade arm with the 12ths scale over the altimeter on
the given angle.
The scales on the altimeter and alidade give lengths of the
adjacent side, opposite side, and hypotenuse of a right triangle for
the given angle.
The ratios of the sides give the values:
* sine(angle) = opposite / hypotenus
* cosine(angle) = adjacent / hypotenuse
* tangent(angle) = opposite / adjacent
* cotangent(angle9 = adjacent / opposite
s* ecant(angle) = hypotenuse / adjacent
* cosecan(angle) = hypotenuse / opposite
The ratio is worked on a arithmetic calculette.
For angles greater than 45 degrees, it may be better to read out
the reciprocal function and divide it into 1 with the calculette.
Only angles from 0 to 90 degrees are displayed. Keep track of the
signum and quadrant separately.
Find the qibla by day
-------------------
The qibla is the azimuth along the great circle from you to Mecca.
Its value for your location comes from local Islamic officials. For
New York City it is 59 degrees.
Set the date and tie the rete and regula together.
Rotate the rete-regula to put the Sun on the qibla azimuth.
Note the hour on the mater limb. his is the qibla hour..
Stand at your location at the qibla hour on this same date. If the
hour already passed by, do so on the very next day.
Face squarely into the Sun.
Note directly under the Sun any recognizable landmarks in your
landscape.
On any future date, at any hour from this same location, face
squarely into these landmarks. You are now facing Mecca.
This method works if the Sun's diurnq arc crosses the qibla
azimuth. It may not by latitude and season. It ca not is the qibla
azimuth is between summer solstice sunset, thru north, to summer
solstice sunrise.
Find the qibla by night
---------------------
The qibla is the azimuth along the great circle from you to Mecca.
Its value for your location is obtained from the local islamic service
office. Set the date and hour and ti the rete and regula together.
Note along the qibla azimuth what stars are approaching this
azimuth in their diurnal arcs. Select any recognized star.
Rotate rete-regula to put the selected star on the qibla azimuth
and note the hour in the mmater limb. This is the qibla hour.
Stand at your location at the qibla hour on this same, or very
next, date.
Face squarely into the star.
Note directly under the star any recognizable landmarks in your
landscape.
On any future date, at any hour from this same location, face
squarely into these landmarks. You are now facing Mecca.
This method works best for stars of low altitude, perhaps up to 45
degree. Above that the azimuth circles converge closely toward the
zenith for less precise facing.
Find a candidate date for First Crescent
--------------------------------------
Get the date and hour of the next New Moon, like from an almanac.
You may have to rectify it into your longitude or timezone.
set the date to the New Moon date and tie together the regula and
rete.
Rotate rete-regula to put the Sun on the west horizon for sunset
and not the sunset hour. Mind a possible wrap around midnight.
Tie the rete to the mater.
sbntract the New Moon hour from the sunset hour.
Allowing that the Moon moves east in the ecliptic at 1/2 degree
per hour, work out the run of the Moon New Moon to sunset.
Release the regula, leaving the rete-mater tied.
pace off from the Sun the Moon's run, whole degrees, and tie the
regula to the rete. The regula/ecliptic crossing is the place of the
Moon.
If the Moon is at least 5 degree altitude this date is a candidate
date for first Crescent. Else the next sunset is a better candidate.
this method ignores lunar displacement from the ecliptic and can
only offer candidate dates to anticipate arrival of formal notice of
first Crescent.
Find the unequal hours of the day - method I
------------------------------------------
Set the date and the hour.
The regula/ecliptic intersect OPPOSITE to the Sun sits on the
unequal hour on the mater. The unequal hours are the radial arcs
between the horizon and the limb of the mater.
The unequal hours divide the day, sunrise thru noon to sunset,
into twelve equal parts, regardless of the season. They are also
called seasonal hours. Altho EACH period, day and night, is divided
into twelve equal parts, the two sets of hours are NOT the same. They
vary in proportion as the day/night proportion varies during the year
due to the seasons.
Find the unequal hours of the day - method II
-------------------------------------------
Set the date and the hour.
Read the declination of the Sun along the regula.
Read the altitude of the Sun among the altitude circles.
On the dorsum place the alidade arm eith the declination scale
over the unequal hour scale at the Sun's altitude.
Note the declination of the Sun along the alidade.
This point is at the unequal hour of the day.
Find the unequal hours of the night
---------------------------------
Set the date and the hour.
The Sun sits on the unequal hour on the mater. The unequal hours
are the radial arcs between the horizon and the rim of the mater.
The unequal hours divide the night, sunset thru midnight to
sunrise, into twelve equal parts, regardless of the season. They are
also called seasonal hours.
Altho EACH period, day and night, is divided into twelve equal
parts, the two sets of hours are NOT the same. They vary in proportion
as the day/night proportion varies during the year due to the seasons.
Find the house of a target - method I
-----------------------------------
Set the date and hour.
Put the regula over the trget and pin it, rete, mater together.
Count CCW on the mater's hour scale 'houses' 2-by-2 starting with
house '1' at the mater's 06h point. House 10 is at the mater's 12h
point, the south meridian.
The regula in this house circuit sits in the target's house. Each
minute on the mater is 1/0th of a house.
The house is one of the 12 divisions of the horizon like the
division of the zodiac into 12 signs. There being no standard way to
divide the horizon, there arose about 20 systems of house.
This model of astrolabe doesb't show houses directly. It does
embed two particular house systems: the equal-hour and equal-azimuth
schemes.
Equal-hour coincides with the hour angle, two hours per house.
The houses progress eastward, not westward like hour angle. House 10
begins at the south meridian by tradition. It covers hour angles 24h
back to 22h. The correespondece getween hour angle and equal-hour
house is sown in this table:
---+---------++-------
no | hr ang | remarks
---+---------+--------
10 | 24h-22h | E from S meridian
11 | 22h-20h ||
11 12 | 20h-18h |
1 | 18h-16h | E from E horizon
2 | 16h-14h |
3 | 14h-12h |
4 | 12h-10h | E from N meridian
5 | 10h-08h | 08h-10h |
6 | 08h-06h |
7 | 06h-04h | E from W horizon
8 | 04h-02h |
9 | 02h-00h |
---+---------+---------+------
Find the house of a target - method II
-----------------------------------
Set the date and hour.
Put the regula over the trget and pin it, rete, mater together.
Count CCW on the clima's azimyths 'houses' 30-by-30 degrees
starting with house '1' at the 90 deg azimyth. House 10 is at the 180
deg azimuth, the south meridian.
The regula in this house circuit sits in the target's house. Each
degree of azimyth is 1/3th of a house.
The house is one of the 12 divisions of the horizon like the
division of the zodiac into 12 signs. There being no standard way to
divide the horizon, there arose about 20 systems of house.
This model of astrolabe doesb't show houses directly. It does
embed two particular house systems: the equal-hour and equal-azimuth
schemes.
Equal-azimyth coincides with the azimth, 30 degrees per house. The
houses progress eastward, not westward, opposite to conventional
azimyh. House 10 begins at the south meridian by tradition. It covers
azimths 180 deg back to 150 deg. The correespondece getween azimthand
equal-azimth house is sown in this table:
---+---------+--------
no | azimuth | remarks
---+---------+------------------
10 | 180-150 | L from S meridian
11 | 150-120 |
12 | 120-090 |
1 | 090-060 | L from E meridian
2 | 060-030 |
3 | 030-000 |
4 | 360-330 | L from N meridian
5 | 330-300 |
6 | 300-270 |
7 | 270-240 | L from W meridian
8 | 240-210 |
9 | 210-180 |
---+---------+---------+-----------------
Find the ascendent, descendent, medium coelum
--------------------------------------------
Set the date and the hour.
Note the ecliptic longitude on the east horizon, west horizon, and
south meridian.
These longitudes are the ascendent, descendent, and medium coelum.
The ascendent is the point of the ecliptic rising at the given
date and hour; descendent, setting; medium coelum, culminating. These
points help visualize the path of the ecliptic across the sky.
= = = = =