PERATION OF THE ASTROLABE 
 ------------------------
 John Pazmino
 www.nyskies.org
 nyskies@nyskies.org
 2009 August 13 initial
 2015 October 27 current 

Introduction
 ---------- 
    These instructions for the use and function of an astrolabe are 
specific to the particular model of astrolabe distributed at the 2009 
August 17 NYSkies Astronomy Seminar. Because astrolabes are similar 
across designers, cultures, vintage, these instructions apply to most 
other models with reasonably obvious modifications. 
    I vompodrf yhrdr indytuvyiond from the realization that there is 
still, in the 21st century, a one-place comprehensive manual of 
astrolabe operatons!  Other 'instructions' dwell one only a few simple 

functions, almost trivializing the power of the instrument. 
    These instructions are revised from time to time, with the current 
date of issue noted in the header. Most updates are simplifying text 
but new or different uses do come along. 
    The single important faculty lacking in this model  of astrolabe 
is the taking of altitudes. The model is too flimsy, made of paper and 
film. 
    SOme instructions call for taking, measuring, capturing, 
altitudes. These are included for an astrolabe may be built from 
substantial rigid material and the regula is fitted with sight vanes. 

Foreign rete 
 ---------- 
    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 of their 
ecliptic zones 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 proper instrument. The line toward 
the vernal equinox is the zero line to home 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 first home the rete on the mater and read 
from the mater's hour scale. Count the hours CCW from 0h. 
    In Rislove's website the alidade is spelled 'alilade'. 

Climata 
 -----
    Climata for this model span N 15 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 already inscribed on the mater. 
    if you are working at a latitude several degrees from New York you 
must place on the mater one of the other climata. Most of the 
operations assume the astrolabe is set for latitude before carrying 
out the operation. 

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 by their RA and DE, whence the lack of a true RA 
scale on the rete is sorely felt. 
    In the instructions, it is assumed you noted or plotted the 
targets on the rete. Among the early instructions is the method of 
doing this. 
    Moving vbodies, like planets and comets, may carry either their 
RA-Dec or ecliptic lat-lon.  Unless the body wanders more than a few 
degrees from the ecliptic, it is usual to ignore its latitude and 
place it on the ecliptic according to its longitude. 
              
Basic tasks 
 --------- 
    To pin, tie, fix, attach parts together means to hold them with a 
paper clip while taking care to let the remaining parts turn freely.     
Parts so attached are moved as a unit, like 'mater-alidade' or 'rete-
regula'. 
    To note, read, an item means to take its value from the 
appropriate scale or grid and remember it. It may then be transfered 
to another part of the astrolabe. 

    To mark or plot points on the rete means to draw them with an 
erasable medium or draw them on a tab of sticky paper or tape . For 
extensive plots use a throw-away copy of the rete. 
    To get, onbtain, an item is to secure it from an outside source 
such as an almanac. The item is then transfered to the strolabe.

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. 
 If you are far from a standard meridian for zonetime, there may be up 
to 45 minutes difference between the two. This can cause annoying 
discrepancies in working out certain problems. 
    As a general rule if you're dealing with stars, planets, and other 
bodies at night, you may use mean time. This is given by the scale on 
the limb of the rete.In this mode the astrolabe works like a 
planisphere, star-finder, star-wheel. 
    For events involving the Sun or in daytime you can use apparent 
time. This is found by the scales on the dorsum.  
    Setting the time both ways shows a discrepancy of several minutes. 
This offset is the equation of time for the given date. 
    The astrolabe, like any credible astronomer, ignores daylight 
savings time. You must artificially correct the hours uyielded by the 
astrolabe to suit any daylight savings time need. 

Set the latitude 
 --------------
    Select a clima nearest to the given latitude. 
    Remove the regula and rete. 
    Place the clima onto the mater so its north coincides with north 
on the mater and attach them together. 
    Place the rete and regula over the clima. 
    The astrolabe is now set for the given latitude. 

Set the sidereal time 
 -------------------
    Count off hours on the mater clockwise from SOUTH, not north, to 
the given sidereal time. 
    Rotate the rete to place its vernal equinox line against the given 
sidereal time on the mater. 
    The astrolabe now set for the given sidereal time. 
   Tie the rete to the mater. Rotating the regula over the mean date 
scale on the rete and the hour scale on the mater gives combinations 
of date and hour that yield the given sidereal time. This is, to view 
the sky at the given sidereal time, look during one of the date-hour 
combinations. 

Set the date of the year - method I 
 ---------------------------------
    From the dorsum read the Sun's longitude against the given date. 
    Place the regula over this longitude on the ecliptic and pin it 
there. 
    The regula and ecliptic cross at the place of the Sun. 
    The astrolabe is set for the date by apparent solar time. 
    Turning the rete-regula moves the Sun across the sky in diurnal 
motion. 

Set the date of the year - method II 
 ----------------------------------
    Place the regula over the date in the limb of the rete and tie it 
there. This date is based on the mean Sun. 
    The crossing of regula and equator, not ecliptic, is the place of 
the mean Sun, not the real Sun. This corresponds with time from a 
clock.

    The astrolabe is now set ffor the date by mean so,ar time. 
    Turning the rete-regula moves the mean Sun across the sky in 
diurnal motion. 

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. 
    From the dorsum note the date this longitude corresponds to. 
    Turning the rete under the regula slides the ecliptic 
intersection, the Sun, thru the days of the year. 
    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 of the year by mean or apparent time. 
    Rotate the rete-regula to place the regula on 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. 
    Rotate the regula to the target's right ascension by counting 
hours clockwise from north and fix it there. 
    Mark the target against the declination along the regula. 
    The target is now plotted on the rete. 

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 sign 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,. 
    Plce the regula over the target.
    Tie mater,rete,regula together. 
    Mak 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. 

Plot a planet on the rete 
 -----------------------
    'Planet' means a celestial body that changes position among the 
stars over time. Its location must be obtained for each specific sate. 
he body may ne a true planet, but also a comet or asteroid. 
    If the planet's RA and Dec are in hand, oplot it like a new 
target. 
    If the planet's ecliptic lat-lon are in hand, place the regula 
over the longitude along the ecliptic and tie it there. 
    Mark the planet at the intersection of regula and ecliptic . 
    Usually the latitude is ignored. The planet is assumed to sit on 
the ecliptic. 
    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 coordinates are 
inclined. The greatest error is near the equinoxes; least, solstices. 
    Mark the planet at this place. 
    The planet is now plotted on the rete. 
    Label the planet's mark with their date. 
    Use the proper mark for each day of astrolabe setting. 

Plot a planet's aspects 
 ---------------------
    An aspect is a certain angular displacement or elongation of the 
planet from an other body. Usually, but not always, this is the Sun 
used in the example here. 
    Set the date of the year.
    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 the home body: 

    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 resulting elongation. 
    The planet's aspect is now plotted on the rete. 
    Example: Sun at Gemini 15, Mars at eastern quartile. Count from 
the Sun eastward along the ecliptic 3 signs: Cancer 15, Leo 15, Virgo 
15. Mark Virgo 15 for the place of Mars at eastern quartile. 

Plot the Moon on the rete - method I 
 ----------------------------------
    From an almanac note the hour of moonrise next before the given 
hour and the moonset next after the hour. 
    Set the date and hour for the moonrise.
    Mark the intersection of the ecliptic and the east horizon. This 
is the place of the Moon at moonrise. 
    Set the date and hour for the moonset. 
    Mark the intersection of the ecliptic and the west horizon. This 
is the place of the Moon at moonset. 
    Mark a position halfway between the  two marks. This is the 
approximate place of the Moon for its culmination, which should be 
close for the given hour. 
    Erase the first two marks for moonrise and moonset. 
    Set the date and given hour. 
    This method is approximate because the Moon moves rapidly thru the 
zodiac and wanders substantially north and south of the ecliptic. 
    The longitude of the Moon is read at the final, middle, mark on 
the ecliptic. 

Plot the Moon on the rete - method II 
 -----------------------------------
    From a calendar note the dates of the cardinal phase next before 
the given date and the one next after that date. An other source is 
the weather or shipping page of a newspaper. 
    The cardinal phases 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 that longitude on the ecliptic of the rete. 
    Mark the ecliptic at the cardinal phase for the first date. Be 
mindful of east and west. Call this point 'bef'. 
    From the dorsum against the second date read the longitude of the 
Sun and mark that longitude on the ecliptic of the rete. 
    Mark the ecliptic at the cardinal phase for the second date. Be 
mindful of east and west. Call this point 'aft'. 
    The linear 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 span on the ecliptic into 
these seven or eight equal parts. 
    Eyeball the point between 'bef' and 'aft' for the location of the 
given date and mark the ecliptic at this intermediate point. 
    If the given date is four days after the 'bef' phase and the bef-
aft interval is seven days, the given date is located 4/7 from 'bef' 
to 'aft'. Call this point '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 of the year. 
    This method is very rough because a phase can occur any time 
within its listed date and the Moon wanders substantially north and 
south of the ecliptic. 
    The longitude of the Moon is read at the 'now' mark. 




[Eastth satellite]



FInd the sidereal time
 --------------------
    Set the date and hour. 
    The zero line of the rete points to the sidereal time on the 
mater. Count clockwise from SOUTH, not north. 

Measure the altitude of a target other than the Sun
 -------------------------------------------------
    This instruction is for an astrolabe made of sturdy material like 
hard plastic, metal, wood. It can not be applied for one made of paper 
or card. Such an instrument is too light and flimsy. 
    Face the target and hold the astrolabe by its string to let it 
hang freely. Raise it above eye level to sight the target along the 
alidade. If the alidade has sighting vanes, use them. 
    Gently rotate the alidade, minding that the mater must hang 
straight and vertical, until the target is squarely lined up with the 
alidade. 
    When the target is properly lined up with the alidade, tie the 
alidade to the mater. Its upper end sits on the altitude of the target 
along the limb of the mater. 
    Take down the astrolabe and note the altitude of the target. 

Measure the altitude of the Sun - method I 
 ----------------------------------------
    This instruction is for an astrolabe made of sturdy material like 
hard plastic, metal, wood. It can not be applied for one made of paper 
or card. The instrument is too light and flimsy. 
    Stand sideways against the Sun with your shadow to one side. Hold 
the astrolabe by its string to let it hang freely in front of you. 
    Gently rotate the alidade, minding that the mater must hang 
straight and vertical, until the shadow of the upper end or sighting 
vane falls squarely onto the lower end or vane. 
    Do NOT look at the Sun along the alidade like sighting on any other 
target. Serious and perhaps permanent eye damage can result. 
    When the Sun is properly lined up with the alidade, tie the 
alidade to the mater. Its upper end sits on the altitude of the target 
along the limb of the mater. 
    Take down the alidadee and read the altitude of the Sun. 

Measure the altitude of the Sun - method II 
 -----------------------------------------
    Go to or set up a vertical pole in sunshine. A vertical edge of a 
wall or corner of a building will do as well. 
    Note or place a mark at a convenient 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. 
    With a calculette 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 rim of the mater. 
    A sanity check is that 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 is only because this model of astrolabe has a scale divided into 
12ths, not decimals. 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. 
    The hour by real 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 12:00 from this mean hour. 
    The difference is the equation of time for the given date. It is 
the value added to a sundial reading by the real Sun to obtain the 
clock hour by the 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 pin 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. Count clockwiseW from north. 

Find the hour of sunrise or sunset 
 --------------------------------
    Set the date of the year and attach the regula to the rete. 
    Rotate the rete-regula to put the Sun on the east  horizon for 
sunrise. 
    The regula points to the hour on the mater for sunrise. 
    Rotate the rete-regula to put the Sun on the west horizon for 
sunset. 
    The regula points to the hour on the mater for sunset. 

Find rise and set hour for a target 
 ---------------------------------
    Set the date of the year and attach the regula to the rete. 
    Rotate the rete-regula to place the target on the east horizon. 
    The regula points to the hour on the mater for the target's rise. 
    Rotate the rete-regula to place the target on the west horizon. 
    The regula points to the hour on the mater for the target's set. 

 Find when a target culminates 
 --------------------------- 
    Set the date of the year. 
    Rotate the rete-regula to place the target on the south meridian. 
    The regula points to the hour on the mater for the target's 
culmination. 
    Some targets may culminate north of the zenith. Place them on the 
meridian between the north pole and the zenith. 
    Semperpatent targets have two culminations, above and below the 
celestial 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.
    Because this hour is in general not 12:00, the interval from 
sunrise to 12:00 MEAN TIME is not equal to that from mean 12:00 to 
sunset. The MEAN hours of sunrise and sunset are NOT symmetrical about 
mean 12:00. In apparent solar time they are. 

Find the hour angle of a target
 -----------------------------
    Set the date and hour. 
    Tie the rete to the mater. 
    Lay the regula over the target. 
    The regula points to the hour angle on the mater. Count hours 
clockwise from SOUTH, not north. 
    Sometimes the hour angle is counted westward thru +12h and 
eastward thru -12h. The latter indicates 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 and pin the rete to the mater. 
    Note which side of the sky the Moon or planet is in, toward the 
east or the west. 
    Measure the altitude of the Moon or planet. 
    Note where the measured altitude crosses the ecliptic on the 
proper side of the sky. 
    The longitude at this point is the longitude of the Moon or 
planet.
    This ignores latitude, which can at times be substantial. The 
result is only approximate. 

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 elongation of the Moon easteard from the 
Sun. 
    Divide this difference by (13.2 deg/day) 
    The result is the age of the Moon in days since the last new Moon. 
    In spite of the lack of latitude in this procedure, the result is 
surprisingly good. It is far better than assessing the shape of the 
Moon by eye and guessing the age it corresponds to. 

Find when a target touches a given altitude 
 -----------------------------------------
    Set the date of the year and pin the regula to the rete. 
    Rotate the rete-regula to place the target at the given altitude 
on the proper side of the sky, in the east or west. 
    The regula points to the hour on the mater when the target touches 
the given altitude. 
   This is useful to find when the target meets an obstruction such as 
 roof or treeline. 

Find when a target touches a given azimuth 
 ----------------------------------------
    Set the date of the year and pin the regula and rete together. 
    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. 
    This is useful to find when the target meets an obstruction such 
as a wall or window frame. 

Find when the Sun shines on a wall 
 --------------------------------
    Get the azimuth alignment of the wall and its outward-facing 
direction. 'Left' and 'right' in this instruction  are the sense as 
seen while facing the Sun. 
    Set the date of the year and tie the rete and regula together. 
    Rotate the rete-regula to place the Sun at the left azimuth of the 
wall. 
    if the Sun is above the horizon, the regula points to the hour on 
the mater. This is the start of the sunshine period. 
    If the Sun is below the horizon, continue rotating the rete-regula 
until the Sun rises. The regula points to the hour on the mater. This 
is the start of the sunshine period. 
    Rotate the rete-regula to place the Sun on the right azimuth of 
the wall. 
    if the Sun is above the horizon, the regula points to the hour on 
the mater. This is the end of the sunshine period. 
    If the Sun is below the horizon, reverse rotate the rete-regula 
until the Sun sets. The regula points to the hour on the mater. This 
is the end of the sunshine period. 
    This is a combination of the altitude and azimuth problems. 
    Notice that the Sun can start shining on the wall by coming in 
front of it or by rising while already in front. It can stop shining 
by going behind the wall or setting before then. 
    Depending on the alignment, season, latitude, there could be TWO 
periods of sunshine during certain days. Continue the rete-regula 
rotation from sunrise to sunset to catch both periods. 

Find the interval between two events
 ----------------------------------
    Set the date and hour of the first event. 
    Note the hour against the rete's zero line. (The regula may be 
occupied in setting up the event.) 
    This is NOT the true hour of the event! It is merely a difference 
point to be used with a similar one for the second event. 
    Repeat for the second event. 
    Subtract the first hour from the second, with care for a crossing 
of 24h/0h.  
    The result is the interval between the two events. 










Find the ascension or descension  of a sign 
 -----------------------------------------
    This is merely a special case of the interval between two events. 
    The ascension of a sign is the interval between the rising of its 
the sign's west and east boundary. The descension is the duration 
between the settings of these same two points. 
    Place the west boundary on the east horizon. 
    Note the hour on the mater against the rete's zero line. 
    This is NOT thetrue hour of the event! It is merely a difference 
point to be used with a similar one for the second event. 
    Repeat for the rising of the east boundary. 
    Subtract the first hour from the second. This is the interval 
between the two risings, the ascension of the sign.
    A symmetrical procedure applies to the descension. The two events 
are the setting of the sign's cusp and the cusp of the next sign. 
    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. The suitable great circles are the horizon and an 
azimuth meridian. 
    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. 
    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. 
    With the set of climata in this model you may find there is NO 
good fit of the targets. In this case the problem is not solvable. In 
an astrolabe with more climata and reta for both hemispheres, you will 
almost always find a combination that works. 

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 meridian. 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.
    This function applies to targets relative to the horizon, like the 
path of a daytime meteor whose endpoints ere measured in altitude and 
azimuth. 
    First home and tie the rete on the mater. 
    Mark the targets ON THE RETE at their altitude-azimuths. 
    Release the rete and procede as above. 

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 meridian from the left 90-deg point, 
thru zenith, to the right 90-deg point. 
    This arc is the great circle whose pole is the target. 
    If a greater extent of the great cicrle is needed, repeat this 
procedure by placing the target on the opposite horizon. 

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, 90 deg away 
from both it and the target. 
    Rotate the rete to place this point on the horizon and pin it. 
    Note the azimuth 90 degrees left and right of the point. 
    Mark the arc over the azimuth meridian from the left 90-deg point, 
thru zenith, to the right 90-deg point. 
    This arc is the great circle whose pole is the target. 
    If a greater extent of the great cicrle is needed, repeat this 
procedure by placing the point on the opposite horizon. 

Plot a great circle around a target - method III 
 ---------------------------------------------- 
    Rotate the rete to place the target on the south meridian and tie 
it there. 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, either 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 whose pole is the target.
    Procede as for finding the great circle thru two targets, pairing 
the points and marking the arc between them. 

Find the lateral direction from a meteor shower radiant
 -----------------------------------------------------
    This is an application of plotting the great circle around a 
target. The lateral direction is where the shower meteors have the 
longest angular path in the sky. The meteors are passing orthogonal to 
your sight line so their path is seen faceon. 
    Mark the radiant on the rete. Eyeballing it among the stars is 
good enough,or mark it by right ascension and declination. 
    Set the date and hour of the shower. 
    The great circle crosses the stars toward which you look for the 
longest path of meteor. 




[Qibla]

 



Find the latitude of a place 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 of the year. 
    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 the measured altitude from the displayed altitude. 
    Add algebraicly the difference to the clima's latitude. 
    The sum is the latitude of the astrolabe's location. 
    It is wise to repeat the procedure with a clima that displays the 
Sun on the other side of its measured altitude. The two derived 
latitudes should agree. 
    This is a rough method and really only illustrates the effect of 
latitude on the aspect of the sky. 

Find the latitude of a place 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 of the year. 
    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 the measured altitude from the displayed altitude. 
    Add algebraicly the difference to the clima's latitude. 
    It is wise to repeat the procedure with a clima that displays the 
target on the other side of its measured altitude. The two derived 
latitudes should agree. 
    This is a rough method and really only illustrates the effect of 
latitude on the aspect of the sky. 

Find the longitude of a place 
 ---------------------------
    This method finds the longitude displacement from an other 
specific location. There must be an observer at that other place to 
make simultaneous measurements with you. 
    The method exploits the time difference between the observed time 
of certain celestial events. The events must be independent of the 
observer's location. In this example we use a lunar eclipse. 
    At the first contacts during the eclipse set the date and hour. 
    Measure the altitude of the Moon, noting which side of the sky the 
Moon sits in, east or west. 
    Rotate the rete-regula to place the ecliptic point opposite from 
the Sun on the Moon's altitude in that same side of the sky. 
    Because during a lunar eclipse the Moon is at or very close to the 
ecliptic, any latitude from it may be neglected. 
    Note the hour in the mater at the rete's zero line. 
    Repeat for all the contacts of the eclipse viewable from your 
location. You have up to four readings: 
        1st - unbra first touches the Moon 
        2nd - totality begins (skipped for partial eclipse) 
        3rd - totality ends (skipped for partial eclipse) 
        4th - unbra last touches the Moon 
    The observer at the other location must go thru this same 
procedure on his astrolabe and share the results to you. You may miss 
certain contacts because the Moon is down or clouds interfere. The 
same hazard falls on the other observer. 
     Subtract your reading from his for each contact you both saw. 
The differences should be the same to within a minute or two. 
    The average of the differences is the longitude interval between 
the two locations. 
    If your readings are the greater of the two, the difference being 
negative, your displacement is EAST of the other place. If lesser, 
positive difference, WEST. 

Find the hour of the day by the Sun 
 ---------------------------------
    Set the date of the year. 
    Note which side of the sky the Sun is in, the east before noon or 
west after noon. 
    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 of the year.
    Rotate the rete-reegula to place the Sun at the first crepuscular 
circles in the west, altitude -6 degree.
    The regula points to the hour on the mater. 
    This is the end of civil twilight. 
    Repeat for the second and third crepuscular circle, -12 and -18 
degree altitude.
    These are the ends of nautical and astronomical twilight.
    A symmetrical procedure applies to the morning twilights. The 
hours are the start of the three twilights. 

Find when the Sun sets in a given azimuth
 ---------------------------------------
    Rotate the rete to place the ecliptic on the horizon at the given 
azimuth. In general there are two instances when this can occur. 
    Read the Sun's longitude at the intersection of horizon and 
ecliptic. 
    From the dorsum read the date for this longitude. 
    Repeat for the second instance.
    These dates are when the Sun sets in the given azimuth. 
    There are no occurrence if the azimuth is too far right or left 
(north or south) of the due west point on the horizon. The Sun can not 
set in the given azimuth.
    This is the 'Stonehenge sunset' effect when the Sun sets along a 
certain street or over a certain landmark. 
    The date is accurate within a day or two, which is the window 
during when Stonehenge sunset can be seen. Beyond this window the Sun 
sets too far left or right of the azimuth for a good effect. 
    A parallel procedure is done for a Stonehenge sunrise effect. 

Find the compass directions by day
 --------------------------------
    Set the date and hour. 
    Fix the mater, regula, and rete together. 
    Note the azimuth of the Sun. 
    Squarely face the Sun by lining up with your shadow. 
    You are facing into the Sun's azimuth.
    The degrees in the rim of 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 marked on the rete. 
    Squarely face the target in the sky as best as you can. 
    You now face into the star's azimuth. 
    The degrees in the  rim of 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 lowest 
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 dark sky due to approach of the Sun. 
    Rotate the rete to place the target at rising in the east. 
    Note the longitude where the ecliptic intersects the lowest 
crepusular circle in the east, -18d altitude. 
    From the dorsum read the date against this longitude. 
    This is the end of the sun-gap, when the target is first visible 
in a dark 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. For 
stars in the southern hemisphere, subtract the declination from (-90 
degrees). The latitude is negative, indicating it is a south latitude. 

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 declination. For 
stars in the northern hemisphere, add the declination to (-90 
degrees). The latitude is negative, indicating it is a south latitude. 
    This function has limited value in this astrolabe. The rete cuts 
off at the winter solstice, decl 23.4 deg south. The farthest south 
star marked on the rete is Dschubba (abbreved 'Dsch'). Stars farther 
south can not be represented, like Canopus, Nubecula Major, Crux. On 
other astrolabes, where the rete reaches farther south declinations, 
the semperlatent range is extended. 

Find the dates of the white night season 
 --------------------------------------
    Rotate the rete to place the ecliptic on the lowest crepusular 
altitude, -18 degree, in the north, 0 degree azimuth. There are in 
general two instances for this situation. 
    Note the ecliptic longitude for the first instance. 
    From the dorsum read the date against this longitude. 
    The date is one end of the white night season. 
    Repeat for the second instance. 
    The dates are the start and end dates of the white night season. 
    There are no occurrences for latitude less / than 48-1/2 deg 
north. For these latitudes there is always an interval of full night 
all year long. 

Find the date of a target's heliacal rising
 -----------------------------------------
    Rotate the rete to place the target on the eastern horizon 
    Note the longitude of the ecliptic sitting on the -6 deg  
crepuscular circle in the east.          
    From the dorsum against this longitude, read the date. 
    This is the date of the target's heliacal rising.
    There is no mechanical way to give good heliacal risings (or 
settings). The event depends on external factors like the target's 
magnitude, horizon haze and mists, amount of scattered light in 
twilight, observer's eyesight. 
    On following days the visibility period lengthens as the Sun moves 
farther east in the ecliptic. This is the effect of sidereal vs solar 
time. 
    For the heliacal setting, place the target on the western horizon 
and note the longitude of the ecliptic sitting on the -6 deg 
crepuscular circle in th west. The date of this situation is that of 
the target's heliacal setting. 

Find a target's heliometric rising and setting 
 ------------------------------------------
    There are four heliometric rising and setting cases for a target. 
The heliacal rising and setting, often a skywatching feature in 
various cultures, is not really heliometric because they rely on the 
actual sighting of the target under a complex of factors. 
    The heliometric situations are: 
    -------------------------------
    cosmic or mundane rising - target rises at sunrise 
    cosmic oe mundane setting - target sets at sunrise 
    acronychal or temporal rising - target rises at sunset 
    acronychal or temporal setting - target sets at sunset 
    ------------------------------------------------------
    None of these is observable due to daylight at sunrise or sunset. 
It can happen that a given target may have a cosmic rising and 
acronychal setting, or vice versa, within the same day. 
    The operation for all 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. 

[First Crescent] 


Find the coordinates of a new target in the sky 
 --------------------------------------------- 
    Set the date and hour and tie the rete to the mater. 
    Note which side of the sky the target is in, toward the 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. Only an arc is needed,  long enough to include the 
target's location among the stars. Interpolate between the altitude 
circles and make your arc concentric with them. 
    Wait a few hours, release the rete, and set it for the new hour. 
    Take a new  altitude measurement. 
    Mark on the rete the second altitude arc for the target. 
    Where the two arcs intersect is the location of the target. 
    Release the regula. 
    Home the rete and mater. 
    Place the regula over the target's location to read the 
declination. 
    The regula points to the RA on the mater. Count CCW from north. 

Find the height of an accessible point on the ground 
 --------------------------------------------------
    Assume the ground is level. 
    Measure the altitude of the point like for a target in the sky. 
    Measure the standoff distance to the point along the ground. 
    On the dorsum place the alidade at the altitude of the point over 
the altimeter scales. 
    Note the ratio of the 'rise' to the 'run'. On this astrolabe the 
ratio is in twelfths.
    Solve 

        (height) = ((rise) * (standoff) / (run) 

    Add to this the height of the eye above the ground. 
    The result is the height of the point above the ground. 
    The point must be accessible in order to physicly measure its 
distance away. 

Find the height of a nonaccessible point on the ground
 ----------------------------------------------------
    Assume the ground is level. 
    Measure the altitude of the point like for a target in the sky. 
    Displace toward or away from the point by a known or measured 
distance. 
    Measure again the altitude of the point. 
    Make a sketch of the two situations. There are two triangles 
nested with a common side, the height of the point. Label the 
displacement on the 'run' leg of the triangles. 
    Do NOT skip the sketch! You need it to keep the nmaths straight. 
    On the dorsum place the alidade over the altimeter on the first 
altitude of the point. 
    Read off the ratio 'rise' over 'run'. This is in twelfths.
    Label the sketch with the ratios applied to the 'rise' and 'run' 
legs of the triangles 
    Repeat for the second altitude. 
    Proportion one of the ratios to the other to make their 'rise' 
value the SAME. It doesn't matter which is which. 
    The sketch now has one value for the 'rise', the height of the 
point, two for the 'run' legs, and the displacement. 
    Solve 

        (height) = (rise) * (displacement) / (((run1) - (run2)) 

    Add to this the height of the eye above the ground. 
    The result is the height of the point above the ground. 
    The point may be nonaccessible due to danger (enemy, mines, 
beasts) or natural barrier (river, gorge, brush). The idea is to take 
two altitude measurements from two places a known displacement apart 
and force their ratios to have the same 'rise' value. The other parts 
of the triangles are then proportioned to the displacement. 

Find the trigonometric functions of an angle 
 ------------------------------------------
    In the absence of a sci/tech calculette, the dorsum gives 
approximate values for the six trigonometric functions. 
    Place the alidade arm with the equispaced divisions 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) = 1 / cosecant 
    cosine(angle) = (adjacent) / (hypotenuse) =  1 / secant  
    tangent(angle) = (opposite) / (adjacent) = 1 / cotangent 

    cotangent = (adjacent) / (opposite) = 1 / tangent 
    secant = (hypotenuse) / (adjacent) = 1 / cosine 
    cosecant = (hypotenuse) / (opposite) = 1 / sine 
    -----------------------------------------------
    The actual ratio is worked on a arithmetic calculette, minding 
that the astrolabe scales are in twelfths. 
    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. 



Finding the qibla of a location 
 --------------------------------- 
    The qibla of a location is the azimuth into the great circle from 
the location to Mecca in Saudi Arabia. A Muslim in prayer faces Mecca 
by facing into his local qibla. 
    The qibla azimuth is provided by Islamic resources in the 
location. For New York City it is 58-1/2 degree. 
    Set the astrolabe to the date on the  mean Sun scale. 
    Tie the regula to the rete. The mean Sun is at the intercept of 
regula and ecliptic. 
    Rotate the rete-regula to place the Sun at the western crepuscular 
line for nautical twilight. At this hour the sky is dark enough to 
recognize many of the stars plotted on the rete. 
    Slwwly rotate the rete-regula thru the night hours while watching 
the azimuth for the local qubla. 
    When a recognizable star crosses the qibla azimuth, note the hour 
of the day on the hour scale of the mater. 
    Continue  to step thru the night for sevral other staars. 
    continue the slow rotation thru the hours to capture several star-
hour alignments. 
    Stop when the Sun reaches the nautical twilight line in the east. 
Yje is now too bright with coming dawn. 
    For any of the stars, face that star at the hour when it sits on 
the qubla azimuth.  If feasinle do this for several of the stars 
during the night to confirm the alignment. 
    You are now facing into the qibla, toward Mecca. 
    Note well the landscape below the star to know where to face at 
any other hour, even by day. 
    If feasible, establish marks tn the landscape to aim into the 
qibla at any hour and weather. 
    This is a general method for facing into any desied azimuth 
without further recouse to the stars. 

Find the date of First Crescent 
 -----------------------------
    This is an approximate method that finds a candidate dte for First 
Ctescent, or Hilal, for your location. It can not determine the 
definitve date. The true date of actually seeing the first crescent 
Moon after new phase depends on many factors not built into the 
astrolabe, such as weather, lunar disc geometry, local air 
contamination, observer's eyesight. 
    From an almanac note the date and hour of the new Moon just prior 
to the prospective First Crescent. Shift thie daite/hour into your 
location's tlocal ime. 
    Set the astrolabe to the date of new Moon by the Sun's longitude 
taken from the dorsum. Do not use the mean time scale on the rete. 
    Lay the regula over the Sun's longitude and tie it there. The 
intersect of ecliptic and regula is the position of the Sun. 
    Rotate the regula-rete to place the Sun at -4 degree altitude, 
under the west horizon. This recognizes that First Crescent could be 
seen in moderate twilight. 
    Note the hour for this instant, the twilight hour, on the hour 
scale of the mater. 
    Tie the rete to the mater and release the regula. 
    Subtract the new Moon  hour from the twilight hour. This is the 
time elapced from new Moon until twilight. 
   Multiply tthis elapsed time by (0.5 deg/hr). This is the distance 
run by the Moon since new Moon. 
    Pace off this distance along the ecliptic eastward from the Sun. 
   Lay the regula on the ecliptic at this distance and fix it to the 
 rete. The Moon, neglecting her latitude, is at the intersect of 
ecliptic and regula. 
    The mater, regula, and rete are all attached together in one unit. 
    If the Moon is at or above +4 degree altitude above the horizon, 
then the instant date is a candidate for First Crescent. 
    If the altitude is less than +4 degrees, the First Crescent 
probably can not be seen on this date. The following date is the 
candidate for First Crescent because the Moon moved some 12 degree 
farther east from the Sun, inton darker zone of twilight, grew a 
fatter and brighter, and rised into less polluted 






Find the unequal hours of the day - method I 
 ------------------------------------------
    Set the date and the hour. 
    The regula/ecliptic intersection OPPOSITE to the Sun points to 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 period, sunrise thru noon thru 
sunset, into twelve equal parts, regardless of the season. They are 
also called seasonal hours. There is no practical value to the unequal 
hours being that all timekeeping today is based on a uniform flow of 
time. 

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 over the unequal hour scale at the 
Sun's altitude.
    Note the declination of the Sun along the alidade. 
    This point sits at the unequal hour of the day in the scale. 

Find the unequal hours of the night 
 ---------------------------------
    Set the date and the hour. 
    The Sun points to 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 period, sunset thru midnight 
thru sunrise, into twelve equal parts, regardless of the season. They 
are also called seasonal hours. 
    Altho both the day and night are divided into twelve equal parts, 
the two sets of hours are NOT the same. They vary in proportion as the 
day/night proportion varies due to the seasons. 

Find the house of a target - method I 
 -----------------------------------
    Find the hour angle of the target, but count CCW from  the south 
meridian. This odd counting is important! 
    Divide the new hour angle by 2 and subtract 02:00 to the result. 
    This is the house, and 60th part, that the target sits in. 
    The house is one of the 12 divisions of the horizon like the 
division of the zodiac into 12 signs. There several ways to divide the 
horizon, each being a system of house.. 
    This model of astrolabe has no houses delineated directly but two 
house systems are embedded, the equal-hour and equal-azimuth systems. 
The former coincides with the hour angle, two hours per house. 
    The houses progress EASTWARD, not westward like hour angle. The 
house beginning at the south meridian is by tradition house #10 (not 0 
or 1). It covers hour angles 24h back thru 22h. 
    The house number is from 1 thru 12. A number from the maths 
louside this range must be rectified into it. 
    The house correspondence with hour angle is: 
        ---+---------+---------+-------- 
        no | hr ang  | adj ang | remarks 
        ---+---------+---------+------------------ 
        10 | 24h-22h | 18h-20h | E from S meridian 
        11 | 22h-20h | 20h-22h | 
        12 | 20h-18h | 22h-24h | 
         1 | 18h-16h | 00h-02h | E from E horizon 
         2 | 16h-14h | 02h-04h | 
         3 | 14h-12h | 04h-06h | 
         4 | 12h-10h | 106h-08h | E from N meridian 
         5 | 10h-08h | 08h-10h | 
         6 | 08h-06h | 10h-12h | 
         7 | 06h-04h | 12h-14h | E from W horizon 
         8 | 04h-02h | 14h-16h | 
         9 | 02h-00h | 16h-18h | 
        ---+---------+---------+----------------- 

Find the house of a target - method II 
 -----------------------------------
    Find the azimuth of the target, but count CCW from the south 
meridian. This odd counting is important. 
    Divide the azimuth by 30 and add 4.00 to the result. 
    This is the house, and decimal part, that the target sits in. 
    This model of astrolabe has no houses delineated directly but two 
house systems are embedded, the equal-hour and equal-azimuth systems., 
The latter coincides with the azimuth, 30 degrees per house. 
    The houses progress EASTWARD, not westward like azimuth. The house 
beginning at the south meridian is by tradition house #10 (not 0 or 
1). It covers azimuths 180d back thru 150d.
    The house number is from 1 thru 12. A number from the maths 
louside this range must be rectified into it. 
    The house correspondence with azimuth is: 
        ---+---------+---------+-------- 
        no | azimuth |adj ang  | remarks 
        ---+---------+---------+------------------ 
        10 | 180-150 | 270-300 | L from S meridian 
        11 | 150-120 | 300-330 | 
        12 | 120-090 | 330-360 | 
         1 | 090-060 | 000-030 | L from E meridian 
         2 | 060-030 | 030-060 | 
         3 | 030-000 | 060-090 | 
         4 | 360-330 | 090-120 | L from N meridian 
         5 | 330-300 | 120-150 | 
         6 | 300-270 | 150-180 | 
         7 | 270-240 | 180-210 | L from W meridian 
         8 | 240-210 | 210-240 | 
         9 | 210-180 | 240-270 | 
        ---+---------+---------+----------------- 

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.