OPERATION OF THE ASTROLABE
------------------------
John Pazmino
www.nyskies.org
nyskies@nyskies.org
2009 August 13 initial
2011 July 4 current
[These instructions for the use and function of an strolabe 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.]
Introduction
----------
These instructions are based on this specific model of astrolabe
from Daniel Rislove's website. Without much error it can be used with
zone time, forgetting daylight savings. 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.
Besides solving practical problems, operation of the astrolabe
reviews and illustrates assorted concepts in skywatching. Sidereal
time is not used much by modern home astronomers but it is the one way
to uniquely specify the rotational position of the celestial sphere
relative to the horizon. It is also the way to appreciate the seasonal
shift of the stars against the Sun.
Similarly, the planetary aspects have no special importance, even
tho they are still listed in astronomy almanacs. They, by manipulating
the astrolabe, show why a planet is in the evening sky in one year but
not in an other.
Plotting the position of the Moon is useful in the absence of an
almanac. It also teaches the correlation between phase (by age or
elongation) and location in the sky by hour of the night.
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 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. Unbolt the
astrolabe, remove the regula and rete. lay the new clima on the mater,
Home its north point at the mater's 0h point and Fix it there. For a
secure fit, use a couple paperclips around the edges.
Then place the rete and regula over the clima and bolt the
astrolabe together. You may leave off the nut if you must change
climata for certain operations.
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'.
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.
A planet is one of the solar system bodies, including asteroids
and comets. They are cataloged by either their RA and DE or by their
ecliptic latitude and longitude.
Unless the planet 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.
Simple 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.
To mark points or lines means to draw them on the rete with an
erasable medium or draw them on a throw-away copy of the rete.
Parts moved as a unit are noted together, like 'mater-alidade' or
'rete-regula'.
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. However, if
you are far from a standard meridian for zonetime, there may be up to
45 minutes difference between the two. This is induced by the very
irregular zone boundaries but it 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. To set the mean date, lay the regula over the
date on the rete and pin it there. Rotating the rete-regula to the
hour on the mater sets the astrolabe to the date and hour. 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. Read out the ecliptic
longitude of the Sun against the date. Then lay the regula over that
longitude on the rete and tie it there. Rotating the rete-regula to
the hour on the mater sets the astrolabe to the date and hour.
If you do this both ways you see a discrepancy of several minutes.
This offset is the equation of time for the given date. A more careful
operation for equation of time is in one of the instructions below.
Range of operations
-----------------
The astrolabe can work problems that would call for a 3D celestial
globe seated in a horizon base. The single important faculty lacking
in this model is the taking of altitudes. The model is too flimsy,
made of paper and film. A celestial globe has no easy way to take
altitudes.
SOme instructions call for taking, measuring, capturing,
altitudes. These are included for the case where the astrolabe may be
built from substantial rigid material and the regula is fitted with
notched sighting vanes.
The set of operations here is a sample of what the astrolabe can
do. The intent is to provide basic skills in manipulating the
instrument for other situations you may come onto.
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
-------------------
Rotate the rete to place its zero line against the given sidereal
time on the mater. Count hours CW from SOUTH, not north.
The astrolabe now set for the given sidereal time.
Rotating the regula over the mean date scale on the rete and the
hour scale on the mater gives combinations of the two 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 ecliptic is the place of the mean Sun,
not the real Sun. This corresponds with time from a clock.
The astrolabe is set for the date by mean solar 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.
Turning the rete under the regula slides the ecliptic
intersection, 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 of the year by mean or apparent time.
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.
Rotate the regula to the target's right ascension by counting
hours CCW 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.
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 and is never visible.
Plot a planet on the rete
-----------------------
If the planet's RA and DE are in hand, procede like for plotting a
new target.
If the planet's ecliptic longitude and latitude 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.
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.
For the stations and greatest elongations, look up the elongation
in an almanac and pace off the equivalent signs-degrees.
Plot the Moon on the rete - method I
----------------------------------
From an almanac get 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 first 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 get the dates of the cardinal phase next before
the given date and the one next after that date. The calendar may have
Moon phases noted in its day boxes. An other source is the weather or
shipping page of a newspaper.
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 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 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.
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. Count CW 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
thick plastic, metal, wood. It can not be applied for one made of
paper or card. The instrument is too light and flimsy.
Face the target and hold the astrolabe by its string to let it
hang freely. Raise it so the target can be sighted 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 mater-alidade and read the altitude of the target.
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 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 mater-alidade and read the altitude of the target.
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.
For very tall poles, 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.
This method is a bit clumsy because the alidade on this model has
no sighting holes or notches. The instrument is too fragile for these
to work well. A sturdy astrolabe is commonly fitted with hinged or
slip-on sights for taking the altitude of the Sun and other targets.
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 CCW from north.
Find the hour of sunrise or sunset
--------------------------------
Set the date of the year.
Rotate the rete-regula to put the Sun on the east side of the
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 side of the
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.
Rotate the rete-regula to place the target on the east side of the
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 side of the
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 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.
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 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.
Note which side of the sky the Moon or planet is in, toward the
east or toward 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 west elongation of the Moon from the Sun.
Divide this difference by (13.2deg/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. This is specially
tough when the Moon looks pretty round for a couple days adjacent to
the exact full Moon.
Find when a target touches a given altitude
-----------------------------------------
Set the date of the year.
Rotate the rete-regula to place the target at the given altitude.
In general this happens twice.
Select the proper instance, that in the east or in the west side
of the sky.
The regula points to the hour on the mater when the target touches
the given altitude.
This is useful to find when the target emerges from or immerges
into an obstruction such as a roof or treeline.
Find when a target touches a given azimuth
----------------------------------------
Set the date of the year.
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 emerges from or immerges
into 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 the instruction here are the sense
as seen while facing the Sun.
Set the date of the year.
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 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. This is the interval
between the two events.
This is a very general procedure for solving problems involving
time intervals. Some examples are:
* duration of view of a target in open sky between tow vertical
obstructions
* duration of view of a target from twilight to its own setting
* duration of twilight from sunset to one of the crepuscular
altitudes
* length of daytime from sunrise to sunset
* length of dark night from moonset to next twilight
* length of wait from sunset to target's own rising
* sequence of culmination of several targets
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
west and east boundary. The descension is the duration between the
settings of these same two points.
Place the west boundary of the sign on the eastern horizon.
Note the hour on the mater against the rete's zero line.
This is NOT the 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.
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.
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 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 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 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 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 observer's longitude
---------------------------
You can find 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.
Squarely face the Sun by lining up with your shadow.
Hold the astrolabe upright in front of you.
Rotate the astrolabe in its own plane, like a wheel, so the regula
over the Sun points straight up.
Tilt the astrolabe back, away from you, faceup, into a horizontal
position.
The degrees in the rim of the mater now line up with the compass
the ground. 0 degrees is to the 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.
Place the regula over this target on the rete. Pin it there.
Squarely face the target in the sky as best as you can.
Hold the astrolabe upright in front of you.
Rotate the astrolabe in its own plane, like a wheel, so the regula
over the target points straight up.
tilt the astrolabe back, away from you, faceup, into a horizontal
position.
The degrees in the rim of the mater now line up with the compass
the ground. 0 degrees is to the 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 crepus ular
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 if the latitude is too far from the north
pole. For these latitudes there is an interval of full night all year
long. The limit is about 48-1/2 degree north latitude.
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 first
crepuscular circle (-6 deg altitude) 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 the ecliptic latitude of the target,
the observer's latitude, the target's magnitude, horizon haze and
mists, amount of scattered light in twilight, to cite a few factors.
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.
A similar procedure applies to heliacal setting. Place the target
on the western 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.
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 when Sun rises
cosmic oe mundane setting - target sets when Sun rises
acronychal or temporal rising - target rises when Sun sets
acronychal or temporal setting - target sets when Sun sets
None of these is observable due to daylight at sunrise or sunset.
They are mechanicly simulated on the astrolabe. 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 to that for the heliacal rising
and setting. 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 target in the sky
---------------------------------------------
Set the date and hour.
Note which side of the sky the target is in, toward the east or
toward the 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, but make it generously long.
Interpolate between the altitude circles and make your arc concentric
with them.
Wait a couple hours and repeat the altitude measurement.
Set the astrolabe to the second date and hour. Within the same
night the Sun moves less than a degree, so the regula remains pinned
to the rete from the first observation.
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 intersection of arcs 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 measuring the altitude
of 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, order 150cm.
The result is the height of the point above the ground.
The point is typicly the top of a wall, tower, hill. It 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 measuring the altitude
of 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 above the eye
level. Label the displacement on the 'run' leg of the triangles.
Do NOT skip the sketch! You need it to keep the numbers 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) / ((run 1) - (run 2))
Add to this the height of the eye above the ground, order 150cm.
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 distance to a point on the ground
----------------------------------------
Assume the ground is level.
Measure the altitude of the point like for measuring the altitude
of a target in the sky.
Typicly the eye is at an elevated place and the altitude is a
negative angle, angle of depression.
On the dorsum place the alidade over the altimeter and on the
altitude of the point.
Note the ratio of the 'run' to the 'rise'. On this astrolabe the
ratio is in twelfths.
Solve
(height) = ((rise) * (distance) / (run))
Add to this the height of the eye above the ground, order 150cm.
The result is the distance of the point.
The point is typicly a person seen from a tower, wall, hill. The
height of the viewing site, plus the height of the eye above it, must
be known.
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.
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.
There is no practical value to the unequal hours being that all
timekeeping today is based on a uniform flow of time. A modern
astrolabe could have a scale for the decimals to track the fraction of
the day elapsed since sunrise.
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.
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 is at the unequal hour of the day.
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 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
-----------------------------------
Find the hour angle of the target, but count CCW from 18h at the
south meridian. This odd counting is important.
Divide the hour angle by 2 and add 01:00 to the result.
This is the house, and 60th part, that the target is in.
The house is one of the 12 divisions of the horizon like the
division of the zodiac into 12 signs. There is no standard way to
divide the horizon so there arose a couple dozen systems 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 odd way of counting makes the maths work to get directly the
correct house and fraction.
The house correspondence with hour angle is:
---+---------+---------+--------
no | hr ang | reverse | 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 | 06h-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 270d on the
south meridian. This odd counting is important.
Divide the azimuth by 30 and add 1.00 to the result.
This is the house, and decimal part, that the target is 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 odd way of counting makes the maths work to get directly the
correct house and fraction.
The house correspondence with azimuth is:
---+---------+---------+--------
no | azimuth | reverse | 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.