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Help file for ARCHAEOCOSMO (archaeoastronomy and geodesy) functions

Introduction

The ARCHAEOCOSMO functions (version 1.01) are described that are used on my web pages, for Excel and as R module (resp. programmed in JavaScript, Visual Basic and R). The input variables are also described.
The functions are available under the GNU GPL license.
More detailed information about the background of these functions is available through my archaeocosmology pages (incl. the JavaScript based pages to calculated them online).

Accuracy around the provided functions

The general idea of the accuracy (better then 0.4 degrees in azimuth/declination) due to normal measurement practices can be seen on this web page. Be aware of the following when using the provided functions:

One has the geodetic longitude (LongA/B) and geodetic latitude (LatA/B) available as defined in WGS84 datum (like from GPS or map).
The heights (HeightEye/Dist) should be from the same reference height point. The best is to use geodetic (like WGS84 datum) heights for apparent altitude determination. So using normal map heights (normally found on maps and related to an average sea level: tidal datum) could provide a systematic error of around 0.01 degrees, this is small compared to the overall measurement errors.
The latitude in astronomy is normally the astronomical latitude (like when determining declination: Lat), but for geodetic environment it is a geodetic latitude for instance related to WGS84 datum (LatA/B). If one equates them, this could provide a difference of upto 0.02 degree. This provides a small systematic error.
The largest variation is normally due to refraction (astronomical [e.g. ParallaxfromGeoAlt()]/terrestrial [e.g. AppAltfromHeights()]). The formula are just not very accurate by themselves.
The max. theoretical variation can be 0.5 degrees: but when looking at a horizon with apparent altitude of around 1 degrees, the variation in refraction would be around 0.05 degrees [pers. comm. A. Young, 2004]. It is assumed that this is not introducing a systematic error, because the conditions in former time are not precisely known.
I am working on getting a better integration of the climatic dependencies in the astronomical refraction (I made it available for terrestrial refraction).
The accuracy is maintained for the period between 3000 BCE and 2500 CE (at least for the Epoch depending durations). The DeltaT formula is not that accurate.
Be aware that all the periods/cycles/durations are mean values, so short term changed are happening.
The author takes no responsibility for any result of the below functions. Author is eager to listen to constructive feedback, let me know.
Some functions (are made known by the orangy color in below table) need Swiss Ephemeris (Moshier or DE431 ephemeris), in that case install Swiss Ephemeris and download the ephemeris files (otherwise inaccuracy for moon will be around 3"). If Swiss Ephemeris library (swedll32.dll) is not installed, these orangy-colored functions will not function (#NODATA!).

Excel Add-In file

The following steps are important (using 32bit Excel):

Install Swiss Ephemeris if one wants to use the below orangy marked functions and accurate DeltaT functions:

Download the file swewin32.zip and extract all files in default directories (c:\sweph\...). Please read its readme file.
Store the file swedll32.dll (or swedll64.dll) into the c:\ARCHAEOCOSMO\AddIns\ of C:\Windows\SysWOW64 directory (which directory is correct is somehwat unclear, if one does not work, try the other! Sorry).
If calculations for stars are needed: download the file sefstars.txt (right click -> Save Link Target As...) into c:\sweph\ephe directory
If DE431 accuracy is wanted: download and unzip all the ephemeris files into c:\sweph\ephe directory.

Stop any Excel program.
An Add-In file (archaeocosmo.xla) for Excel. If you want this file, please drop me an e-mail (it is available under the GNU GPL license). The source code can be seen by using a Module1's password, please drop me an e-mail to acquire the password. It might be that in the future I will start asking for a fee for the distribution of the free ARCHAEOCOSMO functions.
Please put the Add-In file in the C:\ARCHAEOCOSMO\AddIns\
For Windows10: Add this file into Excel by starting up Excel -> File -> Options -> Add-Ins... -> Manage Add-Ins -> Go... -> Browse... to the earlier saved file.
The functions should now be visible in the User Defined function list: Insert Functions (f_x) -> category User Defined.
Change in the VBA file (Developer -> Visual Basic -> ArchaeoCosmoFunctions -> Modules -> Module1): the location of the ephemeris files: Look for line 246 ' Location of ephemeris files ****
Make sure a cell (with in Name box: GNUGPL) has the following text value: Some formula used under GNU GPL from http://www.iol.ie/~geniet/eng/archaeocosmology.htm
You can test (using the initial values of options in the AddIn) the above by putting in a cell: =REarth(50), which should give as a result: 6378120. This functin does not need swedll32.dll by the way (so a nice test for the ARCHAEOCOSMO package on its own).

=HeliacalAngle(2.75, 42, 1, 79.53,-7, 58, 625928.5663, 76.63, 32.34, 60, 0, 1013, 0, 0.16, 0)

Functions

AnomalisticYear(JDNDays)
	Epoch depending duration of Anomalistic Year [Day] Ref: V. Reijs, http://www.archaeocosmology.org/eng/moonfluct.htm
AppAltfromDip(HeightEye, HeightDist, TempE, PresE, WindSpeed)
	Determine the Apparent Altitude due to the horizon dip [°] Ref: converted by V. Reijs, 1944 to SI-units and made Refraction Constant explicit from Thom, A., 1973, page 31
AppAltfromHeights(HeightEye, HeightDist, Distance, TempE, PresE, WindSpeed)
	Determine the Apparent Altitude due to observers eye height and distant earthbound object [°] Ref: converted by V. Reijs, 1999 to SI-units and made Refraction Constant explicit from Thom, A., 1973, page 31
AppAltfromTopoAlt(TopoAlt, TempE, PresE)
	Determine the Apparent Altitude from Topocentric Altitude [°] Ref: Using the numerical inverse of Bennett formula H; Bennett G.G., 1982, The calculation of astronomical refraction in marine navigation, page 255-259
AzifromAppAlt(Lat, AppAlt, GeoDec, Rim, ObjectDist, TempE, PresE)
	Determine the Azimuth from Apparent Altitude [°] Ref: V. Reijs, http://www.archaeocosmology.org/eng/accuracy.htm
AzifromGeoAlt(Lat, GeoAlt, GeoDec, Rim)
	Determine the Azimuth from (Geocentric) Altitude [°] Ref: V. Reijs, http://www.archaeocosmology.org/eng/accuracy.htm
BearingPoints(LatA, LongA, LatB, LongB)
	Determine the Azimuth (bearing) between two points A and B [°] Ref: based on spherical law of cosines
ClimaticPrecession(JDNDays)
	Epoch depending duration of the Climatic Precession [Year] Ref: V. Reijs, http://www.archaeocosmology.org/eng/moonfluct.htm
DaysinSeason(JDNDays, TropType)
	Determine the days of a season Ref: V. Reijs, http://www.archaeocosmology.org/eng/moonfluct.htm
DayfromGeoDec(GeoDec, JDNDays, AfterSummer)
	Determine the Day that the sun is at (Geocentric) Declination [-] Ref: V. Reijs, http://www.archaeocosmology.org/eng/season.htm
DatefromJDut(JDNDaysUT, Optional Argument, Optional CalType)
	Date and Hour from the Julian Date [using UT: Universal Time (a day is the Solar day)], without including effect of DeltaT. Argument can be used to get different results. Different calender outputs can be given (Julian, Gregorian, etc.) Ref: translated from BASIC program of P. Duffett-Smith, Astronomy with your personal computer
DeltaT(JDNDays, COD)
	Determine the DeltaT, if COD=0 it utilized VR's method or Swiss Ephemeris method (depending on a switch in the code; default is the Swiss Ephemeris method if available otherwise VR's method is used). If COD<>0 it uses the given COD for determining the DeltatT. Ref: V. Reijs, http://www.archaeocosmology.org/eng/moonfluct.htm#analysis or Swiss Ephemeris
DistancePoints(LatA, LongA, LatB, LongB)
	Determine the distance between PointA (LatA, LongA) and PointB (LatB, LongB) [m] Ref: R.W. Sinnott, Virtues of the Haversine, Sky and Telescope, vol. 68, no. 2, 1984, p. 159 http://www.movable-type.co.uk/scripts/GIS-FAQ-5.1.html
DraconicMonth(JDNDays)
	Epoch depending duration of Draconic Month [Day] Ref: V. Reijs, http://www.archaeocosmology.org/eng/moonfluct.htm
EarthRotation(JDNDays, COD)
	Epoch depending duration of Earth Rotation [Hour] Ref: V. Reijs, http://www.archaeocosmology.org/eng/moonfluct.htm
EarthRotationperSiderealYear(JDNDays, COD)
	Epoch depending duration of Earth Rotation per Sidereal Year [-] Ref: V. Reijs, http://www.archaeocosmology.org/eng/moonfluct.htm
Eccentricity(JDNDays)
	Epoch depending duration of Eccentricity of earth's orbit [-] Ref: V. Reijs, http://www.archaeocosmology.org/eng/moonfluct.htm
EclipseWhenUT(JDNDaysUT, Lat, Longitude, HeightEye, TempE, PresE, ObjectName, EclipseType, Optional Appalt)
	Determine when next solar or lunar eclipse will happen after JDNDaysUT. AppAlt is the Apparent altitude of the horizon Ref: Swiss Ephemeris
EclipticYear(JDNDays)
	Epoch depending duration of Ecliptic Year [Day] Ref: V. Reijs, http://www.archaeocosmology.org/eng/moonfluct.htm
ExtAnglefromMagn(Magn, Age, SN, AziO, AltM, AziM, MoonDistance, JDNDaysUT, AltS, AziS, Lat, HeightEye, TempS, PresS, RH, VR)
	Determine the extinction angle Ref: Schaefer, http://www.archaeocosmology.org/eng/extinction.htm
GCenLatfromGDetLat(GDetLat)
	Determine the Geocentric latitude from Geodetic latitude Ref : Von Oliver Montenbruck, Astronomie mit dem Personal Computer, page 180
GeoAltfromDAZ(Criterion, DAZ, q)
	Determine the geocentric altitude from the delta azimuth (using a certain two-parameter criterion)
GeoAltfromTopoAlt(TopoAlt, ObjectDist)
	Determine the (Geocentric) Altitude from Topocentric Altitude [°] Ref: V. Reijs, 2002; derivative of http://www.stjarnhimlen.se/comp/ppcomp.html#13 when TopoAlt is the base
GeoDecfromDay(DaysSummer, Obl, TropYear, AnoYear, Ecc, Perihelion)
	Determine (Geocentric) Declination from Days after summersolstice [°] Ref: 'V. Reijs, 2004, http://www.archaeocosmology.org/eng/season.htm
GeoDecfromAppAlt(Lat, AppAlt, Azi, Rim, ObjectDist, TempE, PresE)
	Determine (Geocentric) Declination from Apparent Altitude [°] Ref: http://www.archaeocosmology.org/eng/accuracy.htm
GeoDecfromGeoAlt(Lat, GeoAlt, Azi, Rim)
	Determine (Geocentric) Declination from Geocentric Altitude [°] Ref: http://www.archaeocosmology.org/eng/accuracy.htm
HarmonicSun(PeriodA, PeriodB, Direction)
	Determine the harmonic sum between PeriodA and PeriodB [dimension of PeriodA/B] Ref: V. Reijs, http://www.archaeocosmology.org/eng/moonfluct.htm
HeliacalAngle(Magn, Age, SN, AziO, AltM, AziM, JDNDaysUT, AziS, Lat, HeightEye, Temperature, Pressure, RH, VR, Optional TypeAngle)
	Determine the heliacal angle. TypeAngle determines which angle is calculated. Ref: B. Schaefer, http://www.archaeocosmology.org/eng/extinction.htm
HeliacalJDut(JDNDaysUT, Age, SN, Lat, Longitude, HeightEye, Temperature, Pressure, RH, VR, ObjectName, TypeEvent, Optional AVkind)
	Determine the Julian Day of the heliacal event, depending on the AVkind. It finds the next heliacal rise/set event from the given Julian Day. Ref: B. Schaefer, http://www.archaeocosmology.org/eng/extinction.htm
HeliacalPheno(JDNDaysUT, Age, SN, Lat, Longitude, HeightEye, Temperature, Pressure, RH, VR, ObjectName, TypeEvent, HPheno)
	Determines many aspects (HPheno) around heliacal events of stars, planets and moon. JDNDaysUT should be the date of the event
JDutfromDate(DateString, Optional Hour, Optional DeltaCorrelation)
	Determine Julian Date [using UT: Universal Time (a day is the Solar day)] from date and Hour, without including effect of DeltaT (including and before 1582/10/4: Julian calendar, including and after 1582/10/15: Gregorian calendar) [Day]. DateString can also be a Mayan Long Count number (5 numbers seperated by dots) Ref: P. Bretagnon, Planetary Programs and tables from -4000 to +2800, 1986, page 6
JDttfromDate(DateString, Hour, COD)
	Determine Julian Date [using TT: Terrestial Time (Day =86400 SI Sec)]. When starting from Calendar date and Hour, it includes the effect of DeltaT to get the to Terrestial Time (including and before 1582/10/4: Julian calendar, including and after 1582/10/15: Gregorian calendar) [Day] Ref: P. Bretagnon, Planetary Programs and tables from -4000 to +2800, 1986, page 6
Kuttaka(a, b, c, Choice)
	This procedure determines the x and y for the expression: ay - bx = c (called after the Indian algorithm of Kuttaka). Ref. A. Dutta, Kuttaka, Bhavan and Cakravala, in Studies in the History of Indian Mathematics, 2010, edited by C. S. Seshadri, India, Hindustan Book Agency.
LunarApseCycle(JDNDays)
	Epoch depending duration of Lunar Apse Cycle [Year] Ref: V. Reijs, http://www.archaeocosmology.org/eng/moonfluct.htm
LunarNodalCycle(JDNDays)
	Epoch depending duration of Lunar Nodal Cycle [Year] Ref: V. Reijs, http://www.archaeocosmology.org/eng/moonfluct.htm
LunarSeries(JDNDaysUT, Age, SN, Lat, Longitude, HeightEye, TempE, PresE, RH, VR, Optional DeltaCorrelation, Optional SMType, Optional LunarSeriesType)
	Determine Glyph A, D/E and C/X of Maya Lunar Series (part of Supplementary Series)
LunarSix(JDNDaysUT, Age, SN, Lat, Longitude, HeightEye, TempE, PresE, RH, VR, ObjectName, Rim, AppAltR, AppAltS, Optional LunarSixType)
	Determining the Lunar Six dates [JDN] and their durations [Min] (Huber and Steele [2007]) Ref: V. Reijs, http://www.archaeocosmology.org/eng/lunarsix.htm
LunarSolarPrecession(JDNDays)
	Epoch depending duration of Lunar Solar Precession [Year] Ref: V. Reijs, http://www.archaeocosmology.org/eng/moonfluct.htm
MayaDatefromJDut(JDNDaysUT, Optional MayaDateType, Optional DeltaCorrelation)
	Convert JD day number into Maya calendar (based on DeltaCorrelation): Long Count, Tzolkin, Haab and Glyph G/F. Ref: Maya calendar conversion
ObjectLoc(JDNDaysUT, Lat, Longitude, HeightEye, TempE, PresE, ObjectName, Angle)
	Determine the celestial object's location (Angle can be: azimuth, topocentric altitude, topo/geocentric declination or rectascension), if Swiss Ephemeris method is installed. [°] Ref: Astrodienst, Swiss Ephemeris
Obliquity(JDNDays, Object, Perturbation)
	Epoch depending obliquity of moon or sun [°] Ref: V. Reijs, http://www.archaeocosmology.org/eng/moonfluct.htm
ParallaxfromGeoAlt(GeoAlt, ObjectDist)
	Determine parallax from Geocentric Altitude [°] Ref: Parallax determined by V. Reijs based on earth-celestial object distance, http://www.stjarnhimlen.se/comp/ppcomp.html#13
ParallaxfromTopoAlt(TopoAlt, ObjectDist)
	Determine parallax from (Topocentric) Altitude [°] Ref: parallax formula from http://www.stjarnhimlen.se/comp/ppcomp.html#13, compensation for celestial objects determined by V. Reijs, 2006, parallax determined by V. Reijs based on earth-celestial object distance
PerihelionNumber(JDNDays)
	Epoch depending number of days between summersolstice and perihelion [Day] Ref: V. Reijs, http://www.archaeocosmology.org/eng/season.htm
REarth(LatA)
	Determine radius of the earth at observer's latitude [m] Ref: http://www.aerobaticsweb.org/SSA/BGA/wg84figs.html
RefractConst(JDNDays, Lat, Longitude, HeightEye, TempE, PresE, CloudCover, CeilingHeight, WindSpeed, Optional StabilityValue)
	Determine the Refraction Constant [-] Ref: V. Reijs, 2004, http://www.archaeocosmology.org/eng/stabilityclasses.htm
RefractConstSimple(WindSpeed)
	Determine the Refraction Constant [-] Ref: V. Reijs, 2004, hhttp://www.archaeocosmology.org/eng/stabilityclasses.htm
RiseAngle(Lat, GeoDec, Alt, DeltaAlt, TempE, PresE, ObjectDist, Rim)
	Determine the Rise/set angle of celestial object [°] Ref: V. Reijs, 2006
RiseSet(JDNDaysUT, Lat, Longitude, HeightEye, TempE, PresE, ObjectName, RSEvent, Optional Rim)
	Determine the Rise and Set information of the center (default) or top limb of the Planet, if Swiss Ephemeris method is installed. Ref: Astrodienst, Swiss Ephemeris
SEPM(JDNDaysUT, Lat, Longitude, HeightEye, TempE, PresE, ObjectName, RiseSetComb, Rim, AppAltR, AppAltS, PhaseMin, PhaseMax, SolarEventType)
	Solar Event Phased Moon procedure (includes EFM: Equinoctial Full Moon) Ref: C.M. da Silva [2004] and F. Silva [2011]
SiderealDay(JDNDays, COD)
	Epoch depending duration of Sidereal Day [Hour] Ref: V. Reijs, http://www.archaeocosmology.org/eng/moonfluct.htm
SiderealMonth(JDNDays)
	Epoch depending duration of Sidereal Month [Day] Ref: V. Reijs, http://www.archaeocosmology.org/eng/moonfluct.htm
SiderealYear(JDNDays)
	Epoch depending duration of Sidereal Year [Day] Ref: V. Reijs, http://www.archaeocosmology.org/eng/moonfluct.htm
SolarDay(JDNDays, COD)
	Epoch depending duration of Solar Day [Hour] Ref: V. Reijs, http://www.archaeocosmology.org/eng/moonfluct.htm
SolarEvent(JDNDays, SolarEventType)
	Determining the solar event (like equinox, solstice, cross-quarter days) after the given date [Day]
Sunobliquity(JDNDays)
	Epoch depending obliquity of Sun's orbit (actually of earth) [°] Ref: V. Reijs, http://www.archaeocosmology.org/eng/moonfluct.htm
SynodicMonth(JDNDays)
	Epoch depending duration of Synodic Month [Day] Ref: V. Reijs, http://www.archaeocosmology.org/eng/moonfluct.htm
TopoAltfromAppAlt(AppAlt, TempE, PresE)
	Determine (Topocentric) Altitude from Apparent Altitude [°] Ref: Bennett formula H; Bennett G.G., 1982, The calculation of astronomical refraction in marine navigation, page 255-259
TopoAltfromGeoAlt(GeoAlt, ObjectDist)
	Determine (Topocentric) Altitude from Geocentric Altitude [°] Ref: http://www.stjarnhimlen.se/comp/ppcomp.html#13
TropicalMonth(JDNDays)
	Epoch depending duration of Tropical Month [Day] Ref: V. Reijs, http://www.archaeocosmology.org/eng/moonfluct.htm
TropicalYear(JDNDays, Optional TropType)
	Epoch depending duration of Tropical Year [Day] Ref: V. Reijs, http://www.archaeocosmology.org/eng/moonfluct.htm
VisLimMagn(Age, SN, AltO, AziO, AltM, AziM, MoonDistance, JDNDaysUT, AltS, AziS, Lat, HeightEye, TempS, PresS, RH, VR)
	Determine the limiting visual magnitude in dark skies Ref: B. Schaefer, http://www.archaeocosmology.org/eng/extinction.htm

Input variables for function calls

AfterSummer

Determine Day belonging to certain (geocentric) declination:

0	Days before summer solstice
1	Days after summer solstice

Age

Age of the observer [year]

Angle

Which angle to determine of the planet's position:

0	Topocentric altitude
1	Azimuth
2	Topocentric Declination
3	Topocentric Rectascension
4	Apparent altitude
5	Geocentric Declination
6	Geocentric Rectascension
7	Geocentric altitude
8	Latitude
9	Longitude

AnoYear

Duration Anomalistic Year [day]

AppAlt

Apparent altitude of earthbound object [°]

AppAltR

Apparent altitude of horizon at rising [°]

AppAltS

Apparent altitude of horizon at setting [°]

Argument

The following different Date formats are possible:

-4	the calendar type
-3	the Hour [GMT]
-2	hh:mm:ss [GMT]
-1	yyyy/mm/dd (yyyy=astronomical year)
0	"yyyy [BCE/CE]/mm/dd hh:mm:ss (xxx. cal.)" (yyyy=Calendar year, hh:mm [GMT])
1	yyyy (astronomical year)
2	mm
3	dd
4	hh [GMT]
5	mm [GMT]
6	ss

AVkind

Kind of heliacal model used:

vr	Using Reijs' topocentric implementation of Schaefer's model [default]
pto	Using Ptolemy's model (object's altitude = 0 [°])
min7	Sun's altitude = 7 [°]
min9	Sun's altitude = 9 [°]

Azi

Azimuth of a direction [°]

ProlepticCal

CProlepticCal determines which calendar type is used:

0	use Julian calendar until and incl 1582/10/4 CE and Gregorian after 1582/10/15 CE (normal)
1	use Proleptic Gregorian calendar always
2	use (Proleptic?) Julian calendar always
3	use Islamic calendar (not implemented yet)

CeilingHeight

Height of cloud base (from surface height) [m]

Choice

Which output is provide by Kuttaka:

1	x
2	y
3	c

CloudCover

The percentage of cloud cover [%]

COD

Change of the Day, if zero a default formula is used (derived by V. Reijs from Stephenson and IERS) [msec/century]

Criterion

The different two-parameter criterions can are supported:

1	Fotheringham
2	Maunder
3	Schoch
4	Neugebauer
5	Indian
6	Bruin
7	Yallop (except that the topocentric crescent width is converted to geocentric altitude- and azimuth-differences at reference time of Sun's geocentric altitude is zero)
8	Caldwell (except that the Sun's geocentric altitude is 0, instead of the Sun's apparent altitude)

DateString

Calendar Date before 1582/10/15: Julian calendar [yyyy/mm/dd]
Calendar Date including and after 1582/10/15: Gregorian calendar [yyyy/mm/dd]
where yyyy is astronomical year (so when yyyy<=0, one gets the BCE year by subtracting one from yyyy)
Calendar Date can also be the Long Count of the Maya Calander [Bak'tun.K'atun.Tun.Winal.K'in] using Correlation (see also DeltaCorrelation)

DaysSummer

Number of Days after summersolstice [-]

DAZ

The difference bewteen the lunar and solar azimuth, when Sun's geocentric altitude is zero [deg]

DeltaAppAlt

Apparent Altitude step for determining the angle of celestial object set/rise [°]

DeltaCorrelation

The default Maya calendar correlation is GMT-correlation (584282.5); this can be adjusted by adding DeltaCorrelation

Distance

Distance between observer and distant earthbound object [m]

Direction

If periods are in the same direction:

1	Same direction
-1	Different direction

Ecc

Eccentricity of sun's orbit

EclipseType

The type of eclipse

0	all eclipses (lunar and solar eclipse events)
1	total eclipse (lunar and solar eclipse events)
2	partial eclipse (lunar and solar eclipse events)
3	penumbral eclipse (lunar eclipse event)

Epoch

Reference date for the ephemeris:

1900	J1900: JulianDayNumber = 2415020.0. This is January 0.5, 1900 (midnight between 31 December 1899 and 1 January 1900)
2000	J2000: JulianDayNumber = 2451545.0. This is January 1.5, 2000 (noon on 1 January 2000)

GDetLat

Geodetic latitude of observer [°]

GeoAlt

Geocentric Altitude of object [°]

GeoDec

(Geocentric) Declination of object [°]

HeightEye

Eye height (using same reference height as HeightDist) [m]

HeightDist

Height of distant earthbound object (using same reference height as HeightEye) [m]

Hour

A value between 0 and 23.9999 [GMT Hour]

HPheno

0	(Topocentric) Altitude of object @JDNDaysUT [°]
1	Apparent altitude of object @JDNDaysUT [°]
2	Geocentric altitude of object @JDNDaysUT [°]
3	Azimuth of object @JDNDaysUT [°]
4	(Topo/geocentric) Altitude of sun @JDNDaysUT [°]
5	Azimuth of sun @JDNDaysUT [°]
6	Actual topocentric AV @JDNDaysUT [°]
7	Actual (geocentric) AV @JDNDaysUT [°]
8	Actual difference between object's and sun's azimuth @JDNDaysUT [°]
9	Actual topocentric longitude difference between object and sun (comparable to topocentric elongation) @JDNDaysUT [°]
10	extinction coefficient [-]
11	Smallest Topocentric AV on that day [°]
12	First time object is visible, according to Schaefer/VR [JDN]
13	Best time the object is visible, according to Schaefer/VR [JDN]
14	Last time object is visisble, according to Schaefer/VR [JDN]
15	Best time the object is visible, according to Yallop [JDN]
16	Cresent width of moon @JDNDaysUT [°]
17	Yallop criterion value (q) @JDNDaysUT [-]
18	Yallop criterion category @JDNDaysUT [string]
19	Topocentric horizon parallax of object @JDNDaysUT [°]
20	Magnitude of object @JDNDaysUT [-]
21	Apparent rise/set time of object [JDN]
22	Apparent rise/set time of sun [JDN]
23	Lag: rise/set time of object minus Rise/set time of sun [JDN]
24	Visibility duration using Schaefer/VR [JDN]
25	Cresent length of moon [°]
26	(Geocentric) elongation [°]
30	Maunder criterion @JDNDaysUT (pos. moon visible, negative moon invisible) [-]
31	Indian criterion @JDNDaysUT (pos. moon visible, negative moon invisible) [-]
32	Bruin criterion @JDNDaysUT (pos. moon visible, negative moon invisible) [-]
33	Caldwell&Laney criterion @JDNDaysUT (pos. moon visible, negative moon invisible) [-]
34	Schoch criterion @JDNDaysUT (pos. moon visible, negative moon invisible) [-]
35	Neugebauer criterion @JDNDaysUT (pos. moon visible, negative moon invisible) [-]
36	Fotheringham criterion @JDNDaysUT (pos. moon visible, negative moon invisible) [-]
37	Yallop criterion @JDNDaysUT (pos. moon visible, negative moon invisible) [-]
38
39	Time when sun at (topocentric) altitude of zero [JDN]

JDNDays

The astronomical date using JulianDayNumber [Day], using terrestrial time

JDNDaysUT

The astronomical date using JulianDayNumber [Day], using universal time

Julcent

The number of Julian Centuries (each 36525 [Year])

Lat

(Astronomical) Latitude of observer [°] (South is negative)

LatA

Geodetic latitude of observer's eye (WGS84 datum) [°]

LatB

Geodetic latitude of distant earthbound object (WGS84 datum) [°]

LongA

Geodetic longitude of observer's eye (WGS84 datum) [°]

LongB

Geodetic longitude of distant earthbound object (WGS84 datum) [°]

Longitude

(Astronomical) Longitude of observer [°] (West is negative)

LunarSeriesType

0	Glyph A (length based on dates of First crescents) [days]
1	Glyph A (length based on dates of Last crescents) [days]
2	Glyph A (length based on dates of Average First and Last moons) [days]
3	Glyph A (length based on dates of conjunction) [days]
4	Glyph A (length based on dates of First Rise after First crescent) [days]
5	Glyph A (length based on 18 years lunar cycle [Linden]) [days]
6	Glyph D/E (age of moon based on date of First crescent) [days]
7	Glyph D/E (age of moon based on date of Last crescent) [days]
8	Glyph D/E (age of moon based on date of Average First and Last moon) [days]
9	Glyph D/E (age of moon based on date of conjunction) [days]
10	Glyph D/E (age of moon based of First Rise after First crescent) [days]
11	Glyph D/E (age of moon based of first New moon before creation date [0.0.0.0.0]) [days]
12	Glyph X [0..17]
13	Glyph C [1..6]

LunarSixType

0	Date of first crescent (na_N) [JDN]
1	Date when ŠU happens [JDN]
2	Date when na happens [JDN]
3	Date when ME happens [JDN]
4	Date when GE₆ happens [JDN]
5	Date of last crescent (KUR) [JDN]
6	na_N [Min]
7	ŠÚ [Min]
8	na [Min]
9	ME [Min]
10	GE₆[Min]
11	KUR [Min]
12	Lunation length of precious month (First crescent is following up a full (>=30days) or hollow (<=29 days) month) [days]

Magn

Visual Magnitude of celestial object [-]

MayaDateType

Type of information about Maya date:

-2	ut [Hour]
-1	All info
0	Long Count [baktun.katun.tun.winal.kin]
1	Tzolkin [day:God]
2	Haab [day.God]
3	Lord of the night (Glyph G) [1..9]
4	Lord of the Earth (Glyph Z) [1..7]
5	Tzolkin day
6	Tzolkin God
7	Haab day
8	Haab God

Object

The celestial object under study:

moonmajor	The moon at major standstill event
moonminor	The moon at minor standstill event
solstice	The sun at solstice

ObjectDist

The celestial object under study:

moonfurthest	The moon furthest from earth
moonavg	The moon on average distance
moonnearest	The moon closest to earth
sun	The sun on average distance to earth
star	Very far away
topo	Topocentric (same as far away)

ObjectName

A common name of a celestial object, like; sun, moon, sirius, etc.

Obl

Obliquity of earth [°]

Perihelion

The number of days between summersolstice and perihelion

PeriodA

A duration of a period/cycle [same dimension as PeriodB]

PeriodB

A duration of a period/cycle [same dimension as PeriodA]

Perturbation

Lunar perturbation to be taken into account:

-1	Negative perturbation
0	No perturbation
1	Positive perturbation

PhaseMax

The mazimum lunar phase, between 0 and 1

PhaseMin

The minimum lunar phase, between 0 and 1

PhenoEvent

Type of phenomena to be calculated:

0	Phase angle (earth-planet-sun)
1	Phase (illuminated fraction of disc)
2	Elongation of planet
3	Apparent diameter of disc
4	Apparent Magnitude

PresE

Air pressure at eye level (station pressure) [mbar]

PresS

Air pressure at sea level [mbar]

Yallop's q [-]

Rim

Describes which part of the celestial object is at the altitude also in the function call:

-1	Celestial object just fully above given altitude
0	Centre of celestial object at the given altitude
1	Celestial object just below given altitude

RiseSetComb

The combination of Sun and Moon events:

0	Sun rise/Moon rise
1	Sun set/Moon rise
2	Sun rise/Moon set
3	Sun set/Moon set

Relative humidy [%]

RSEvent

Describes the type of event:

1	Rise event
2	Set event
4	Upper meridian transit event
8	Lower meridian transit event

SMType

The type of Synodic month used for the Mayan calendar:

1	Copan Synodic month and Moon's Age at 0.0.0.0.0 : 22 D/E
2	Palenque Synodic month and Moon's Age at 0.0.0.0.0 : 24 D/E
3	Classic Synodic month and Moon's Age at 0.0.0.0.0 : 2 D/E
4	Modern Synodic month and Moon's Age at 0.0.0.0.0 : 11.5 D/E
5	Copan Synodic month and Moon's Age at 0.0.0.0.0 : 24 D/E
6	Copan Synodic month and Moon's Age at 0.0.0.0.0 : 23 D/E

Snellen factor of the visual aquity of the observer [-]

SolarEventType

This is a solar event type:

0	Vernal equinox
1	May cross quarter
2	Summer solstice
3	August cross quarter
4	Autumnal equinox
5	November cross quarter
6	Winter solstice
7	February cross quarter

StabilityValue

Describes which stability paarmeter needs to be calculated:

0	Refraction constant [-]
1	Stability Class [-]
2	Temperature Gradient [°K/m]

TempE

Temperature at eye level (station temperature) [°C]

TempS

Temperature at sea level [°C]

TopoAlt

(Topocentric) Altitude of earthbound object [°]

TropType

The type of season/Tropical Year:

mean	using mean sun
spring	Start at spring equinox
summer	Start at summer solstice
autumn	Start at autumn equinox
winter	Start at winter solstice

TropYear

Duration of Tropical Year [Day]

TypeAngle

The type of heliacal angle taht will be calculated:

0	Object's altitude
1	Object's altitude - Sun's altitude (AV)
2	Sun's altitude (Arcus Visionis)

TypeEvent

The type of heliacal event:

1	Heliacal rise/morning first
2	Heliacal set/evening last
3	Cosmical set/evening first
4	Acronycal rise/morning last

VR>=1: VR is Standard Visbility Range (epsilon=0.02) [km]
1>VR>0: VR is the total atmsopheric coeffcient (k_tot)
VR=0: the other atmospheric parameters determine the total atmsopheric coeffcient (k_tot)

WindSpeed

Windspeed at 10 m height [m/sec]

Yeartype

Type of Year that is being using for the emphemeris:

tropical	Tropical Year duration (duration depending of JDNDays)
julian	Julian Year duration (365.25 [Day])

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Major content related changes: April 19, 2006

Copyright (c) 2006 - 2007, Victor Reijs.
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License".