                      RIYAL CALCULATION SOFTWARE


I- DESCRIPTION

   RIYAL is a compact and fast DOS program that calculates accurate
astronomical positions and a wide range of astrological measurements
of the following bodies:

- Sun, Moon, and planets.
- the centaurs: Chiron, Pholus, Nessus, Asbolus, Chariklo, 1994TA
  (Pylenor), Hylonome, 1998QM107, 1998SG35, 1999HD12, 1999JV127,  
  1998TF35, 1995SN55, 1998BU48, 1999OX3, 1999UG5, 1999XX143,
  2000CO104, 2000EC98, 2000GM137, 2000FZ53, 1996RX33, 2000QB243,
  2000QC243, 2000SN331, 1996AR20, 1996AS20, 2001BL41, 2001KF77,
  2001PT13, and 2001SQ73.
- the unclassified "Damoclian" objects: 944 Hidalgo, 5335 Damocles,
  1996PW, 1997MD10, 1998QJ1, 1998WU24, 1999LE31, 1999RG33 (#15504),
  1999LD31 (#20461), 2000AB229, 2000DG8, 2000HE46, 1998HO121,
  2000VU2, 2000QJ46, and 2001QF6.
- the scattered-disk objects: 1996TL66 (#15874), 1995TL8, 1999TD10
  (#29981), 1999CF119, 1999CY118, 1999CZ118, 1996GQ21 (#26181),
  1999RZ215, 1999RD215, 1999DE9 (#26375), 2000EE173, 2000PF30,
  2000PJ30, 2000PH30, 2000CR105, 2000OO67, and 2000OM67.
- the trans-neptunian "cubewanos" 1992QB1 (#15760), 1996TO66
  (#19308), 1995SM55 (#24835), 1998WH24 (#19521), Varuna (#20000),
  2001KA77, and 2001QF298.
- the plutinos 1993SB (#15788), 1994TB (#15820), 1996TP66 (#15875),
  1999TC36, 2000EB173, and 2001KX76 (#28978).
- the 8 Hamburg School "Uranian" planets (longitude only).
- the first 10 asteroids: Ceres, Pallas, Juno, Vesta, Astraea, Hebe,
  Iris, Flora, Metis, and Hygeia.
- additional main-belt asteroids: 1181 Lilith.
- Apollo asteroids: 5143 Heracles, 2001OG108.
- Amor asteroids: 3552 Don Quixote

   It gives the the tropical and sidereal longitude, latitude, right
ascension, declination, stellar magnitude, heliocentric coordinates,
geocentric and heliocentric distance values, draconic longitudes,
geocentric nodes and apsides, geocentric velocities, the true and
mean lunar Node, the true, mean, corrected, and "natural" lunar
apogee and perigee, the topocentric longitude of the Moon, the lunar
phase and velocity, the Russian White Moon, the hypothetical Dark
Moon, the mean and osculating Black Sun, the planetary hour, the
Galactic Center and Pole, the Vertex, and the night and day parts of
Fortune.

   It also includes the Sabian symbols and a catalog of the brightest
1078 fixed stars, and can draw single or double chart wheels in
640x480 and 800x600 colored graphics (geocentric or heliocentric). It
also calculates precession-corrected direct and converse transits,
tropical and sidereal solar (progressed) and lunar returns,
paranatellontas, midpoints, the "speculum" for primary directions,
directions to the angles, azimuths and altitudes, secondary
progressed lunations and eclipses, secondary and tertiary direct and
converse progressions, Davison relationship charts, aspects and
phases, elements and qualities, essential dignities, planetary
pictures, harmonics, and Solar arcs.

   Riyal also calculates the angles and house cusps in 12 different
house systems for any latitude, including those above the polar
circles. The program can also produce a Table of Houses for any
latitude (including polar), and a sequential daily ephemerides of all
centaurs or of the Sun, Moon, and 8 planets, for any length of time,
and send it either to the screen or to a file. There is also an
astro-cartography module and a tabulation of Placidus and Campanus
"mundoscopes".

   The calculations cover the period 4700 BC to 9000 AD for the
principal planets (Pluto only -4700 to +3000), 601 AD to 2018 for the
main centaurs, and 1701-2018 for the the other centaurs, the
asteroids, and the trans-neptunians.

   The word "Riyal" is Arabic, and comes from the name of astrologer
Abu-l-Hasan 'Ali ibn Abi-l-Riyal (ca.965-1040), born in Magreb and
author, around 1037, of the "Kitab al-Bari 'Fi Ahkam an-Nugum" or
"Liber Completus In Iudiciis Astrorum", a monumental medieval
astrological reference very popular during the Renaissance.

   RIYAL is going to be a smaller, stripped-off version of a big
astrological program I made for the Atari ST, called "Abenragel", the
latinization of "Ibn Riyal". Abenragel's book has a special interest
because there is a translation to old Castilian made in 1256 in the
court of Alfonso X, "The Wise", named "Libro Conplido de los Iudizios
de las Estrellas", and published by the Real Academia Española of
Language in 1954. This translation, though incomplete, is of immense
linguistic and historical interest.



II- INSTALLATION

   If you downloaded this program from a place that is not Riyal's
homepage (www.expreso.co.cr/centaurs), then you have an old version.
Please check the end of this "readme.txt" file for information.

The "Riyalpack.exe" package contain 21 files:

  - 4 minor planet ephemeris files (they are described below in this
    document). Only the file "centaurs" is needed for the program to
    function properly:
   .centaurs.fle
   .long.fle
   .tnpsdo.fle
   .asteroid.fle
   .damocles.fle
  - lunaf.fle   = arguments and coefficients of ELP2000-85
  - vsopm.fle   = arguments and coefficients of VSOP87A
  - deltat.fle  = values of delta-t from 1620 to 2010
  - usno1.fle   = USNO catalog of 1078 stars
  - names.fle   = fixed stars names and identifications (editable)
  - world.map   = simple 10,000-point world coordinates
  - sabians.fle = Sabian Symbols
  - pluton.gif  = graphic of Pluto errors from 4700 BC to 600 AD
  - readme.txt  = this document
  - riyal.exe   = the program's executable
  - riyal.cgf   = personal configuration defaults (editable)
  - riyal.fnt   = the font used to draw the wheel
  - 3 alternative icons for Windows:
   .riyal1.ico
   .riyal2.ico
   .riyalz.ico
  - gfaba573.ovl= run-only module libraries

   Unpack the archives to any directory you like, but make sure all
the files are together in the same directory. Make a Windows shortcut
to "Riyal.exe" and specify the size of the window you want. The
Windows desktop will disappear for a second but it will come back if
you specified "normal window" in the shortcut properties. If the
desktop doesn't reappear, press "Alt" + "Enter".

   Riyal's package includes shortcut icons to be used by the Windows
shortcuts. They are a gift by Zane Stein of an original drawing he
made for this program.

   Remember that conventional DOS memory is very small. If Riyal
doesn't run in your system, it may be that your DOS memory is being
eaten by some other terminate-and-stay-resident (TSR) application;
you will have to check for that, so that you can have enough of it.
The amount of free DOS memory is shown in blue in the lower right
corner of the menu screen. Please write if you have a problem.

   This version of Riyal will not work in machines without a numeric
co-processor, like old 386's and 486SX's. There is a special version
that works in these machines, adjusted to work in black and white.
Please be aware that this special version is no longer updated. It
can be downloaded complete from:

   http://www.expreso.co.cr/centaurs/riyal/program/riyalsx.zip
         
   
   There are a few tips about using DOS under Windows95/98 that you
should know:

-work always from a window, not in full screen mode.

-once you have the size of window and fonts you want, click on the
 icon at the upper left corner and unmark "toolbar".

-you can cut and paste any part of a DOS text window; for example, you
 can cut one column --or part of a column-- and paste it to the text
 or message you are writing: a-)click the upper left icon, choose
 "edit" and then "mark", b-)select the text you want by dragging the
 mouse with the button pressed, and c-)right click. The portion
 selected is now in the clipboard, ready to be pasted. Often, when all
 one needs is a few positions, this makes unnecessary to redirect
 output to a file.

-when one chooses to draw a graphic wheel, DOS goes automatically to
 fullscreen mode and the Windows GUI disappears. Press "alt"+"enter"
 and you will have the wheel reduced in a nice small window, with all
 the Windows' functionality back and the wheel still on sight.

-you can put the graphic wheel in the clipboard by pressing "print
 screen". (this works only in the 640x480 mode).



III- RUNNING THE PROGRAM

   When you start the program, it gives the date of the present
version and asks whether you want to re-direct its output to a file.
If you press "P", Riyal will present you a file selector with the
default file called "Riyaldat.txt", in its own directory. If the file
you specify does not exist it is created, otherwise the output is
appended to the existing file; the file is never over-written.

   RIYAL.CGF. When first run, Riyal reads a file called "riyal.cgf",
which contains values of the time zone, longitude and latitude of the
user, plus flags that instruct the program whether to work with delta-
T, geometric positions, topocentric or geocentric positions, and the
sidereal year and sidereal bija corrections or not. This file must be
edited in order to have the desired defaults. There are only 7
entries, one line each:

1-) The first line is the amount to be added to your computer time in
order to have GMT (with a "-" sign if you are ahead of Greenwich).

2-) and 3-) The second and third lines are the strings for the
geographic longitude and the latitude, respectively, used by the input
routines. They are formatted and must have an exact number of spaces,
with leading zeroes (or spaces) where necessary (002w33, _12e29,
102w33, _9n56, 18s24...).

The last 4 lines are flags:

4-) the fourth line must be "0" (if "1" the program will calculate the
true geometric positions of planets, as opposed to the "apparent"
position corrected for light-time which are normally used);

5-) the fifth line (must be "1") instructs the program to work with
delta-T or Universal Time (a "0" here would assume "Ephemeris Time"),

6-) the sixth line is either "1" (sidereal reference frame) or "'0"
(tropical reference frame).

7-) the seventh and last line instructs the program whether to work
with geocentric ("0") or with topocentric ("1") positions.

   The program will first ask for the date. You will be given default
values to be edited, taken from your computer date and time and
"riyal.cgf". To enter your data, you must overwrite the system's date,
or erase it and write a new one, and then press "Enter".

   It will accept dates from 4713 BC to 9000 AD, but Pluto is not
displayed after 2999AD, and the asteroids will appear only from
February 5, 1701 to September 10, 2018. With the additional
"long.fle" ephemeris file, Riyal calculates the main centaurs plus
1999TD10, 1996TL66, Varuna and 2001KX76 from December 2, 600 AD to
July 7, 2018 AD. Take notice that the input is formatted, with "day"
first (2 digits), then "month" (2 digits) and the "year" written
fully (4 digits).

   You can use anything as separator in the input strings, and blanks
can be entered instead of "0", but the number of spaces must be
maintained. Press the "Insert" key in order to over-write the default
values, or delete them and write the whole string again. Remember
that the "insert" key of your computer is a toggle. You need to press
it only once at the start of a session in order to change the default
"insert mode" of the keyboard to "overwrite mode". Each time you press
it, you cancel the previous state.

   BCE DATES: If you want to enter BCE dates, simply add "B" or "b"
at the end of the string, like "01.01.2800b". The year 0 is 1b, the
year -1 is 2b, etc.

   OLD STYLE DATES: if the input date is in the "Old Style" Julian
calendar (for example, dates in Yugoslavia before 1919 or in Russia
before 1917), Riyal will process them if you add the letter "O" or
"o" to the end of the date string. The date is then interpreted as
"Old Style" and will be converted automatically. All dates prior to
January 1 1582 are considered as Old Style by default, but if the year
is 1582 or if you want to enter New Style dates prior to 1582, you can
do it by adding "N" or "n" at the end of the date string.

   After you enter the date and press "Enter", the program will
ask for the time. It must be entered in GMT or Universal Time. The
program accepts inputs of up to 36 hours and will convert
automatically to the next day. By entering a letter code at the end
of the time string, overwriting the default "s" for "seconds", the
program will automatically make the following assumptions about the
time being entered, and convert it accordingly:

   g = Greenwich Mean Time (UT) -- this is the default (="s")
   h = Standard Time (expected International Time Zone)
   d = Daylight Saving Time (+1h)
   l = Local Mean Time (usually before 1900)
   t = True Apparent Solar Time
   r = Sunrise
   z = Sunset

   The input time is converted to UT according to the code above, and
appears in the header output in inverse video. Please take note that
if sunrise or sunset time is chosen, the corresponding UT will not
appear at first in the planets listing. You can check the UT
corresponding to sunrise or sunset the second time the header
appears, for example by pressing "K" in the Menu and looking at the
header.

   After the time is entered, the program asks for the coordinates.
If you don't know them, you can leave the default values, since the
planetary coordinates will not be affected if you entered the time as
GMT. The coordinates you enter each time, become the defaults until
you enter a new set.

   Then the program asks for the name you want to give to the chart.
You can leave this blank and simply press "Enter", or you can write
the name you want to appear before the header as a title in the file
output. Capital letters are not necessary because the program will
capitalize all the letters. This name appears only in the file output
and in the white wheel.

   After you have entered the data, the results are shown in sorted
vertical order from 0 to 30 degrees, longitudes only (for the full
display of coordinates you must use the "Y" routine). If the sidereal
option is disabled in the "riyal.cfg" file, the sidereal longitudes
will not appear. The positions of the newest centaurs with very
badly-known orbits do not appear in this main sorted display.

   After this first listing of positions, you will be presented with
the menu, which allows you to go back and forth within the program.

   COLOR USAGE: The angles and the true lunar node appear in white,
while the planets, Sun, and Moon in yellow, and you will see in pink
the centaurs with well-known orbits. The transneptunians appear in
cyan, and the damocloids in green. Closer and faster asteroids are
shown in blue. Between 1992 and 2005 very recently discovered objects
appear in normal light-gray, but outside this time-span, some will
appear dark-gray, meaning that their positions are not certain and
should not be used.

   REDISPLAY WITH HARMONICS: this option, if you simply press
"Return" ('Enter') will redisplay the radix data (harmonic 1) without
having to go through the input routines again. Any other number from
"2" to "99" can be entered, and the corresponding positions in the
harmonic chart will be given (e.g., the "Navamsa" --harmonic 9,
"Panchamsa" --harmonic 5, etc.). Pressing "0" (zero) displays the
positions in the DRACONIC ZODIAC, using the true node as the zero
point. The draconic and harmonic positions appear in zodiacal (not 30-
degree) order.

   SINGLE-BODY EPHEMERIS: In the "L" routine you are given the choice
of generating multiple-body or single-body ephemeris of any of the
nearly 70 bodies included in the program. If you simply press "Enter",
Riyal will produce a single-body ephemeris by default. You will be
asked to choose among 3 intervals of tabulation: 1 day, 10 days
(default) or 400 days. When asked which body you want, you must enter
its Riyal name, of which the program will use only the first 3 letters
(upper-case letters are not needed). The quantities included are:
geocentric longitude, latitude, distance, and velocity, heliocentric
longitude, heliocentric distance, and the heliocentric "angle of
crossing" (the angle between the direction of a planet's motion and
the direction perpendicular to the radius vector). If the Moon is
chosen the program will give its distance in Km and the positions of
its true ascending node and apogee. Pressing "P" will SCROLL through
the ephemeris backwards, while "ESC" interrupts the routine.

   DAILY EPHEMERIDES:  This routine handles only the regular planets
and centaurs (all the other asteroids are excluded). Daily
ephemerides for any length of time can be seen in the screen or sent
to a file. The default option ("Enter") shows only 9 centaurs (those
that have more accurate orbits), while "N" shows the rest with
accurate orbits. File output in this rotine behaves a little
different from screen-only. If you are sending the output to a file,
it is recommended that you view it or print it with a DOS --and not
a Windows-- font (like "Terminal"), so that the column bar separators
appear correctly. If the "P" (planets) option is chosen, the
ephemeris will include the Moon and the sidereal time at Greenwich
0h, while the default ("Centaurs") option will generate a daily
ephemeris for all the centaurs simultaneously in a row.

   With the "K" option, it is possible to construct an ephemeris of
only two bodies, at any interval in days and for any time period
desired (if the internal ephemeris supports it), and in any
combination of regular planets and/or centaurs, including the MEAN
lunar node, Varuna, KX76, TD10, and TL66 (but not the other
asteroids). If the first and second planet input choice are the same,
Riyal will tabulate the planet's heliocentric node, aphelion, and
geocentric ascending and descending nodes; if it is the Moon, the
program will tabulate the osculating, the mean, and the "natural"
lunar apogee and perigee.

   THE HOUSES ROUTINE: house cusps calculated with all the different
house systems will be sequentially displayed by pressing any key. The
"P" key cycles backwards and the "Enter" and "Esc" key will exit the
cycle and return you to the menu. The last system displayed before
leaving the cycle will be used by all subsequent calculations and by
the wheel drawing routine. If the houses are above the Polar circle
and Riyal finds that it cannot be done, it warns you and calculates
smoothly using the Alchabitius system.

   THE WHEEL DRAWING: Pressing "1" in the menu will draw a 640x480
colored graphics wheel. If "2" is pressed instead, the wheel will be
drawn over a white --not black-- screen. The drawing can be copied to
the Windows clipboard by pressing the "Print Screen" key (to the
right of "F12"), from where it can be pasted to any Windows graphics
program, and printed if desired. (The program will ask you a name for
the drawing when it is done over a white screen). HELIOCENTRIC charts
can be drawn pressing "3" (black screen) or "4" (white screen).
Pressing keys 5-8 produces the same results but the wheel is drawn
without the centaurs. If your system is VESA-compliant, pressing "9"
will draw the wheel in 800x600 (black) (Don't use these keys if your
card or your monitor has trouble with this DOS resolution.)

   THE DOUBLE WHEEL: When there is a second matrix of positions in
addition to a radical (transits, Davison chart, solar and lunar
returns), you will be given the option to draw a normal wheel or a bi-
wheel with the radical positions in the inner wheel and the transiting
positions in the outside wheel. To disable it, you must choose option
"B" in the menu and press "Enter" with the default harmonic "1"; this
erases the second chart. It is possible to draw the secondary or
tertiary progressions by pressing  "Esc" once the calculation is
complete, without finishing the whole routine. Otherwise only the last
(tertiary converse) will be stored and displayed.

   ASPECTS AND PHASES: This routine calculates mutual distances. The
first column gives the phase (new=1, crescent=2, first quarter=3,
gibbous=4, full=5, disseminating=6, last quarter=7, balsamic=8).
Phases are established with the perspective of the faster-moving
planet cycling with respect to the slower-moving, and the parameter
used to assertain this is the semi-major axis of the orbit. The
second column gives the TRUE angular distance between the two points,
as they would be seen in the sky. The 3rd column gives the distance
along the ecliptic, which is the one used to measure the aspect. The
fourth column, if applicable, gives the aspect and its orb. A fifth
column, when applicable, lists the parallel or contra-parallel of
declination and its orb.

   TRANSITS AND RETURNS: Transiting positions as well as solar and
lunar returns are calculated in the tropical zodiac but using the
sidereal year. The display shows the radical positions in the first
column and the precession-corrected positions in the second column,
with the amount of accumulated precession in the title field.
(Likewise, progressions and solar arcs are calculated using the
sidereal --not the tropical-- year. This sidereal framework can be
disabled with a flag in the "riyal.cgf" file).

   PROGRESSED SOLAR RETURNS: You have the option to progress the solar
return (tropical or sidereal), which is done by the PSSR "anniversary
second" method of siderealists. The progession is shown day by day
from one anniversary to the next, with the progressed angles of the
return and the conjunctions of all radical, solar, and transiting
bodies. The columns, from left to right, are: date, progressed
Sidereal Time, progressed Midheaven, progressed Ascendant, plus Right
Ascension of the Midheaven. Then follow the planets that are in
conjunction with the progressed horizon or meridian that day, with
their corresponding measure of right ascension, so that the
approximate time of the day can be calculated ("m"=Midheaven, "i"=
I.C., "d"=Descendant, "a"=Ascendant, "S"=solar, "R"=radical, "T"=
transiting). The data applies to the actual physical planet, not its
ecliptical longitude (the same as with the parans). If Riyal is
working in sidereal mode, all coordinates except the progressed
Sidereal Time will be precession-corrected from the time of birth.

   SABIAN SYMBOLS: The Sabian Symbols are the mimeographed version of
Marc Edmund Jones used prior to the publication of his book in 1953.
They are included in Riyal through the courtesy of Sabian symbols
expert Lynda Hill, who kindly provided me with a copy of the text.

   URANIAN PLANETS: The 8 Uranian "transneptunian" planets are
displayed with the "O" routine. They can be calculated for any date,
and only the longitudes are given. Since the object of Riyal is to
encourage research on distant and slow-moving REAL bodies, the
Uranians and other "hypotheticals", being speculative mathematical
points that cannot physically exist, fall beyond its purpose. They are
shown only for reference or completeness, and are excluded from all
the other routines.

   COMPLETE SORTED DISPLAY: All the Riyal asteroids that have a name
are presented here. After the first page, Riyal will show all 90+
objects (all centaurs, asteroids, trans-neptunians, and scattered-
disk objects) included in the program, together in sorted 30 degree
order, including the osculating lunar apogee, lunar node, and angles.

   TABLE OF HOUSES: This routine works with the house system that was
previously chosen in the "G" routine. It asks for the coordinates
(you can ignore the longitude by simply pressing "Enter"), for a
date, and for the interval in minutes (1-9), and it will construct a
Table of Houses for any latitude from 0 to 89,59 degrees, with
sidereal time as argument. For polar latitudes, the screen output
changes color when the Midheaven is below the horizon, except in the
Koch system, which produces erroneous cusps and appears all colored;
although Riyal will show Koch cusps at any latitude, the results are
meaningless near the Poles. The Topocentric system uses its own
"polar ascendants" that have nothing to do with the real horizon. The
Placidus cusps present no problems only partially, as long as the
Midheaven is not below the horizon. The anomalous Placidus cusps are
not shown (see the explanation later below). 

   GEODETIC CHARTS: Johndro "geodetic right ascension equivalence"
charts using the Placidus system and the Greenwich meridian as the
zero point can be calculated and drawn by choosing the "Geodesic"
house system in the "G" routine. It can be displayed immediatly after
Placidus by pressing "P".

   PARANATELLONTAS: This routine consists of temporal distances from
the angles. i.e., the times of rising and setting of celestial
objects. A minus sign ("-") indicates time in the past. When the orb
is less than 1 minute of time (15'), the parans are highlighted. In
the case of transits, solar and lunar returns, etc., the radical
positions ("r") are included in the tabulation with the transiting
ones ("t"), and the positions are corrected for precession (unless
this has been disabled in the "cgf" file).

   THE SPECULUM: The speculum includes 2 semiarcs. The first, on the
left, is the actual one, and in parenthesis is given its complement.
Then follows a letter, "N" meaning "nocturnal" and "D" meaning
diurnal, which indicates whether the object is above or below the
horizon. The second column after the meridian distance is the
normalized distance. After the directions to the angles are shown, a
second speculum appears (3rd display) which includes right ascension,
ascensional difference under the planet's topocentric pole, oblique
ascension with its zodiacal equivalent (the "oblique longitudes"), and
the "topocentric" or conic pole. If it is a secondary chart (transits,
returns...) the positions are corrected for precession.

   PRIMARY DIRECTIONS are not implemented in this version of the
program, with the exception of the directions to the angles. They are
a direct conversion of the true planet's distance to the horizon and
meridian using Naibod's arc (Naibod's Arc is not "the mean motion of
the Sun" but the diurnal movement of the celestial sphere, or the mean
rythm of progression of sidereal time, which represents the essence of
the spherical dynamics of the Earth and the logical and concrete
relationship between time and space).

   MUNDOSCOPES: The last page of the Speculum displays the azimuths
and altitudes, plus two aditional tables showing the planetary
positions IN MUNDO with respect to the equator ("MundoPla") and to the
prime vertical ("MundoCam"). For clarity they are shown in their
zodiacal equivalents, Aries corresponding to the first house,
Capricorn to the tenth, etc.

   DARK MOON: This is the hypothetical "second moon" of the Earth
calculated by Waltemath (hence the "W.") and popularized by Sepharial,
often called "Lilith". Mathematically, it is a speculative point
moving around the Earth in an ellipse with eccentricity 0.1587,
inclined 2.5 degrees to the ecliptic, and with a period of 119.227434
days. The positions of Riyal are identical to those available in Solar
fire version 4.

   WHITE MOON: The "White Moon" is based on data provided by Russian
astrologer Margaret Almazova, who comments on a long oral tradition
in his country regarding its use. According to her, its origin is
really unknown, in spite of his countryman Pavel Globa's claims that
the present ephemeris is the result of his insight. The meaning of
the White Moon --a positive counterpart of the "Black Moon"-- is well
established in the practice and experience of Russian astrologers,
and Almazova summarizes it as "invisible spiritual support in life
which must be nourished (by sign and house) in order that the effect
of a shagreen leather does not emerge". Mathematically speaking, it
is an imaginary point with a circular and co-planar orbit, like the
Uranian planets, except that its orbit is geocentric. Its motion is
likewise linear and completes a cycle in 7 years (2556.409663 days).
According to the data provided by Almazova its position on 1-1-1900
at 0h GMT was 18,45 Leo.

   COORDINATES CONVERSION: This is a simple routine that converts
right ascension and declination to their ecliptical counterparts
(longitude and latitude). It gives the choice between "astrometric"
(measured with respect to the ecliptic of J2000) and "apparent"
(measured with respect to the ecliptic of date). Different values of
the obliquity of the ecliptic will be used for each. The "apparent"
choice will use the ecliptic of the date which has been entered in the
program before displaying the menu, and will calculate precession from
J2000 to that date (the radix).

   ASTRO-CARTOGRAPHY: Routine "R" produces a world-map with a simple
rectangular projection built from a small database of 10600 coordinate
points. The mouse pointer is used to indicate the coordinates within
the map in the lower part of the screen (left-clicking), and to return
to the menu (right-clicking plus any other key). Only the bodies shown
in the main display (regular planets, centaurs, Varuna, KX76, TD10,
and TL66) can be shown, limited to one at a time. The "IC" and "MC"
lines are the only ones labelled; the rising curve is always between
the IC and the MC, while the setting curve is between the MC and the
IC; the sequence is: IC-rise-MC-set-IC. If the sidereal functionality
of the program has not been disabled, this routine will perform
precession from the time of the radical when the date corresponds to a
secondary chart (returns, transits, etc.), so the results may not be
comparable with results obtained with other software in this case (you
must enter the data as radical in order to make the comparison).



IV- ACCURACY AND SOURCES

   The accuracy of the software is better than 1 arcsecond at all
times several centuries before and after the year 2000. This includes
the Moon, the planets, and all the centaurs, but the arcsecond
precison of the program's display (routine "Y") can sometimes result
in errors of 1 arcsecond due to rounding.

   For the Moon, Riyal uses the complete ELP2000-85 theory developed
by Michelle Chapront-Touze and Jean Chapront (1988). The maximum
error in longitude is 1/2 of an arcsecond (0.5") at present, and
13 arcseconds in 1500 BC. According to Steve Moshier, the maximum
error in the period 4000BC to 3500BC is 1'22". The polynomials of
time of the mean longitude and the Delaunay arguments are adjusted to
DE403 instead of DE200, and are taken from the 2nd edition (1998) of
Jean Meeus "Astronomical Algorithms".

   For the Sun and the planets Mercury through Neptune, Riyal uses
the complete VSOP87-A theory in rectangular variables from the
Bureau des Longitudes. Theoretically, the accuracy of VSOP87 is said
to be 1" from 2000 BC to 6000 AD for Mercury, Venus, Earth (Sun),
and Mars, 1" from 1 BC to 4000 AD for Jupiter and Saturn, and 1" from
4000 BC to 8000 AD for Uranus and Neptune.

   In practice, the VSOP87 theory rapidly deteriorates after 2000
years in the positions of the major planets, due to an erroneous mass
of Neptune in JPL's DE200 (the model used to fit the integration
constants of VSOP87), and to the fact that the claimed 1" accuracy of
the Jupiter and Saturn part of the theory reached back only 2000
years. Steve Moshier calculated an approximation of these errors by
comparing Jean Meeus' truncated VSOP87-D version with an extension of
the DE200 model, and for the period from 5001 BC to 1 BC he gives the
following maximum errors:

       -1000/-1    -2000/-1000    -3000/-2000   -4000/-3000

 Ju      16.9"        44.6"          2'39"         7'42"
 Sa      21.7"        1'58"          5'08"        17'08"
 Ur       3.6"         7.8"            12"           57"
 Np      38.9"        38.3"            52"         1'18"
 
   Note that these errors correspond to the Jean Meeus truncated
version of VSOP87D. The full VSOP87 used by Riyal is slightly more
accurate, but suffers from the inaccuracies of DE200. Since the
constants of VSOP87 and ELP2000 were made to fit DE200, comparison
with the present DE406 JPL standard yields larger errors in ancient
dates for all the planets and the Moon. Newer theories, fitted to
DE404/DE406, have already been developed at the Bureau des Longitudes
but they are not publicly available.
   
   Pluto is not part of the VSOP87 theory, and is calculated by
interpolating a table of positions derived from DE406. The maximum
software error is 1/10th of an arcsecond (0.1"), far below the
precision of the program's display in routine "Y". Before the year
600 AD and after 2018, an approximate parabola is used which gives
maximum errors less than or equal to 5 arcminutes 94% of the time.
Errors larger than 5 arcminutes begin to appear only before 1700 BC,
and after that the errors are always less than 8 arcminutes until
4500 BC (see "pluton.gif" for a graphical representation of the
errors from 4700 BC to 600 AD)..

[NOTE: a 1-arcsecond accuracy for Pluto from -3000 to +3000, adapted
from Steve Moshier's analytical development based on JPL DE404, is
in preparation].

   The centaurs and trans-neptunians are interpolated from a table of
numerically integrated positions calculated with the software "Solex
7f5" of Aldo Vitagliano. This has an accuracy comparable to that of
the JPL Horizons integrator and the Swiss Ephemeris. Here is a sample
of the maximum possible errors in the period 1900-2018:
            
              Chiron   = 0.4"         Pholus   = 0.5"
              Nessus   = 0.1"         Pylenor  = 0.1"
              Asbolus  = 1.2"         Hylonome = 0.2"
              Chariklo = 0.3"         1998SG35 = 2.2"
            
   To calculate these errors, 1082 apparent geocentric longitudes
separated by 40 days from 1900 to 2018 were compared with the
longitudes calculated by the Solex program using the same orbital
elements. The larger error of Asbolus and of SG35 is due to the large
interpolation step used by Riyal (200 days), since at perihelion they
move faster than the others. SG35 at perihelion moves exceptionally
fast compared with all the other centaurs, therefore its error above
1" is the exception. Errors of more than 1" in the slower bodies
(including all transneptunians) are caused by inconsistencies or
errors in the ephemeris files used for the comparison and are not
related to the program's internal accuracy.

   There are other errors, much larger, caused not by a faulty
ephemeris but by uncertainties in the osculating elements used for the
numerical integration. The orbits of all the recently-discovered,
poorly-observed bodies are not well known by astronomers, and accurate
positions for the past or future cannot be calculated; their ephemeris
after only a few years from the present have a very large margin of
error. A table with the current error estimates calculated by
astronomers of all the slow-moving objects of Riyal can be found in
the author's site:

   http://www.expreso.co.cr/centaurs/astronom/accuracy.html

   HERACLES, DAMOCLES, AND OTHER ASTEROIDS: because they can move very
fast compared with the slow-moving centaurs, the accuracy of Riyal's
interpolation (at steps of 80 days in this case) is diminished for
these bodies. The errors are about 1 arcminute, reaching 2 arcminutues
only occasionally depending on the body. Here are some maximum errors
in a sample of 1082 positions from 1900 to 2018 every 40 days:

   Ceres    =    4.8"  -  96% are less than 3 arcseconds
   Pallas   = 1'37.8"  -  92% are less than 20 arcseconds
   Juno     = 2'01.0"  -  93% are less than 40 arcseconds
   Vesta    =   23.4"  -  92% are less than 10 arcseconds
   Damocles = 1'41.1"  -  97% are less than 5 arcseconds
   Heracles =   23.9"  -  97% are less than 5 arcseconds


   DELTA-T: The program compensates internally for delta-t, but after
1/1/2011 it makes no correction. The values of delta-t are taken from
the IERS data, including the long-term predictions. For dates before
1622 it uses the parabolic fits given by the Chapronts in "Lunar
Tables and Programs" (1991), adjusted to the new value of the Lunar
secular acceleration (The parabola 391 AD to 948 AD is used for all
dates prior to 948). If you are going to compare Riyal's positions
with positions calculated by another program, especially before 1622
or after 2011, you must take delta-t into account.

   DISTANCE VALUES: The "distance values" are percentages of the
possible geocentric and heliocentric distance along the instantaneous
orbit. 100 means closest and 0 means farthest.

   GEOCENTRIC APSIDES AND NODES: The geocentric nodes and apsides are
of the true heliocentric osculating orbits, not the mean orbits, and
are usually accurate as displayed, but a-) they are reduced to the
ecliptic heliocentrically and then converted to geocentric without
latitude, therefore small differences may appear in the geocentric
positions when comparing with ouput from other software, and b-) low-
eccentricty orbits can have errors of a few arcminutes in the apogee.
The osculating "true" node of the Moon is accurate to within 0.4 arc-
minutes at present, and the osculating apogee may reach errors of 1.3
arcminutes at present, but these errors slowly increase with time. The
reduction to the ecliptic of the apogee (or the aphelion) is applied
also to the Moon.

   URANIAN PLANETS: The orbits of the 8 Uranian planets are assumed
to be co-planar, circular, and unperturbed. These positions do not
incorporate the small refinements added later by James Neely to the
ephemeris of the first four.

   GALACTIC CENTER: The Galactic Pole and Sagittarius A* at the
galactic center are treated as stellar objects. The position of the
Galactic Center at epoch J2000 was taken from Yusef-Zadeh, Choate, &
Cotton in "The Astrophysical Journal", Volume 518 (1999), Issue 1, pp.
L33-L35. The Galactic Pole is the conventional (and old) IAU
definition for B1950.

   FIXED STARS: the list of 1078 bright stars is the same used for
many years by the United States Naval Observatory, and includes all
stars brighter than magnitude 4.75. The transformation algorithm was
taken from "The Astronomical Almanac" of 1981, pages B36-37, and
accounts for the effects of precession, proper motion, nutation,
annual parallax and annual aberration, but the result is limited by
the 0.1s precision of the source right ascensions. The overall
accuracy of the positions is therefore around 2 arcseconds. The
sources are the FK5 catalogue and --if not found there-- the "Yale
Bright Star Catalog". Star names are stored in a separate plain-text
file ("names.fle") that can be edited. Proper names are given priority
over code designations.

   PRECESSION AND NUTATION: Riyal uses the numerical expressions and
precession formulas of the Bureau des Longitudes (Astronomy and
Astrophysics 282:663,1994). The positions and velocities of VSOP87A
are precessed with the transformation matrix given by its authors,
Bretagnon and Francou, in "Astronomy and Astrophysics" 202:314, 1988
(Table 4), adjusted to the new value of precesion. The Greenwich Mean
Sidereal Time and the largest 49 coefficiets of the Nutation are also
calculated with the new BdL formulas of Bretagnon and Rocher. The
accuracy of these formulas is said to be 1" in 4000 BC.



V. THE LUNAR APOGEE OR BLACK MOON

   Riyal gives 4 positions of the lunar apogee or "Black Moon": the
traditional mean apogee (reduced to the ecliptic), the osculating or
true apogee, the "natural Apogee", and the "corrected" apogee. It
uses the osculating value in the "sort all" tabulation because its
erratic motion best describes the Black Moon symbolism, which I have
explained in http://www.expreso.co.cr/centaurs/essays/lilith.html.

   The astronomical reality of the osculating apogee can be described
as an ellipse that changes very fast from instant to instant. The true
lunar trajectory in space can be described mathematically by a Keplerian
ellipse only very roughly, because its shape changes shape very fast and
irregularly, but it is precisely that the changes are so erratic or
"wild" what makes the symbolism of this point so powerful.

   When the position of the Moon at the time of apogee is compared
with the position of the mean Black Moon, one finds that the
difference is --in great part-- a sinusoid with a period of 206 days
and oscillates between -5.4 and +5.7 degrees, whereas when one
compares this mean Black Moon with the theoretical osculating apogee
at times falling between two apogee dates, the difference can reach
up to 30 degrees.

   The position called by Riyal "Natural Apogee" simply applies an
interpolation to find the approximate intermediate values between the
Moon position at one apogee occurrence and the next. When the apogee
and perigee are calculated this way, they are never 180 degrees
apart. The perigee must be calculated separately.

   This approach to the lunar apogee or Black Moon, based on past and
future coordinate points instead of instantaneous positions and
geometrical projections, represents a mixture of temporal planes and
contradicts how all other radical astronomical points in the chart
are calculated. It was outlined by Miguel García in Spain ("Realidad
y ficción astronómica de Lilith", Cuadernos de Investigación
astrológica Mercurio-3, nº 6) and is the one followed by Dieter Koch,
who calls it "interpolated" apogee (I followed his suggestions about
how to calculate it before including it in Riyal).

   The positions given by Riyal are based on the formulas for the
times of apogee and perigee of Jean Meeus, found in "Astronomical
Algorithms". The accuracy of the apogee according to Meeus is 3
minutes of time, which added to the necessarily approximate
interpolation results in several arcminutes of accuracy for the
position of the natural apogee in Riyal. Meeus states that the
accuracy of the perigee is 31 minutes of time, which would result
in probable errors of about 1 degree in the position of the natural
perigee.

   The so-called "corrected" apogee is included in Riyal for the sake
of completeness. This is an artificial simplification of the problem
of finding the "true" apogee from the mean value, in vogue for some
years in Europe. The position given here is only a rounded
approximation of this astronomically erroneous Black Moon, of which
several published ephemerides exist which agree only roughly among
themselves.

   A detailed astronomical discussion of all 4 different apogees can be
found at: http://www.expreso.co.cr/centaurs/posts/apogee.html



VI. SIDEREAL POSITIONS

   Riyal works by default in the sidereal reference frame. The dates
of aspects of solar arc directions and secondary and tertiary
progressions are calculated sidereally, i.e., using the sidereal year
instead of the tropical, with a "bija" correction equivalent to about
one day for every year of life. A tropical date at 60 years of age,
for example, would occur roughly 60 days before the one listed.
Similarly, by default, the transiting positions contain a bija
correction, and the solar and lunar returns are sidereal. All of this
can be disabled by writing "0" ("zero") instead of "1" in the last
line of the "Riyal.cfg" configuration file read by the program at
startup.

   The use of precession does not imply using any of the traditional
sidereal zodiacs. It means that we are using a "sidereal reference
frame", i.e., fixed in space, unlike the tropical zodiac, which
rotates with respect to the sidereal. Movement along this fixed space
is then measured in sidereal units of time instead of tropical. The
result is that as time passes, all progressions, transits, returns,
etc., happen a little later than if we use a tropical measurement.

   Most astrological software, with the supposed capability of working
in the sidereal zodiac, mistakenly calculate using the tropical year.
If one uses the sidereal zodiac, then one has to use the sidereal
year. The time of a sidereal progression must be different from the
time of a tropical progression. Failure to make this distinction is
inconsistent and gives wrong results.

   When comparing positions from different dates, like in transits or
in synastry (routine "C"), most people would simply take them from
the ephemeris and then compare, without making any correction for
precession. That is the generally accepted practice, so you would not
be making anything wrong. It is really a minority who use precession.

   In the case of a radix set in the year 1095, for example, the
tropical positions of 1999 will be ahead 12.6 degrees, so that you
would have to subtract this quantity in order to refer them to the
tropical zodiac of 1095 instead of that of 1999. This is what it is
about: since the year 1095 is the radical, then all other positions
should be measured with respect to the fixed zodiac of the time of the
radix.

   Riyal does this for you if you have not disabled the sidereal
functionality in the "riyal.cfg" file. But the situation can get very
confusing when you are checking transits of more than 1 radix, because
the transits of one radix cannot be compared with the transits of the
other. This is where the use of positions in the sidereal zodiac comes
in handy, and it is the reason why I show them by default in the main
Riyal display. In other words, each radix establishes its own fixed
zodiac, so that positions referenced to different radices cannot be
compared. In this case, all one needs to do is reference all radices
and transiting positions to a sidereal zodiac, and then the problem
disappears.

   The fiducial zero point of the sidereal zodiac used by the program
is the Fagan/Bradley "Synetic Vernal Point".



VII. THE PLANETARY WEIGHTING ROUTINE

   Here is an explanation of how the weighting and quantification
(routine "N") is done. The quantification numbers are based on this
author's experience and are of course a little arbitrary.

   First the program considers the main essential dignities, excluding
the centaurs: if in exaltation add 100; if in its domicile add 100; if
in mutual reception add 60 to each; if it is "singleton by
disposition" add 100; if it is the final dispositor add 100 (it
actually adds 10 for each extra planet that is disposed). It passes
this routine twice: one with the traditional rulerships and another
with the new rulerships of Uranus, Neptune, and Pluto, so that if a
planet rules 2 signs in the modern rulership scheme, the values above
are doubled.

   Then the program considers accidental dignities: if stationary add
100; add the percentage of the geocentric distance (0=farthest, 100=
closest); add the declination doubled (e.g.18 degrees=36); if in an
angle add 60; if in the 1st add 60; if in the 10th add 60; if ruler of
the Ascendant add 90; if less than 15 degrees from the Ascendant add
90; if less than 5 degrees from the ascendant add 60; if in the
ascending sign add 50; if less than 5 degrees from the Descendant add
90; if less than 24 degrees from the MC add 90; if less than 5 degrees
from the MC add 60; if in the MC sign add 50; if less than 5 degrees
from the IC add 90.

   Then the program considers aspects with the luminaries: if it rules
the Sun add 50; if in hard (harmonic 4) aspect to the Sun add 200
(orb=6); if the above is less than 2.5 orb add 100 -->add another 100
to the Sun; if in trine to the Sun add 200 (orb=6); if in sextile to
the Sun add 200 (orb=2); if in cazimi add 100; if in any aspect with
the Sun of less than 1 degree add 100 -->add another 100 to the Sun;
if in parallel to the Sun (orb=1) add 90; if it rules the Moon add 50; 
if in hard aspect to the Moon add 200 (orb=3); if the above is less
than 1.5 orb add 100 -->add another 100 to the Moon; if in trine to
the Moon add 200 (orb=3); if in sextile to the Moon add 200 (orb=2);
if in any aspect with the Moon of less than 1 degree add 100 --> add
another 100 to the Moon; if in parallel to the Moon (orb=1) add 90.

   Then follow the aspects with the Lunar Nodes and Part of Fortune:
if conjunct the Part of Fortune (orb=2) add 100; if in hard aspect
(harmonic 4, orb=2) with the Nodes add 100.

   After the accidental dignities come additional Marc Edmund Jones
focal determinators (centaurs excluded): if singleton by hemisphere
add 200; add 100 to each planet in the "wing" of the pattern; add 100
to any leading or receiving planet; add 100 to the leading if
locomotive or bowl; add 200 if it is handle of a bucket; add 90 if of
oriental appearance.



VIII. THE HOUSES IN POLAR LATITUDES

   Riyal will calculate houses for polar latitudes with mathematical
rigour in any of the available systems except (1) Koch at all times
and (2) Placidus when the Midheaven is below the horizon. In these
cases the user is warned and the program changes to Alchabitius. In
the case of the so-called "Topocentric" system, its arbitrary and
artificial "solution" for the polar regions is used.

   It is said repeatedly that house systems cannot be used in polar
latitudes. This is not true. The problem is not with the house
systems but with the conventional methods or algorithms used to
calculate them.

   All house systems work in polar latitudes; the problem is that
"sometimes they don't". This ambiguity in the mechanics or geometry
of polar houses is the cause of great and unnecessary confusion, and
puts in evidence the poor treatment it has received in the
astrological literature.

   Above 66,33 degrees --the Artic and Antartic polar circles-- the
division of houses is taken to extremes, and houses are gradually
deformed to the point where one begins to doubt the whole concept of
houses.

   In these latitudes, the horizon can coincide with the ecliptic.
When this happens the Ascendant is undefined, and all systems except
the "Meridian" (Zariel) and that of J.B. Morin are useless. Right
after this, the Ascendant "changes phase" and the Midheaven is below
the horizon.

   When the Midheaven is in this situation, Riyal warns you with the
message << Polar Ambiguity! >>. Press "Enter" for the calculation to
end normally. Strictly the houses are inverted 180 degrees, but the
program leaves them "normal" to avoid confusion. Please be aware that
when the Midheaven is below the horizon the Ascendant must always be
inverted. The optional inversion of all the houses is a separate
operation.

   Additionally, complete sectors of the ecliptic can be circumpolar.
This is not a mathematical problem but a question of definition,
since the fact that a diurnal circle never intercepts the horizon
doesn't stop us from trisecting it the way the Placidus system
requires. The semiarcs will be exactly 180 degrees. Riyal supplements
the definition of the Placidus house system by using circumpolar
cusps, and indicates with "*" when it is proceeding this way.

   (It is worth mentioning, in passing, that the system "of Placidus"
was not invented by Placidus. Giovanni Antonii Magini (1555-1617),
professor of mathematics at the University of Bologna, in "Tabulae
Primi Mobilis, quas Directionem Vulgo Dicunt" (1602), builds
astrological charts with this method and performs "placidian"
directions, when Placidus had not even been born! Magini's book was
examined by the mathematician M. Delhambre in "Histoire de
L'Astronomie au Moyen Age" [Paris, 1819], who calls him "the clearest
and most intelligible of all astrologers".)

   With the supplementary definition mentioned, it is possible to
calculate the cusps of Magini-Placidus without difficulty for most of
the sidereal times at a given latitude, but during a certain period
of the day it will not be possible to use the Magini-Placidus system.
This "blank space" corresponds to the time when the Midheaven is
below the horizon, and increases with the latitude from 1.6 hours at
67 degrees until it reaches 12 hours at the pole.



IX. CRITERIA USED FOR SELECTING RIYAL'S BODIES.

   The criteria used to select which bodies to include in the program
varies according to the group to which the body belongs:

CENTAURS: all the known centaurs are included, and are displayed in
routine "Y" ("Full display"). The main display (routines "A" and "B")
shows only those that have orbits accurate enough for research, i.e.,
that their positions throughout the 20th Century will change only
little --hopefully a few arcminutes only.

The classification is done using E. Bowell's Astorb database
"Greatest Peak Ephemeris Uncertainty after 10 years": if it is less
than or equal to 3 arcminutes, it is included in the main display; if
it is less than or equal to 10 arcseconds, it is included in the
"long.fle" ephemeris file (600 AD to 2020).

DAMOCLOIDS: all the known damocloids are included. Generally all
the damocloids have more accurate orbits than centaurs, because
the orbital arc observed in a short time-span is larger, due to
their coming much closer to the Earth and the resulting faster
orbital velocity.

TRANSNEPTUNIANS: all transneptunians (cubewanos, scattered disk
objects, plutinos) brighter than or equal to absolute magnitude 5.0
(probable diameter near 460-470 Km) are included; the only exception
is QB1, which is smaller (probably around 170Km) but is included
because of its historical interest (it was the first to be found).

Additionally, all the "long range" scattered disk objects that go
beyond 100 AU and which have been observed at 2 or more oppositions
are included. At present, the sdo's that do not reach 100 AU are
excluded even if their orbits are accurate --with the notable
exception of 1995TL8, which is included because of its relative
brightness and "antiquity" with respect to the others. I may change
my mind on this in the near future and include all of them observed
at 2 or more oppositions. If the observations cover 2 oppositions but
the orbit is still very inaccurate, it is excluded.

Among the plutinos, in addition to the brightest ones, those with
the closest perihelion distances approaching Uranus are included.

Transitional objects, such as 1999TD10, 2000EE173, 1999XS35,
2001OG108, Hidalgo, QJ46, and Don Quixote, are always included. These
are usually either large eccentricity transneptunian objects that
penetrate inside Neptune's orbit and approach the world of Uranus
and Saturn, or Earth-approaching cometary asteroids with long orbital
periods (like XS35). If the object only penetrates Neptune slightly
but does not approach Uranus, it is excluded.

MAIN BELT ASTEROIDS: The first 10 main-belt asteroids to be discovered
are included. Other than this, the criteria is more subjective: 1181
Lilith is included because of its interest in research regarding the
lunar apogee or Black Moon and the possible Lilithian overtones of the
feminine centaurs.

APOLLOS: Heracles is included because it is of special interest in
centaur-related mythological themes. 1999XS35 and 2001OG108, oddly
classified as Apollos, reach beyond Uranus at aphelion and must be
included.

AMORS: Don Quixote is a transitional asteroid and is included because
of its large orbital range outside the Earth's orbit, like a "smaller"
version of XS35 and OG108. Other objects similar to Don Quixote will
be excluded until they have received a name.

(suggestions about how to improve these criteria, the above
explanation, or to include other specific bodies, are welcome)



X. HOW TO UPDATE

   The safest thing is to download "Riyalpack.exe" and overwrite
everything. The only personalized file in Riyal is "riyal.cgf", which
contains a few personal preferences, time zone, geographic location,
etc.. This file can be easily re-edited with Notepad, or you can have
a copy of it stored somewhere so that you can substitute the Riyal's
default each time you overwrite your personal file with the one that
comes in Riyalpack.exe

   There are other times when the only change to the program is in the
ephemeris files, an "orbital update", without adding anything new or
changing any code. In those cases, one needs to download only the
individual ephemeris files, depending on the object that was updated.
These files consist of the following sequences:

   a - "damocles.fle" (J2000 orbital elements 1700-2020 every 80 days):
don quixote, heracles, damocles, md10, wu24, xs35, og108, qj46.

   b - "tnpsdo.fle" (J2000 XYZ coordinates 1700-2020 every 200 days):
rz215, cf119, cy118, cz118, pf30, pj30, om67, gq21, de9, rd215,
ee173, eb173, wh24, sm55, tc36, cr105, oo67, 1993sb, 1994tb, 96tp66,
tl8, qf298, ka77, ph30, qb1, to66.

   c - "long.fle" (J2000 XYZ coordinates every 200 days from 600AD
to 2020 AD): pluto, chiron, pholus, nessus, asbolus, 94ta, hylonome,
chariklo, tf35, bu48, qm107, qc243, pt13, ug5, varuna, kx76, td10,
tl66.

   d - "asteroid.fle" (J2000 XYZ coordinates 1700-2020 every 80
days): ceres, pallas, juno, vesta, astraea, hebe, iris, flora, metis,
hygeia, lilit, hidalgo, le31, rg33, ld31, qj1, dg8, ho121, vu2,
ab229, he46, qf6, 96pw.

   a - "centaurs.fle" (J2000 XYZ coordinates 1700-2020 every 200
days): pluto, chiron, pholus, nessus, asbolus, 94ta, hylonome,
chariklo, tf35, bu48, qm107, qc243, pt13, ug5, varuna, kx76, td10,
tl66, sg35, ox3, xx143, gm137, fz53, qb243, ec98, hd12, jv127, sn55,
co104, rx33, ar20, as20, bl41, kf77, sq73, sn331.

   It is not necessary to download the whole package when updating.
Each file can be downloaded individually depending on the date and
time stamp that appear in the server's "...centaurs/riyal" directory.
All the necessary links are in the download page:

   http://www.expreso.co.cr/centaurs/riyal.html-ssi



XI- LICENSE AND SUPPORT

   Since Riyal is a gift, I am not responsible for all the... blah,
blah...

   This program is in continual development; there are frequent
updates, so it is suggested that you check my "What's New" page often:

       http://www.expreso.co.cr/centaurs/whatsnew.html
       
to see the latest additions and bug corrections. Riyal's versions are
labelled like "24/3/2001", which gives the date (day/month/year) of
the last upload.

   As with all freeware, you don't have to pay anything and can use
Riyal freely, as long as you respect its authorship and do not steal
this program for commercial purposes. The only thing I ask is that you
give me the credit for the work I have done and I am sharing with you,
so please do not make money with it!

   I hope this program will be useful to all those doing research on
the centaurs. Enjoy!

Juan Antonio Revilla
apartado 1562
San José - 1000
Costa Rica.
