Urania/48

The Astronomical Companion

for the

HP-48SX/GX

Pocket Calculator

You may jump directly to the following sections:
• Preface
• Installation
• Introduction
• Urania/48
• Moon/48
• AstroTools/48
• Saturn/48
• RNGC/48
• Auxiliary programs
• Variables
• Appendix: Literature, Acknowledgements
• Back to Urania/48 Home Page

Preface

The size and computing power of the HP48 allow to make it the ideal tool for calculations somewhere far off civilization, desktop PCs and power lines, under a dark night sky. Urania/48 makes it unnecessary for the observer to look up positions in printed planetary ephemerides or look into tables of data transformation, all this and much more is calculated to good accuracy using modern theories of planetary motion.
On the other hand, Urania/48 cannot replace star maps and atlases or good PC programs, which can of course keep far more data and can find them faster.
Basic knowledge of astronomical terminology will be required to use Urania/48.

A sentence about this online manual: It is a HTML version of parts of the printed manual included with the registered version. I am sure I have missed some special characters while changing from DTP to HTML, sorry for that. The manual is more detailed in many aspects. It is assumed that the user is familiar with the HP48 and its usage, as well as with astronomical terminology.

Installation

The libraries have ID numbers in the range 1600...1610. To avoid conflicts between software, please make sure you have no other libraries with the same IDs installed. Installing Urania/48 requires at least a 128kB RAM card. The libraries are installed as usual, although their sizes may demand some preparations:

1. Make sure you have at least one port memory bank available on your RAM card(s).
2. Make sure you have enough free system memory. Make a backup and reset the calculator, if necessary.
3. Upload the desired library onto your HP48.
4. Recall the library onto the stack and purge the original variable.
5. Select a port number of a free port and STO the library there. The core libraries are U48AASHA.LIB and URANIA48.LIB. You should also upload U48AUX.LIB if you want to use the data managing programs for sites, comets and asteroids. Optionally, load U48MOON.LIB and store it in a port of your choice. If you have the HP-48GX and a large (512kB or more) RAM card in slot 2, you can also upload up to three more libraries which allow you to access the data of the Revised New General Catalogue: U48RNGC1.LIB, U48RNGC2.LIB and U48RNGC3.LIB. The first and smallest contains the most important data: Position, magnitude, type, constellation. The other two contain the original encoded Dreyer or RNGC descriptions, respectively. Only U48RNGC1.LIB is included with the evaluation version.
6. Switch the calculator off, then back on. A warmstart brings the libraries into action. Note that AARes/48 and the RNGC/48 libraries don't autoattach to the home directory: They are only used by Urania/48, so there is no need to add additional labels to the library menu. If you like, do it manually: Type, e.g., 1602 ATTACH to include a RNGC label into the library menu.
7. Select a directory of your choice, e.g. ASTRO, and enter it. Now you may upload the data files COMET.DAT and ASTEROID.DAT, as well as the auxiliary programs SITE, its list of sites, SITE.DAT, and DATA. These allow to manage your sites of observation and add or delete data of comets and asteroids right on the machine, instead of having to edit the cometary and asteroid data on a PC and uploading them. (You might of course prefer the PC method.) SITE and SITE.DAT are not really necessary in low memory conditions, but DATA is very helpful for the often changing comets. You might edit the program source a bit to make the programs smaller, or delete some entries from the data lists. Run SITE to select or enter your site of observation. Your directory should now contain four variables: Long, Lat, Alt, Zone. See the table below for their contents. Should you enter a new site in SITE, enter the time zone without daylight saving time, this will be asked while selecting the site. If you prefer not to use SITE, enter these four variables manually, or Urania/48 will refuse to work. To allow Jupiter's Great Red Spot to appear in the program, it needs the jovigraphic longitude in the variable GRS.DAT. In 1996, a good value is 51. There are more variables, called Press, Temp, (Delta)T.USR, (epsilon).USR, DSTAR.DAT, VSTAR.DAT and DSO.DAT. A detailed description of these will be given later.

Introduction

Valid range of dates: -4712...+9999
All programs needing time input to work were programmed so that if there are too few arguments on the stack, i.e. date and time missing, those data are read from the internal clock. This saves the user from unnecessary keystrokes. Input and output format for calendar dates depends on the current state of system flag -42: MM.DDYYYY if flag is clear, DD.MMYYYY if set. This is the same format as used by the system. Time inputs are always in 24 hours format. Display of output then depends on system flag -41 (12/24 hours).
Sometimes the display is too small to show all data at once. Then you may use the cursor keys to scroll the display. PICT is not used for display, so user graphics are saved. However, if you want to keep the display, you can STO its contens into PICT.

For each command a stack diagram will be given. Input values are needed on the stack or in the command line before a command is started. "Date" means a calendar date in the current HP48 date format, i.e. DD.MMYYYY if flag -42 is set, or MM.DDYYYY if flag -42 is cleared. "Time" is input in 24 hours format, HH.MMSSddd. Degrees are used either with minutes, seconds and decimal seconds (DD.MMSSddd) or in decimal degrees (DD.dddd).
Equatorial and Hour Angle coordinates use the hour-minute-seconds (HH.MMSS) resp. degree-minute-second (DD.MMSS) format, the other coordinate systems use decimal degrees DD.dddd.

Library 1609 - Urania/48

 Input for all finder programs 
 2: Date
 1: Time (of Zone)             ->  2: _HH.MMSS
or                                 1: _DD.MMSS
 1: --- ( -> current time )

(alpha)DAT,  (delta)DAT:  Equatorial coordinates for equinox of date

(alpha)2000, (delta)2000: Equatorial coordinates for equinox J2000.0

MAG:                      Apparent visual magnitude

Rise:  Time of Rise        AZ(NESW):  Azimuth
Set:   Time  of  Set       ALTITUDE:  Apparent  Altitude  (Incl.refraction)
Trans: Time of Transit     HOUR ANG.: Hour Angle

Menu PLANET

For all programs in the menu, except HACLK
 2: Date
 1: Time (of Zone)             ->  2: _HH.MMSS
or                                 1: _DD.MMSS
 1: --- ( -> current time )

Page 1:  MERC VENU MARS  JUPIT SATUR HACLK
Page 2:  URAN NEPT PLUTO ASTER COME  HACLK
Page 3:  SUN  MOON MPHY  JUMO  SAMO  HACLK

L, B, R: Heliocentric  ecliptical Longitude,  Latitude  and
         Distance (AU) from the Sun.
lambda, beta, Delta: Geocentric ecliptical Longitude, 
                     Latitude and Distance
                     (AU and Light Minutes) from Earth.
EL: Elongation from the Sun.
Data valid for equinox of date, except PLUTO, here position is
computed for equinox J2000.0.

MAG:    Apparent visual magnitude
Ø:      Apparent polar diameter
ILL:    Illuminated fraction of disk, percent

PLUTO    There is still no complete theory of Pluto's motion.
    Therefore,  this calculation is only valid for  the  years
    1885..2099!  For  other times, you  will  need  osculating
    orbital elements and treat Pluto like an asteroid.

ASTER Selection  of an asteroid from  the  external  list
      ASTEROID.DAT
T:      Orbital period
EL:     Elongation from the Sun.
PH.ANG: Phase Angle Sun-Asteroid-Earth.
MAG:    Apparent visual magnitude.

COME  Selection of a comet from the external list COMET.DAT
     Type of orbit, orbital period T, if elliptical.
EL: Elongation from the Sun.
    MAG: Apparent visual magnitude.
    Should a comet move on an extremely hyperbolic track
    (maybe with e>1.3), the algorithm of the calculation
    might fail. In this case, the program will error, and no
    calculation is possible for such rare comets.
SUN 
 Physical Ephemeris (after Carrigton):
 CENTR: Heliographic Longitude L and Latitude B of the
        center of the Sun's disk.
 PA(AXIS): Position Angle of the northern end point of
           the rotational axis, measured from the northernmost
           point eastward along the Sun's limb.
 ROTATION NR.: Rotation number after Carrington.
 BEGIN: Begin of this rotation.

MOON 
    Geocentric ecliptical and Geocentric 
    and topocentric equatorial coordinates. 
    Geocentric distance and angular diameter.
    Illuminated Fraction with small icon
    Elongation from the Sun.
    Equatorial horizontal parallax.
    
MPHY  
    Physical   Ephemeris:  
    Libration, PA of Axis,
    Elongation, Phase Angle
    Illuminated Fraction, PA of the bright limb
    subsolar point, Colongitude of the Sun,
    Longitude of Morning and Evening Terminator.

JUMO     CM I, CM II: Longitude of central medidians I and II
    of the visible disk, thus regarding the small light defect
    inflicted by the phase angle of Jupiter to the Sun. The  4
    great  Moons  can  be identified with the  given  symbols.
    Numbers listed near the names are the apparent jovicentric
    (X-)  distances  of  the Moons from  Jupiter's  center  in
    Jupiter's radii. In the graphic below the moons are  drawn
    as  seen in a astronomical (inverting) telescope.  In  the
    enlarged  graphic in the upper right corner  you  can  see
    Jupiter's  disk, possibly with a transiting moon  or  with
    the  Great Red Spot (GRS), if visible. To enable this, you
    have  to  put  a real number representing the  jovigraphic
    longitude of the GRS into the global variable GRS.DAT.
    With  the + / - keys, you can advance/go back in  time  by
    one minute at a time, by pressing left-shift first you can 
    jump in 10 minute steps.

SAMO Access to Saturn/48 / SAMOON.  See there for description.

HACLK Direct Access to the Hour Angle Clock


Menu STAR:    BRIGH BINAR VAR            HACLK

BRIGH

328 bright stars are available. Selection is done in 2 steps: First, a name or part of it is entered. All found stars are listed, of which you select the right one.
The following criteria were considered when the stars were selected for the list:

1. All stars to mag 3.0
2. At least one star of every constellation
3. Stars with proper names, as listed in Lit.[4], and some more.
4. Some fainter stars that are important within constellations.

By this, the catalogue of stars fainter than mag 3.0 gets very sparse, but still every constellation can be found in the sky. Star names are saved in the following format: "ß Cst Name1 Name2 ..", where ß is the Bayer Designation (, , , ..), Cst is the usual 3 letter constellation designation and Name1 etc. are the proper names,.e.g.: "a CrB Alphecca Gemma ". The program lets you input a name ur part of it. Here, also different spelling is considered, so e.g. Beteigeuze and Betelgeuse are both valid. Two part names are written in one part, e.g. DenebKaitos. Upper-/lowercase input is both valid. To find all stars of a constellation, just enter the 3 letter constellation code. A menu with the greek letters may help. In the final selection, choose from all found stars or retry.

Following data are listed:

MAG(V):  Apparent magnitude (in the V-Band of the UBV system)
M(ABS):    Absolute  Magnitude: This is the Magnitude  of  the
     star  seen  from  a  distance of 10  Parsec  (32,6  Light
     Years).It is a measure of true luminosity.
B-V: Spectroscopic  color index: this number gets higher  with
     increased "redness" of the star
SP:  Spectral type and luminosity class
DIST:Distance in Parsec and Light Years
COORD.:  The  coordinates  are shown for  standard  epoch  and
     equinox J2000.0 and for epoch and equinox of date.  Here,
     also proper motion as well as Nutation and Aberration are
     considered.

BINAR, VAR
Selection of binary resp. variable stars from lists. There  is
a  default  database  built  into the  library. The manual for
the registered version describes how to use a custom database.

BINAR
Separation and Position Angle are of J2000.0.
SEP: Separation of the components
PA:  Position  angle of the fainter component,  measured  from
     North towards the East.
MAG: Apparent magnitudes of the components
SP:  Spectral types of the components

VAR
TYPE: One of 35 Variable types
PER: Period measured in days
MAG: Maximum and minimum magnitudes of the star
SP:  Spectral class


Menu DSO MESSI OTHER              HACLK

If  you  have  RNGC1/48 installed, DSO will call DSO.NGC.  See
there for more information.

MESSI       Finder program for Messier objects
 3: Date
 2: Time(of Zone)
 1: Messier number
or:                               ->  2: _HH.MMSS
 2: ---                               1: _DD.MMSS
 1: Messier number (-> current time)

OTHER       Finder program for other DSOs
 2: Date
 1: Time(of Zone)                 ->  2: _HH.MMSS
or:                                   1: _DD.MMSS
 1: ---            (-> current time)

The database for more DSOs and how to expand it is 
described in the manual of the registered version.

Data:
Name, Constellation.
Comments,  e.g.  NGC  numbers for Messier  objects  or  proper
      names.
OBJECT TYPE
MAG: Apparent magnitude.
DIM: Dimension: Arc seconds for Planetary Nebulae, arc minutes
     for others.
DIST: Distance in Parsec and Light Years.


MAP  draws  either a Planisphere or a horizontal cylindric map
Call with
 2: Date
 1: Time(of Zone)
or
 1: --- ( -> current time)

On this map you find the stars which are currently above the horizon, along with the planets (Mercury to Saturn) and the Sun. The Moon is drawn with a phase icon. In addition, there are the cardinal directions, site of observer and time. On the horizontal map you will also find grid lines for 0, 30, 60 and 90 degrees of altitude and every 45ø in azimuth.

Selection criteria for the star catalogue (see STAR / BRIGH) sometimes lead to relatively bright unnamed stars being not drawn, while faint main stars of small constellations appear unnaturally bright.

Above 60ø altitude, constellations in the horizontal map appear strongly distorted. Therefore, for all-sky observation, the planispere should be preferred.

Maps for dates before 1950 and after 2050 will take more time, because Precession will be accounted for.

TCLK Running clock display of current Zone Time and Mean Local
     Sidereal Time.

     Stack is not changed.

HCLK Running clock display of Date, Time, Mean Local Sidereal
     Time, and current Hour Angle, Declination, Azimuth and
     Altitude of the object at the given coordinates. Includes
     refraction.
     Stack is not changed. (Or a 0 is added to level 1 if
     called only with R.A. of the object.)
     Call:
      2: _HH.MMSS
      1: _DD.MMSS
     or                          ->  2: _HH.MMSS
      1: _HH.MMSS (->=0)             1: _DD.MMSS

ECLMAP   Ecliptical map of the planets, of 3 types:
1.) Ecliptic 360..0ø Longitude, 10ø Latitude, Sun, Moon (with
    phase) and Planets (Mercury to Neptune).
2.) Elongation from the Sun:
    This map is mainly a quick overview where the planets can  be
    found  in relation to the Sun. Visibility conditions  can  be
    thus found quickly. Marks for EVENING resp. MORNING indicate,
    when the objects drawn below are best visible.
 a) Centered on the Sun.
 b) Centered on the Gegenschein (the point opposite the Sun).
The  horizontal  lines represent the ecliptic  and  ecliptical
latitudes +5 and -5.
Call:
 2: Date
 1: Time(of Zone)
or
 1: --- (-> current time)

SEASONS   Calculates  the beginning of  the  seasons  for  any
year.
An error in the computed position of the Earth on its orbit of
only  2.5  arc  seconds will result here in an  error  of  one
minute   (of  time).  The  results  of  this  program  should,
therefore,  be only few minutes off. Several tests  showed  an
error of usually less than two minutes.
Call:
 1: Year
or
 1: --- (-> current year)

ECLIPSES  Calculates the most important data for  eclipses  of
Sun and Moon.
At  the  start  of the program, you may select  the  types  of
eclipse  to find. Now, dates of possible eclipses are checked.
If  there is no eclipse, mean date and time (DT) of the  event
are  showed  briefly, and calculation resumes. If  an  eclipse
occurs, a screen full with data will be shown. With the + /  -
keys,  you  can  advance into the future or go back  in  time,
respectively.  If  you  press (LS)-(+)/(LS)-(-), you  advance  by  10
intervals at a time (i.e. 10 or 5 months, resp.).

Lunar Eclipses
Date,  Time  (DT) of the eclipse, Type, event in ascending  or
descending node.
Position  of  the Moon in mid-eclipse (north/south  of  shadow
center):  gamma  is  the  smallest  distance  of   the  Moon's
center  to  the  axis of Earth's shadow in  units  of  Earth's
equator  radius.  Radii of umbra/penumbra in  Earth's  equator
radii  in  Moon's distance. Maximal magnitude  of  eclipse  in
Umbra  or  Penumbra,  resp. Times (of  Zone)  of  the  various
phases.

Solar Eclipses
Date,  Time  (DT) of the eclipse, Type, event in ascending  or
descending node. Area of visibility on the Earth: Moon's umbra
sweeps across the Earth's surface in a narrow track of only  a
few  km width. Gamma here is the smallest distance of the axis  
of the Moon's shadow from the center of the Earth in  units of
Earth's  equator radii. In connection with the time of maximal
eclipse,  the  area  of  visibility  can  be  deduced.   E.g.:
24.10.1995, 4:34 DT, g=0.352: Visible in subtropical  northern
latitudes of the Middle and Far East. (In Europe, the  Sun  is
still  below the horizon.) More exact calculations are  rather
lengthy,  so  they  are  omitted  here  and  left  to  greater
computers.  Radii  of Umbra/Penumbra on the fundamental  plane
(the  plane  through the center of the Earth perpendicular  to
the shadow's axis). Time (of Zone) of maximum eclipse.

Call:
  1: Start date of search  
 or  
  1:  ---  (->  current date)

APSIDES    Calculates  the  great  planets'  nearest  passages
through Perihelion and Aphelion.
The returned dates "surround" the calling date.
The  errors  are:  Mercury...Mars: hours;  Jupiter:  2  weeks;
Saturn: 1 month; Uranus, Neptune: up to several months.  These
errors  are  due to the simple algorithm used here which  uses
undisturbed orbits.
Call:
 1: Date     or  1: --- (-> current Date)

EQTM  Calculates  the Equation of Time, the  difference  in
right  ascension between True (apparent) and Mean (fictitious)
Sun.  If  the  value  is positive, the True  Sun  crosses  the
meridian before the Mean Sun - a Sundial is "early".
Call:
 2: Date
 1: Time(of Zone)         ->  1: :Eq.of Time (HMS): HH.MMSS
or
 1: --- (-> current time)

ANA      Draws the Analemma of the Equation of Time for a year
and the position of the Sun on it.
If you draw the Equation of Time against the Sun's declination
for  a  whole  year, the result is the famous  "figure-8".  It
represents  the  position of the true Sun at mean  noon.  This
graph  is  scaled: The vertical line represents the  meridian,
the  horizontal line declinations of 20ø, 10ø, 0ø, -10ø, -20ø.
The length of the lines corresponds to 20 Minutes. The greater
dots on the track mark the first days of the months, the thick
dot represents the Sun for the required date.
Below the Analemma (press Q) you find the date for the plotted
position of the Sun.
You should watch the change of the shape during the millennia!
Call:
 1: Date    or       1: --- (-> current date)

(UpDnX)     Calculates times of rise, transit and  set  of  an
object for the required date, even for objects in motion!
Call:
3: RA, HH.MMSS   or 3: { RA1 RA2 RA3 }
2: Dec, DD.MMSS     2: { Dec1 Dec2 Dec3 }
1: Date             1: Date
or:
3: ----          or 3: -----
2: RA, HH.MMSS      2: { RA1 RA2 RA3 }     (->  current Date)
1: Dec, DD.MMSS     1: { Dec1 Dec2 Dec3 }

With 3 (or 2) real numbers on the stack, the object is assumed
not  to be in motion (e.g. star), and the times are calculated
more  quickly. With 2 lists of 3 real numbers each and a  date
(or  just 2 lists), also times for moving objects (such as the
Moon  or  rapid  comets and asteroids) can be calculated  more
accurately. Symbols here are: 1, 1 Right ascension (HH.MMSSS),
declination (DD.MMSS) of the previous day, 2, 2 RA,  decl.  of
the  day in question and 3, 3 RA, decl. of the following  day,
each time for 0h DT. These values can be calculated with other
programs or taken from an almanac.

Result:
 3: :Rise:      HH.MM    "circum-"   "not"       "POLE!"
 2: :Set:       HH.MM    "polar"     "visible"   "Not"
 1: :Transit:   HH.MM    HH.MM       HH.MM       "defined"

TLOC    Returns Mean Sidereal Time for any date.
Call: 2: Date
      1: Time(of Zone)           -> 1: :Sidereal Time: HH.MMSS
  or  1: --  -> current time

PARANG    Calculates the Parallactic Angle of an object.  This
is the angle between the vertical and the North-South-Axis. It
is  the  amount of apparent rotation of an object (e.g.  Moon,
planet  or constellation) far from the meridian. (For example,
the  setting  crescent  of the Moon  in  the  evening  sky  of
temperate northern latitudes is noticeably tilted.)
Call: 2: Hour Angle, HH.MMSS
       1:  ,  DD.MMSS                     -> 1: q,  Par.Angle,
DD.ddd

ECLHOR   Calculates the intersections of the ecliptic with the
horizon and the inclination of the ecliptic to the horizon.
Call:    2: Date
         1: Time(of Zone)
  or     1: --  -> current time
Result:  3: :: DDD.ddddd   This ecl. Longitude is rising
         2: :: DDD.ddddd   This ecl. Longitude is setting
         1: :: DDD.ddddd   Angle between ecliptic and southern
horizon

REFR+         Adjusts  a geometric (calculated)  position  for
refraction. In this altitude we can see the object.
1: h,geom_DD.ddd            ->    1: ho,apparent_DD.ddd

REFR-         Adjusts  an  apparent  (observed)  position  for
refraction. Returns thus the Geometric Altitude.
1: ho,apparent_DD.ddd       ->    1: h,geom_DD.ddd

Those calculations assume by default air temperature of 10øC and pressure of 1010mbar. You might store real numbers as Celsius temperature in the global variable 'Temp' and pressure in mbar in 'Press' to account for different atmospheric conditions.
Note that these commands are not true reverse operations, the formulae used are just simplified models of the effects of the atmosphere. Three decimal places are given, but please bear in mind that below ca. 5ø far lower precision should be assumed.

Coordinate Transformations

For equatorial coordinates and hour angle, the hour/minute/second resp. degree/minute/second format is used, for all other systems decimal degrees

adlb    Equatorial ->  Ecliptical
2: _HH.MMSS       ->     2: _DD.dddd
1: _DD.MMSS              1: _DD.dddd

lbad    Ecliptical -> Equatorial
2: _DD.dddd       ->     2: _HH.MMSS
1: _DD.dddd              1: _DD.MMSS

adlb, lbad: These programs by default use the obliquity of the
ecliptic  for  the  epoch J2000.0. If  you  want  to  use  the
ecliptic  for a different epoch, just put a year number  (also
with  decimals) into the global variable '(epsilon).USR'. The 
programs calculate the mean obliquity for this date and store 
the value again into (epsilon).USR, tagged with the year.   
Further transformations then don't have to recalculate it.

HdAa Hour Angle/Declination ->  Azimuth / Altitude
2: _HH.MMSS       ->     2: Az(NESW)_DD.dddd
1: _DD.MMSS              1: Altitude_DD.dddd

AaHd Azimuth / Altitude -> Hour Angle/Declination
2: Az(NESW)_DD.dddd   ->  2: _HH.MMSS
1: Altitude_DD.dddd       1: _DD.MMSS

adLB Equatorial -> Galactical II
2: _HH.MMSS       ->     2: l_DD.dddd
1: _DD.MMSS              1: b_DD.dddd

LBad Galactical II -> Equatorial
2: l_DD.dddd       ->     2: _HH.MMSS
1: b_DD.dddd              1: _DD.MMSS

These tranformations are valid for equatorial coordinates
of System B1950.0! For coordinates of other equinoxes at least
precession  must be accounted for. For this you  may  use  the
programs PreQ, Pre4 or Pre5 from AstroTools/48.

Date and Time Utilities

The Julian Calendar is used for dates until October 4th, 1582. The following day is October 15th, 1582 in the Gregorian Calendar, introduced at that date. Therefore, 10 days should be invalid. In Urania/48, those 10 days (October 5...14, 1582) are simply interpreted as of the Julian Calendar, i.e. 5.10.1582 =15.10.1582. In some countries, the Julian Calendar was in use far longer, e.g. in the UK and USA until 1752.

ZT->JD        Time of Zone  Julian Day
2: Date
1: Time(of Zone)         ->   1: JD_DDDDDDD.ddddd
or
1: --- (-> curr. Time)

JD->ZT        Julian Day  Time of Zone
1: JD_DDDDDDD.ddddd           ->   2: Date
                                   1: Time(of Zone)
UT->JD        Universal Time(UT)  Julian Day
2: Date
1: Time(UT)                ->   1: JD_DDDDDDD.ddddd

JD->UT        Julian Day  Universal Time(UT)
1: JD_DDDDDDD.ddddd           ->   2: Date
                                   1: Time(UT)

->Y.FP        Calculates Year with decimals
2: Date
1: Time                       ->   1: YYYY.dddddddd
or
1: ---- (-> curr. Time)
Y.FP->        Reverse to åY.FP
1: YYYY.dddddddd              ->   2: Date
                                   1: Time

->N.Y    Calculates Day Number within the Year
1: Date
or                            ->   1: DDD.YYYY
1: ---- (-> curr. Date)

N.Y->    Reverse to åN.Y
1: DDD.YYYY                   ->   1: Date
where    DDD Day number
    YYYYYear number
The sign is for the year

Date+      Calculates from a date and a  day  count  a  new
date.  This  command works similar to the built-in DATE+,  but
you can also use dates before Oct. 15., 1582.
2: Date
1: Day count                 ->   1: Date

(D)DAY     Calculates the difference between two dates in  days.
This command works similar to the built-in DDAYS, but you  can
also use dates before Oct. 15., 1582.
2: Date1
1: Date2                      ->   1: Day number
Please  note that while you can omit the year with  DATE+  and
DDAYS  to  use  the  current  year,  while the commands here
understand year 0 in this case.

WDAY    Calculates the Day of Week for any date.
1: Date                       ->   1: "DayName"

EASTER   Calculates date of Easter for any year.
1: Year number
or                          ->   1: :Easter: Date
1: --- (-> curr. Year)
Stellar magnitudes and distances

Smag     Calculates  the  combined  magnitude  from  component
magnitudes of e.g. a binary star.
 2: mag1
 1: mag2                      -> 1: mag_comb

dmag     Calculates  difference in  magnitudes  from  a  given
brightness ratio.
 1: Brightness_ratio          -> 1: mag, magnitudes
Example: Star A is 7 times brighter than star B. What  is  the
difference in stellar magnitudes?
    Answer: 2.11

magR    Calculates brightness ratio from two given magnitudes
 2: mag1
 1: mag2                       -> 1: Brightness_ratio
The ratio is here always >1
Example: Polaris, mag=2.12; Vega, mag=0.14
    Result: Vega is 6.19 brighter than Polaris

Mabs     Calculates absolute Magnitude from apparent magnitude
and distance of a star.
        Useful e.g. for working with data from a catalogue.
 2: mag(apparent)
 1: distance(Parsec)         -> 1: Mag(absolute)

LY->PC        Conversion Light Years  Parsec
 1: distance, LY             -> 1: distance, pc

PC->LY        Conversion Parsec  Light Year
 1: distance, pc             -> 1: distance, LY


Other Programs

SPHDIST  Calculates Great Circle Angular Distance between  two
points on a Sphere (e.g. celestial sphere). This program works
for all angular modi (DEG/RAD/GRAD) !
4: l1, deg/rad/grad
3: b1, deg/rad/grad
2:  l2,  deg/rad/grad     ->   1:  Angular  distance, deg/rad/grad
1: b2, deg/rad/grad

GEODIST   Calculates distance between two sites on the surface
of  the  Earth, accounting for the oblateness of  the  Earth's
globe.  The  error is of the magnitude of the  square  of  the
oblateness of the Earth, approx. 0.001124 % ( ! )
Longitudes  are  positive  east of  Greenwich.  Latitudes  are
positive north of the equator.
This  program works for all angular modi, input has to be done
in decimal degrees.
4: l1, DD.dddd
3: b1, DD.dddd
2: l2, DD.dddd                 ->  1: Distance in km
1: b2, DD.dddd


->HMd     Conversion degrees with decimals   degrees,  minutes,
fractions of minutes
1: DD.dddd                ->  1: DD.MMdd

HMd->    Reverse of the above
1: DD.MMdd                    ->  1: DD.dddd

->hms, hms->    Work like the built-in commands  ->HMS, HMS->
These commands are only included here to avoid jumping through
the menus

Library 1608 - Moon/48

POSITN.M Access to Urania/48 / PLANET / MOON
PHYSIC.M Access of Urania/48 / PLANET / MPHY
 2: Date
 1: Time(of Zone)
or
 1: ---  (-> curr. Time)

The following 4 programs are called similarly:
1: Date          or   1: ---- (curr. Date)

PHASES.M Times of main phases, 8 at a time, advance/go back in
time with + / -.
The  mean  error in the present time (1980...2020) amounts  to
3.72 seconds, the maximal is 17.4 seconds.
Usually,  1  event  before and 7 after the  calling  date  are
found.
dMAXIMA.M Times  and  amounts of greatest northern  /  southern
declinations, 8 at a time, advance/go back in time with + / -.
The  mean  error in the present time (1977...2022) amounts  to
approx.  3  minutes  and 10", the maximal is  10  minutes/26".
Usually,  1  event  before and 7 after the  calling  date  are
found.
APSIDES.M Times of passages through Apogee or Perigee, 4  at  a
time,   appropriate   distances   and   horizontal   parallax,
advance/go back in time with + / -. The maximal error for  the
present time (1977...2022) is 31 Minutes/0.124" Parallax (12km
distance) in Perigee, 3 Minutes/0.051" Parallax (6km distance)
in  Apogee.  Usually, 1 event before and 3 after  the  calling
date are found.
NODES.M   Times of passages through the nodes, 8  at  a  time.
Advance/go back in time with + / -.
The  error for the present time (1980...2020) is in most cases
less  than  2  minutes,  also  in  ancient  times  it  is  not
significantly larger. Usually, 1 event before and 7 after  the
calling date are found.

oALTITD.M Calculates  the Altitude of the  Sun  above  a  given
location on the Moon's surface.
 4:  selenogr. Longitude , DD.ddd (0=center, positive towards
      the West)
 3: selenogr. Latitude  , DD.ddd (North = positive)
 2: Date
 1: Time(of Zone)
or                               -> 1: :Alt.of  Sun: DD.ddd
 3: ---- (-> curr. Time)
 2: selenogr. Longitude , DD.ddd
 1: selenogr. Latitude  , DD.ddd

SPEED.M  Calculates the angular speed of the Moon both in ecl.
Longitude and in Elongation to the Sun.
 2: Date
 1: Time(of Zone)              ->  2: :(HMS): DD.MMSS_ø/h
or                                 1: :Elong:  DD.MMSS_ø/h
 1: ---- (-> curr. Time)

Library 1607 - AstroTools/48

Sometimes, a user may need more than the data presented by Urania/48. To avoid rewriting basic code and filling the calculator's memory, AstroTools/48 allows access to most internal commands of Urania/48. A layer of protection common for User-RPL commands avoids undesired results if used with wrong arguments, so usage should be safe. It is mainly intended for owners of Lit[1], who can directly look up what the programs do. Detailed description of all programs is far beyond the scope of this manual. From the remarks listed here you will get some insight into how Urania/48 was programmed and also notes about accuracy.

The library comes in two versions. U48AUX.LIB only contains the most important commands which are also used by SITE and DATA. 48TOOLS.LIB contains all the listed commands.

The following commands are available in both versions of the library

MAPS     Finds map numbers in Sky Atlas 2000.0 and Uranometria 2000.0.
2: a, HH.MMd               2 :SkyAtlas: "MM"
1: d, DD.MM            ->  1 :Uranom: "VV, MMM"
where MM or MMM is the map number, VV is the volume ("I", "II"
or "I&II").

MESSIERdat    Quick access to data of Messier objects
                          2: a, HH.MMd
1: ObjectNr           ->  1: d, DD.MM

  or
                          8: "Messier Nr   Cst"
                          7: "Name"
                          6: :a: HH.MMd
                          5: :d: DD.MM
1: -ObjectNr          ->  4: :mag:  mm.m
                          3: :Type: "ObjType"
                          2: :Dim:  "Dimensions"
                          1: :Dist: D_pc

NGCdat   Quick access to data of NGC objects, if installed
                          2: :a1975:  HH.MMd
1: ObjectNr           ->  1: :d1975:  DD.MM
or
                          8: "NGC Nr"
                          7: :a1975:  HH.MMd
                          6: :d1975:  DD.MM
                          5: :mag:     mm.m
1: -ObjectNr          ->  4: :Type:   "ObjType"
                          3: :Const:  "Cst"
                          2: :Dreyer: "Description"
                          1: :RNGC:   "Description"

CHOOS2    Modified CHOOSE for HP-48GX or replacement for HP-48SX.
Call:
3: "Prompt"           ( e.g. "SELECT:")
2: { Obj1 Obj2 .. Objn }
1: Pos_start
Exit:  After OK        ->  2: Objk
                           1: 1
       After CANCL     ->  1: 0
If Objm is a list, the first element from that list is shown.
SX:  No window is shown and only one line is shown at a  time,
but you can still work with it.
GX: FullScreen-CHOOSE! With negative Pos_start  you may force
the usual CHOOSE-Box.
After  calling, Element Pos_start from the list  on  Pos.2  is
displayed. With (up) or (down) you may select other elements from  the
list,  as indicated by small arrows on the right (GX) or  left
(SX)  side. When you have found the element, press OK
and  continue  the  calling program.  If no selection  seems
appropriate,  CANCL will return just  0.  CHOOS2  thus
works very similar to CHOOSE on the GX models.

SCROLL    Final stage for programs with graphic output to  the
text or graphic screen.
This program allows:
1.)Scrolling with the cursor keys.
   With left-shifted cursor keys you scroll the screen by
   approx. one display width/height.
   With right-shifted cursor keys you jump to the respective
   edge.
2.)Copies current screen into PICT with (STO). This is useful for
   programs with output to the text display
   (User-RPL commands DISP, ->LCD etc.). If you already look at
   PICT, the screen will look slightly disturbed, but nothing
   harmful will happen.
3.)Turn off the HP48 with (OFF) (normal behavior)
4.)Leave this environment with (ON)
5.)If, in your program, you use  local variables 'k', 'step'
   and 'End', you can get similar behavior to JUMO and
   ECLIPSES of Urania/48 and the programs of Moon/48:
   k   : Real, a counter
   step: Real, increment
   End : Flag, Program end flag, (ON) stores TRUE in here
         + / - in-/decrements k by step,
         (LS)+ resp. (LS)- by 10*step
   (Flag here means a System-RPL Flag TRUE or FALSE.
   You may get TRUE with  ½ #03A81h SYSEVAL ¯
               FALSE with ½ #03AC0h SYSEVAL ¯.)
   This function should only be used by experienced
   programmers. 

DRWCIRCLE Draws circles in text display or PICT.
3: { #x  #y }  2 Binary Integers (User Binary), Position  of
               center
2: r           Radius, pixels; if negative, a white circle  is
               plotted
1: 0 -> text display  / 1 -> PICT

GX?     Detects calculator model:
SX:  -> 0
GX:  -> 1

Library 1606 - Saturn/48

Library 1602 - RNGC1/48

 3: Date
 2: Time(of Zone)
 1: NGC number
or:                                    ->  2: _HH.MMSS
 2: ---                                    1: _DD.MMSS
 1: NGC number (-> current time)

Data:
Number, Constellation
OBJECT TYPE
DREYER, RNGC description with installed libraries RNGC2/48 and RNGC3/48.
MAG: Apparent magnitude, if available
(alpha)2000, (delta)2000: Equatorial coordinates for equinox J2000.0
(alpha)DAT, (delta)DAT: Equatorial coordinates for equinox of date

NBRW = BROWS.NGC  NGC browser for objects in "numerical vicinity"
1: NGC number     ->  1: NGC number
or:
1: ------- (->1)

The browser will list the objects in the numerical vicinity of the entered number. Number, object type and constellation are given. If the program is aborted with CANCL, the number on the stack remains unchanged. If you accept with OK, the currently highlighted number is returned. This command works only on the HP-48GX!

Library 1601 - RNGC2/48
Library 1600 - RNGC3/48

These are only included with the registered version. They provide the coded descriptions from the original (1888) and Revised (1970s) NGC catalogues.

Auxiliary programs

These programs may also be stored in a port of a RAM card to free more system memory.

PHENO          Calculates   the   most   important   planetary
phenomena  of  the  major planets (Oppositions,  Conjunctions,
greatest Elongations) for the requested year.
Call: 1: Year
        or
      1: --- (-> curr. Year)

DATA
Program  to  edit  the data  lists  ASTEROID.DAT  and COMET.DAT
Allows adding/changing/deleting object data. To add data,  you
will   need  orbital  elements  listed  e.g.  in  astronomical
magazines or newsgroups.

SITE
Program  to  edit  the  list  SITE.DAT  and   select observing sites:
Allows choosing/adding/deleting sites.

Variables used with Urania/48

Variables marked with a (*) are essential, the others are optional. Missing or bad (*)-marked variables will result in an error.

Observing Site
Long(*)   Geogr. Longitude,  -180..360ø, positive east of Greenwich. 
          Format DD.ddd
Lat  (*)  Geogr.Latitude, -90..90ø, positive north of equator.
          Format DD.ddd
Alt  (*)  Altitude  above sea level,  meters.  Only  used  for
          computing topocentric position of the Moon.
Zone(*)   Time  zone, positive east of Greenwich. 
          E.g.  CET=+1, CEDT=+2

(D)T.USR  (Delta)T, the time difference between Universal Time UT
          and Dynamical Time DT (until 1984 Ephemeris Time ET) is
          by default taken  from  a  list  or calculated. If  you
          wish to use a different  value, store a real number for 
          (D)T in seconds under this  name.  (Interesting for 
          historians or for future  years)
(e).USR   The coordinate transformation programs by  default  
          use (epsilon)o,2000. If you need a different  value,
          store  a  year  (with decimals) under this name, the
          programs calculate  o,Year and store this value back,
          tagged  with  the year. The following transformations
          will then be faster.
Temp, Press: Refraction is calculated for air temperatur  of
             10øC and air pressure of 1010 mbar. For other 
             conditions, store according values here. 
GRS.DAT  Jovigraphic longitude of Jupiter's Great Red Spot. 

ASTEROID.DAT (*)   Data list for Asteroids
Format:
{ { "Name"    (max. 22 characters)
     Equinox  (e.g.1950, 2000)
     T       (Epoch, e.g. 1995.6789)
     Mo      (Mean Anomaly for date T; degrees)
     omega   (Argument of Perihelion; degrees)
     Omega   (Longitude of ascending Node; degrees)
     i       (Inclination; degrees)
     a       (Semimajor Axis of orbit, AU)
     e       (Numerical Excentricity of orbit, <1 )
     H       (Magnitude parameter, mean abs. magnitude)
     G       (Magnitude/inclination parameter)
  }
  { "Name"  ... }        (Next entry)
  ...                    (More entries)
}

Data for some asteroids are provided

COMET.DAT(*) Data list for Comets
Format:
{ { "Name"    (max. 22 characters)
    Equinox      (e.g.1950, 2000)
    T            (Perihelion date, e.g. 1995.6789)
    omega        (Argument of Perihelion; degrees)
    Omega        (Longitude of ascending Node; degrees)
    i            (Inclination; degrees)
    q            (Perihelion distance, AU)
    e            (Numerical Excentricity of the orbit,[0..~1.3])
    H10      (Reduced magnitude)
  }
  { "Name" ... }         (Next entry)
   ...                   (more entries)
}

Data for some comets are provided.

DSTAR.DAT, VSTAR.DAT and DSO.DAT
             are described in the printed manual for registered users.

Appendix

Literature
1. Jean Meeus, Astronomical Algorithms
   Willmann-Bell, Inc.
   USA 1991
2. Jean Meeus, Astronomical Formulae for Calculators
   4th Edition, Enlarged & Revised
   Willmann-Bell, Inc., USA 1988
3. Yale Bright Star Catalogue, 5th Revised Edition
   NASA Astronomical Data Center CD ROM
4. A. Hirshfeld, R. Sinnott
   Sky Catalogue 2000.0, 1. Edition 1982 (Vol.1) and 1985 (Vol.2)
   Cambridge University Press & Sky Publishing Corporation
5. Robert Burnham, Jr.
   Burnham's Celestial Handbook
   Dover Publications
   New York, 1978
6. Richard Hinckley Allen
   Star Names - Their Lore and Meaning
   Dover Publications
   New York, 1963
7. Sky&Telescope Magazine
   Sky Publishing Corp., USA
8. Explanatory Supplement to the Astronomical Almanac
   US Naval Observatory, 1992

© Georg ZOTTI, 1996 - 10 - 14
gzotti@cg.tuwien.ac.at