From aurs01!aurw90!gingell@mcnc.org Wed Jun 12 17:48:00 1991
Subject: Sky: The Pocket Planetarium for the HP48SX
    
Sky is a new planetarium program for all HP48 calculators with at least 10K
to spare. Designed for naked eye observers, the program produces a graphic
display of the heavens. You also get the numbers, in a clear, useful
format. This file contains two directories: Sky, (6578.5 bytes) & Skys,
(9548 bytes) and a text file: Sky.doc, which includes step by step
instructions for using the program and more.

----------------------------------------------------------------------------
    
The Sky: A Pocket Planetarium for the HP 48sx Handheld Computer
  copyright  Chris Heilman  20 March 1991

When you look at the night sky do you wonder which planets you are seeing, or
need to know the phase and position of the moon to amaze the natives, or would
you just like to beat Horkheimer at his own game?  If so then read on.

Like a planetarium, this program lets you view the sky and the heavenly bodies
at any time, date, latitude or longitude.  Over one hundred sixty stars, nine
planets, the sun and moon are shown in a circular plot of the sky.

Although the program is not made for astronomers, astronomical terms and
concepts are used.  Chief among these is the concept of sky coordinates.
Numeric data about the position of the planets, sun and moon is available in
any of three coordinate systems.  Optional programs are available to plot the
sky in alternate coordinates.  (See the optional program section.)

Using the Program

  o  Transfer the file 'Sky' to your HP48, into any directory you like.  When
     the transfer is complete, you will have a new directory called 'Sky'.

     ( This program requires that you have at least 4500 bytes remaining after
     the program is loaded.  Less memory will result in an error while trying
     to run the display.  Numeric results, however, will be calculated with
     less memory available. )

  o  Open the new directory and examine the first two pages of menus.  (Use
     {VAR} to see the first page followed by {NXT} for the second.) These are
     'Sky's user words.  Subsequent pages are filled with support words that
     are used by the program.  Normally you will not need to access them.

In order for the display to be correct for your location, you must set your
coordinates.  These are your geographical longitude, latitude and time zone
correction.  Longitude and latitude are positive West of the prime meridian
and North of the equator.  The time zone correction is the number of hours to
ADD to your local time to give Universal Time (Greenwich Mean Time).  The
preset coordinates are for the observatory at Phoenix College (Arizona).

  o  Enter your longitude in decimal degrees.  Press {orange shift} {Long}.

  o  Enter your latitude in decimal degrees.  Press {orange shift} {Lat}.

  o  Enter your time zone correction in hours.  Press {orange shift} {Zone}.

  o  Press {Long}, {Lat} or {Zone} to review the data.

Now as long as you don't move too far, you need only do the next two steps
each time you want to see a display of the sky.

  o  Press the first key of the first menu: {NOW}.  This places the time and
     date on the stack.  The entries are tagged to remind you of the correct
     order.  If you wish to use another date and time, just enter them on the
     stack in the same order and format (don't tag them).

  o  Press the second key, {SKY}.  This starts the program that calculates and
     draws all of the sky objects.  As soon as the key is pressed, the screen
     is cleared, the date and time, the version name, a copyright notice and
     an indication of how long you have to wait are printed.  If you are
     running the standard version, the delay is about three minutes.Description of the Display

A few seconds after pressing {SKY} the screen turns black and plotting begins.
If you listen, ticking is heard as objects are plotted.  After 179 ticks the
hourglass annunciator disappears and you may inspect the display.

The display is a circle, just larger than the diagonal of the screen.  The
center of the display is the zenith.  Scroll around with the four arrow keys.
The circle is the ideal horizon.  North is the top of the display and South,
the bottom.  Unlike a compass, West (setting) is to the right and East
(rising) is left.  When the calculator is held overhead with the top pointing
North, the display is oriented to the real sky.  The effect is a fisheye view 
of the sky. Within the circle, symbols represent various celestial objects.

Most of the objects shown are stars.  One hundred and sixty eight stars, in 47
constellations, are available, about half are drawn at any time.  Stars are
divided into eight categories according to magnitude (brightness). In general,
bright stars are larger and more complex than dimmer stars.  The dimmest stars
are a single dot.  The brightest stars (Sirius and Canopus) have eight points
and a hole in the center.  Most stars are three by three with four points. The
position of all stars and other objects are located at the top left corner of
the symbol.

Each planet has a symbol although Pluto, Neptune and Uranus are not (usually)
visible with the naked eye.  Pluto's symbol is a combined PL, Neptune's a
trident and Uranus has a circle under a cross with a dot in the middle.

Naked eye planets have symbols that are surrounded by boxes.  Saturn's is a
lower case 'k' crossed like a 't'.  Jupiter's is a fancy '4'.  Mars' is the
circle and arrow male symbol and Venus' is the circle and cross female symbol.
Mercury's looks like a short Venus with horns.  These are attempts to render
the standard planetary symbols into small graphic objects.

The sun and moon have circular symbols.  The sun's has a dot in the middle.
The moon shows the approximate phase.  The phase is not WYSIWYG, but an icon
much like a calendar's representation.

Planets and other objects that are below the horizon are not displayed.  The
optional programs 'Zodiac' and 'Map' show a full three hundred sixty degrees
so parts of both hemispheres are shown.

Coordinate Systems

Three celestial coordinate systems, Equatorial, Ecliptic and Horizonal are
used by the program.  Each uses spherical coordinates about different axes.

Equatorial coordinates are plotted with respect to the rotation axis of the
Earth.  The Earth's equator projects to the celestial equator, thus the name.
The coordinates of stars and other 'fixed' objects change only very slowly in
this coordinate system, so it is ideal for cataloging sky objects.  Equatorial
coordinates consist of the right ascension (celestial longitude) abbreviated
'alpha' and declination (celestial latitude), 'delta'.

The ecliptic is a great circle, inclined about 23 degrees to the celestial
equator, on which the Sun is always found.  The Sun goes through the thirteen
constellations intersected by the ecliptic called the Zodiac. Most objects
also orbiting the Sun are inclined to the ecliptic by less than a few degrees,
therefore ecliptic coordinates are easily calculated for planetary orbits.
Ecliptic longitude is abbreviated 'lamda' and ecliptic latitude is 'beta'.Horizonal coordinates are also known as alt-az coordinates.  They describe the
altitude above the horizon and the azimuth, that is the compass direction in
degrees.  With horizonal coordinates you can find things in the sky.  Because
they change according to the location and time of observation, the time, date
longitude and latitude are needed to calculate horizonal coordinates.  The
symbol for altitude is a lower case 'a' and azimuth is a capital 'A'.

Calculating and Using Numeric Data

In addition to the chart like display, this program can also calculate the
positions of planets and the sun and moon.  Coordinates in any of the three
systems above can be changed to any other with a few keystrokes.

To obtain planetary coordinates:

  o  Put the planet number on the stack.  Mercury is one and Pluto, nine.

  o  Press {NOW} or enter the date and time you wish.

  o  Press {PLAN}ET.  The results, 'lamda' and 'beta' are returned to the
     stack in tagged format.

  ... Sun coordinates:

  o  Press {NOW} or enter the date and time you wish.

  o  Press {SUN}.  The results are 'lamda' for the Sun (with a dot) and an
     untagged value, the mean solar anomaly.  'Beta' for the Sun is always
     zero, so just DROP the anomaly and enter a zero.

  ... Moon coordinates:

  o  Press {NOW} or enter the date and time you wish.

  o  Press {MOON}.  The results, placed on the stack, are 'lamda', 'beta'
     and 'phase'.  The 'phase' describes the fraction of the moon that is
     bright.  A full moon has a phase of one, a new moon zero.  DROP the
     'phase' to leave the coordinates on the stack.

To convert between Ecliptic and Equatorial coordinate systems:

  o  Enter the Ecliptic or Equatorial coordinates on the stack.  You may use
     the above techniques to obtain 'lamda' and 'beta'.

  o  Press {E->C} to convert Ecliptic to Equatorial (_Celestial) coordinates.

  o  Press {C->E} to convert Equatorial to Ecliptic coordinates.  The results
     of these conversions are tagged.

  ... Horizonal and Equatorial coordinate systems:

  o  Enter the Horizonal or Equatorial coordinates on the stack.

  o  Press {NOW} or enter the date and time you wish.

  o  Press {H->C} to convert Horizonal to Equatorial coordinates.

  o  Press {C->E} to convert Equatorial to Horizonal coordinates.  The results
     of these conversions are tagged.Optional Programs

The file 'Skys' contains two optional programs which can be added to 'Sky'.
The programs in the directory 'Skys' are 'Zodiac' and 'Map'.  They plot in
Ecliptic and Equatorial coordinates respectively.  Although they require an
additional 10 kbytes, they run in less than thirty seconds.

'Zodiac' displays the neighborhood of the ecliptic from 'beta' of +16 to -24.
This provides that all of the celestial objects will always be shown.  The
stars are displayed with constellation lines shown and labeled.

'Map' draws most of the sky: from declination -60 to +60 for the full circle
of  right ascension.  Stars and constellations are labeled but lines are not
drawn.  In both of these programs, the {COORD} display reads the correct
angles for right ascension and declination, as well as placing the values on
the stack for further calculations with the 'ENTER' key.

To use the optional programs:

  o  Download the 'Skys' directory and open it.

  o  Press {blue shift} {MAP} {'} {MAP} {ENTER}
     {blue shift} {ZODIAC} {'} {ZODIAC} {ENTER}.

  o  Go to the 'Sky' directory and press {STO} {STO}.

  o  Press {NOW} {MAP} or {NOW} {ZODIAC}.

If you prefer the display of one of the optional programs to that of the
original, replace the variable 'Sky' with 'Map' or 'Zodiac'.

Copyright Statement

This program and the associated artwork is protected by the copyright laws
of the United States.  However, the right to distribute this program for
free is granted by the author to all users.  The right to charge for this
work in part or whole is reserved to the author.  Contact the author at: 
Chris Heilman, PO box 8345, Phoenix AZ 85066 or CompuServe at [70566,1474].

References

1) Young, Charles August, Uranography, 1936 Ginn and Co.
    I chose which stars to display from this document.
2) Brown, Peter Lancaster, Star_&_Planet_Spotting, 1927 Sterling Publish. Co.
    Used to verify positional data.
3) Allen, Richard Hinkely, Star_Names_and_Their_Meanings, 1899 G. E. Stechert
4) Rey, H. A., The_Stars, 1952 Houghton Mifflin Co.
    The constellation lines came from here.
5) Duffett-Smith, Peter, Practical_Astronomy_with_your_Calculator, 1987
    This is the main source for algorithms and orbital data.
6) Cox, John and Richard Monkhouse, 3-D_Star_Maps, 1989 Swallow Publish. Ltd.
    Used to double check ref. 1 and get more names.
7) -, _Astronomy_, published monthly by Kalmbach Publishing Co.
8) -, _Sky_and_Telescope_, published monthly by Sky Publishing Corporation
    You've got to read them both to keep up.
9) Finseth, Craig A., MPHASE, public domain from HP bbs
    A neat, highly accurate, graphical moonphase calculator.  Inspiring. 
10) Berry, Richard, STARS.BAS, public domain from CompuServe
     The source for star position and magnitude data.
11) Reed, Scott, GHADEC.48, public domain from CompuServeAppendix A

The following stars are displayed in the order shown.  The calculator clicks
once for each star if it is displayed or not.

Constellation  Name                     alpha, delta,  mag
                                         deg.   deg.    
  Pices        Alrisha                   30.5    2.8   3.8
               beta, fish               346.0    3.8   4.5
               gamma, fish              349.3    3.3   3.7
               delta                     12.2    7.6   4.4
               zeta                      18.4    7.6   4.9
               iota, fish               355.0    5.6   4.1
               kappa, fish              351.7    1.3   4.9
               lamda, fish              355.5    1.8   4.5
               nu                        25.4    5.5   4.4
               theta, fish              352.0    6.4   4.3
  Aries        Hamai                     31.8   23.5   2.0
               Sharaton                  28.7   20.8   2.6
               delta                     47.9   19.7   4.4
               epsilon                   44.8   21.3   4.6
               zeta                      48.7   21.1   4.9
  Taurus       Aldeberan                 69.0   16.5   0.9
               Al Nath                   81.6   28.6   1.7
               Al Hecka                  84.4   21.2   3.0
               Alcyone, Pleiades         56.9   24.1   2.9
               lamda, variable           60.2   12.5   3.5
  Geminii      Castor                   113.7   31.9   1.6
               Pollux                   116.3   28.0   1.1
               Alhena                    99.4   16.4   1.9
               mu                        95.8   22.5   2.9
  Cancer       Acubens                  134.6   11.9   4.3
               beta                     124.1    9.2   3.5
               Asellius Aus.            131.2   18.2   3.9
               iota                     131.7   28.8   4.0
  Leo          Regulus                  152.1   12.0   1.4
               Denebola                 177.3   14.6   2.1
               gamma                    155.0   19.9   2.0
               Zosma                    168.5   20.5   2.6
               Algenubi                 146.5   23.8   3.0
  Virgo        Spica                    201.4  -11.3   0.9
               Porrima                  190.5   -1.6   2.8
  Libra        Zubenelgenubi            222.8  -16.2   2.8
               Zubeneschamli            229.4   -9.5   2.6
               iota                     228.2  -19.9   4.5
  Scorpius     Antares                  247.5  -26.5   0.9
               Acrab                    241.5  -19.9   2.6
               Dschubba                 240.2  -22.7   2.3
               epsilon                  252.7  -34.4   2.3
               Shaula                   263.5  -37.2   1.6
               Lesath                   265.7  -39.1   2.4
               theta                    264.4  -43.1   1.9
               pi                       239.8  -26.2   2.9
  Ophiucius    Rasalhague               263.7   12.6   2.1
               eta                      257.7  -15.8   2.4
               theta                    260.6  -25.1   3.3
               70, close, sunlike       271.4    2.5   4.0
  Sagitarius   Alnasl                   271.6  -30.5   3.0
               Kaus Med.                275.4  -29.9   2.7
               Kaus Aus.                276.2  -34.5   1.9
               Aschella                 285.8  -30.0   2.6
               eta, teapot              274.5  -36.9   3.1
               Kaus Bor.                277.1  -25.5   2.8
               pi                       287.6  -21.1   2.9
               phi, teapot              281.5  -27.1   3.2
               Nunki                    283.9  -26.4   2.0
               tau                      286.8  -27.8   3.3
  Capricornus  Dabih                    305.4  -14.9   3.1
               Deneb                    326.9  -16.2   2.9
               Dorsam                   316.6  -17.3   4.1
  Aquarius     Sadalmelik               331.6   -0.4   3.0
               Sodalsu'ud               323.0   -5.7   2.9
               Sadachbia                335.5   -1.5   3.8
               Skat                     343.8  -15.9   3.3
               zeta, water jar          337.2    0.0   3.7
               eta, water jar           339.0   -0.2   4.0
               pi, water jar            336.3    1.4   4.7
  Ursa Minor   Polaris                   38.0   89.3   2.0
               Kochab                   222.7   74.2   2.1
               Pherkard                 230.2   71.8   3.1
               epsilon                  251.5   82.0   4.2
  Ursa Major   Dubhe                    165.9   61.8   1.8
               Merak                    165.5   56.4   2.4
               Phekda                   178.5   53.7   2.4
               Mergrez                  183.9   57.0   3.3
               Alioth                   193.5   56.0   1.8
               Mizar                    201.0   54.9   2.1
               Benetnash                206.9   49.3   1.9
  Draco        Thuban                   211.1   64.4   3.7
               Rastaban                 262.6   52.3   2.8
               Etamin                   269.2   51.5   2.2
               Nodus II                 288.2   67.7   3.1
               Nodus I                  257.2   65.7   3.2
               eta                      246.0   61.5   2.7
               Edasich                  231.2   59.0   3.3
  Cephus       Alderamin                319.7   62.6   2.4
               Alphirk                  322.2   70.6   3.2
               Alrai                    354.8   77.6   3.2
  Cassiopea    Shedir                    10.1   56.5   2.2
               Caph                       2.3   59.2   2.3
               Cih                       14.2   60.7   2.5
               Rucba                     21.5   60.2   2.7
               Segin                     28.6   63.7   3.4
  Corona Bor.  alpha                    233.7   26.7   2.2
               beta                     232.0   29.1   3.7
               delta                    237.4   26.1   4.6
               epsilon                  239.4   26.9   4.2
               theta                    233.2   31.4   4.1
  Orion        Betelgeuse                88.8    7.4   0.5
               Rigel                     78.7   -8.3   0.1
               Bellatrix                 81.3    6.4   1.6
               Mintaka, belt             83.1   -0.4   2.2
               Alnilam, belt             84.2   -1.3   1.7
               Alnitak, belt             85.3   -2.1   1.8
               Saiph                     87.1   -9.8   2.1
               Meissa                    83.8    9.9   3.4
               Tabit                     72.5    7.0   3.2
  Auriga       Capella                   79.2   46.0   0.1
               Menkalinan                89.9   45.0   1.9
               theta                     89.9   37.2   2.6
               Hassalel                  74.3   33.2   2.7
  Andromedea   Sirrah, square             2.1   29.1   2.1
               M31, nearest galaxy       11.2   41.3   6.0
  Pegasus      Markab, square           346.2   15.2   2.5
               Schcheat, square         346.0   28.1   2.4
               Algenib, square            3.3   15.2   2.8
  Hydra        Alfard                   142.0   -8.8   2.0
               beta                     178.3  -34.0   4.3
               gamma                    199.8  -23.3   3.0
               Alkes                    162.5  -16.3   3.1
  Cetus        Menkar                    45.6    4.1   2.5
               Deneb Kaitos              11.0  -18.1   2.1
               Mira, variable            34.9   -3.1   2.0
               tau, close, sunlike       26.1  -16.0   3.5
  Eridanus     gamma                     59.6  -13.6   3.0
               epsilon, close, sunlike   53.3   -9.6   3.7
  Centaurus    alpha, close, sunlike    220.0  -61.1   0.0
               mu                       207.5  -42.6   3.0
  Lupus        alpha                    220.6  -47.5   2.3
               beta                     224.7  -43.2   2.7
               gamma                    233.9  -41.3   2.8
               delta                    230.5  -40.8   3.2
  Columba      Phact                     85.0  -34.2   2.6
               beta                      87.9  -35.9   3.1
               gamma                     89.5  -35.4   4.4
  Canis Major  Sirius                   101.4  -16.8  -1.5
               delta                    107.2  -26.5   1.8
               epsilon                  104.8  -29.1   1.5
  Hercules     alpha                    258.7   14.2   3.1
               beta                     247.6   21.3   2.8
  Lyra         Vega                     279.2   38.8   0.0
               beta, variable           282.5   33.4   3.5
  Cygnus       Deneb                    310.4   45.3   1.3
               beta                     292.7   28.0   3.1
  Grus         alpha                    332.2  -47.1   1.7
               beta                     340.8  -47.0   2.1
  Lepus        alpha                     83.3  -17.9   2.6
               epsilon                   76.5  -22.5   3.2
  Phoenix      alpha                      6.7  -42.4   2.4
               gamma                     22.2  -43.4   3.4
  Bootes       Arcturus                 213.9   19.2   0.0
               Nekkar                   225.5   40.4   3.5
  Coma         12                       185.6   25.9   4.8
               23                       188.7   22.6   4.8
  Triangulum   alpha                     28.3   29.6   3.4
               beta                      32.4   35.0   3.0
  Perseus      Algeneb                   51.1   49.9   1.8
               Algol, variable           47.1   41.0   2.1
  Canis Minor  Procyon                  114.8    5.2   0.4
  Picis Aus.   Fomalhaut                344.5  -29.7   1.2
  Carina       Canopus                   96.1  -52.8  -0.7
  Aquila       Altair                   297.7    8.9   0.8
  Vela         gamma                    122.5  -47.4   1.8
  Serpens      Ukukalhai                236.1    6.4   2.7
  Puppis       zeta                     121.0  -40.1   2.3
Appendix B

The following data are used to calculate planetary orbits:

          Period in  Longitude  Longitude Eccen-   Semimaj. Inclin-  Acending
          tropical   at Epoch   at Peri.  tricity  Axis      ation   Node Long 
          year       degrees    degrees   no unit  a.u.     degrees  degrees  
Mercury   0.240852  60.750646  77.299833 .205633 0.387099  7.00454   48.21274
Venus     0.615211  88.455855 131.430236 .006778 0.723332  3.394535  76.58982
Earth     1.00004   99.403308 102.768413 .016713 1.000000  0          0
Mars      1.880932 240.739474 335.874939 .093396 1.523688  1.849736  49.480308
Jupiter  11.863075  90.638185  14.170747 .048482 5.202561  1.303613 100.353142
Saturn   29.471362 287.690033  92.861407 .055581 9.554747  2.48898  113.576139
Uranus   84.039492 271.063148 172.884833 .046321 19.21814  0.773059  73.926961
Neptune 164.79246  282.349556  48.009758 .009003 30.10957  1.770646 131.670599
Pluto   246.77027  221.4127   224.133    .24624  39.3414  17.142    110.144

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