             *************************************************
             *************************************************                  
             **                Program RISESET              **
             **                                             **
             ** Rise and Set Conditions of Earth Satellites **
             **                                             **
             **           Written by C. David Eagle         **
             **                                             **
             **    Copyright (c) 1995 by Science Software   **
             *************************************************
             *************************************************

RISESET is an interactive computer program for the IBM-PC and true compatible 
computers which computes the rise and set times of an Earth satellite relative
to an observer anywhere in the world. Program RISESET can also create polar
plots of the azinuth and elevation of a satellite during visibility passes. 
This program uses the NORAD SGP4 propagator for orbit predictions and is 
designed to read a single satellite from a database of Two Line Elements sets 
(TLEs) posted on many BBSs such as the RPV Hotline (310) 544-8977 and the 
Celestial BBS (205) 409-9280. TLEs are also available from NASA. A sample TLE 
database is included with this program. The SGP4 algorithm is valid for Earth 
satellites with orbital periods less than 225 minutes. This corresponds to 
satellites in circular orbits with altitudes less than about 5875 kilometers.

Program RISESET requires a computer with 16 color VGA graphics capability, 300 
kilobytes of conventional memory and about one megabyte of hard drive space. A
hardware coprocessor is highly recommended and will be used if present.

The software will calculate rise/set times and geometry and provide a screen 
display of the information and/or a data file. Rise and set is computed with
respect to an oblate Earth and the effect of atmospheric refraction is 
included. Rise, maximum elevation angle, and set events are predicted using 
the numerical methods described in "Efficient Computation of Satellite 
Visibility Periods", by Michael A. Chylla and C. David Eagle, AAS 92-146, 
presented at the AAS/AIAA Spaceflight Mechanics Meeting, February 24-26, 1992, 
Colorado Springs, Colorado.

The following is a brief description of each of the program prompts and the 
correct user response. Please note the proper units and numeric range for each 
data item. If you input an invalid response, the software will redisplay the
prompt and wait for another input.

RISESET will begin by asking you for the name of the TLE database file with
the following prompt:

    Please input the name of the Two Line Element database file
    (be sure to include the filename extension)
      
A typical response to this prompt might be TLE682.TXT, for example.

The program will then ask you to input the name of the satellite with the 
following display:

    Please input the name of the satellite
      
A typical response to this prompt might be MIR, for example. Please note that
the response to these first two prompts is not case sensitive.

After the RISESET program opens the TLE database file and finds the selected 
satellite, it will display the epoch calendar date and Universal Time of the 
TLE data set. It will also display the contents of the Two Line Element set.

The next prompt defines the initial calendar date of the simulation:

    Please input the initial calendar date of the simulation
    (month [1 - 12], day [1 - 31], year [YYYY])
      
Be sure to include all four digits of the calendar year. For best results use
the most recent TLE data and an initial date close to the epoch of the TLE.

The total simulation time, in days, is specified by the user's response to the 
following prompt:

    Please input the simulation duration (days)
      
RISESET will ask for the ground site coordinates via this next menu:

      Observer Data Menu

      < 1 > Data file

      < 2 > User input

      Selection (1 or 2)

Option < 1 > will read a simple ASCII data file named OBSERVER.DAT which 
contains the geographic coordinates of the ground site. The following shows 
the contents of a typical observer data file:

      Geographic latitude of the ground site
      (degrees [-90 to +90], minutes [0 - 60], seconds [0 - 60])
      (north latitude is positive, south latitude is negative)
      40, 0, 0      

      Geographic longitude of the ground site
      (degrees [0 - 360], minutes [0 - 60], seconds [0 - 60])
      (east longitude is positive, west longitude is negative)
      -80, 0, 0      

      Altitude of the ground site (meters)
      (positive above sea level, negative below sea level)
      0

Do not delete any of the comment lines in this file or change the name of this
file. Simply modify the observer coordinates for your simulation. Please note
the valid range of input data and the proper units.

Option < 2 > of this menu will ask you to interactively input the geographic 
coordinates of the ground site with the following three prompts:

      Please input the geographic latitude of the ground site
      (degrees [-90 to +90], minutes [0 - 60], seconds [0 - 60])
      (north latitude is positive, south latitude is negative)

      Please input the geographic longitude of the ground site
      (degrees [0 - 360], minutes [0 - 60], seconds [0 - 60])
      (east longitude is positive, west longitude is negative)

      Please input the altitude of the ground site (meters)
      (positive above sea level, negative below sea level)

RISESET will also allow the user to specify a minimum elevation angle 
constraint. The prompt for this program option is:

    Would you like to enforce a minimum elevation angle constraint
    (y = yes, n = no)
         
If you select y for yes, the software will print

    Please input a minimum elevation angle constraint (degrees)
      
and you can input a minimum elevation angle. Otherwise, the program will
calculate rise and set conditions at an elevation angle of 0 degrees.

You also have the option of creating a simple comma-delimited ASCII data file
of rise, maximum elevation, and set times and geometry. This prompt is:

    Would you like to create a data file of visibility conditions
    (y = yes, n = no)
      
If you select y for yes, the program will ask you to input a name for the data
file with the following message:

    Please input the output file name
    (be sure to include the file name extension)
      
RISESET also wants to know if you would like to display the visibility
conditions on your screen as they're calculated. The prompt for this program
option is:

    Would you like to display visibility conditions on your screen
    (y = yes, n = no)
      
Finally, RISESET will ask if you would like to create a polar plot of topo-    
centric azimuth versus elevation during visibility passes. The prompt for this
request is as follows:

    Would you like to display a polar plot of each visibility pass
    (y = yes, n = no)  
    
Please note that the polar display elevation angle circular contours and 
azimuth "lines" are in increments of 30 degrees. The outermost elevation
contour is represents an elevation angle of 0 degrees (the horizon), the next 
elevation contour is 30 degrees, etc. The azimuth is measured positive 
clockwise from North. For example, the first azimuth line represents an 
azimuth angle of 30 degrees, the next is 60 degrees and so forth.

After all calculations are complete, the program will prompt you for another
selection with the following:

    Another selection (y = yes, n = no)
       
A response of n for no will terminate RISESET and return you to DOS. A yes
response will recycle the software and repeat all the program prompts.

The following are several typical screen displays generated by RISESET.                                                                                
                                                                                
                               Rise Conditions                                  
                                                                                
         Calendar date                          July 31, 1995                   
                                                                                
         Universal time                        05 h  35 m  26 s                 
                                                                                
         Azimuth                (degrees)        171.977830                     
         Azimuth rate           (deg/sec)        -1.710172D-01                  
                                                                                
         Elevation              (degrees)          5.000000                     
         Elevation rate         (deg/sec)         5.591484D-02                  
                                                                                
         Slant range         (kilometers)        1805.765                       
         Slant range rate    (km/sec)            -4.740895D+00                  
                                                                                
                                                                                
         Satellite latitude     (degrees)         23.456325                     
                                                                                
         Satellite longitude    (degrees)        284.897889                     
                                                                                
         Satellite altitude  (kilometers)         396.358                       
                                                                                
                        < press any key to continue >                           
                                                                                

                               Rise Conditions                                  
                                                                                
         Satellite right ascension               08 h  39 m  56 s               
                                                                                
         Satellite declination  (degrees)        -45.746119                     
                                                                                
                                                                                
         Shadow condition                          Sunlight                     
                                                                                
                        < press any key to continue >                           
                                                                                

                         Maximum Elevation Conditions                           
                                                                                
         Calendar date                          July 31, 1995                   
                                                                                
         Universal time                        05 h  38 m  16 s                 
                                                                                
         Azimuth                (degrees)        128.068772                     
         Azimuth rate           (deg/sec)        -3.208471D-01                  
                                                                                
         Elevation              (degrees)         11.603614                     
         Elevation rate         (deg/sec)         5.797838D-07                  
                                                                                
         Slant range         (kilometers)        1344.146                       
         Slant range rate    (km/sec)             3.312017D-02                  
                                                                                
                                                                                
         Satellite latitude     (degrees)         31.384788                     
                                                                                
         Satellite longitude    (degrees)        292.900330                     
                                                                                
         Satellite altitude  (kilometers)         397.854                       
                                                                                
                        < press any key to continue >                           
                                                                                

                         Maximum Elevation Conditions                           
                                                                                
         Satellite right ascension               08 h  39 m  57 s               
                                                                                
         Satellite declination  (degrees)        -20.227349                     
                                                                                
                                                                                
         Shadow condition                          Sunlight                     
                                                                                
                        < press any key to continue >                           
                                                                                

                               Set Conditions                                   
                                                                                
         Calendar date                          July 31, 1995                   
                                                                                
         Universal time                        05 h  41 m  07 s                 
                                                                                
         Azimuth                (degrees)         84.300005                     
         Azimuth rate           (deg/sec)        -1.683297D-01                  
                                                                                
         Elevation              (degrees)          5.000000                     
         Elevation rate         (deg/sec)        -5.551634D-02                  
                                                                                
         Slant range         (kilometers)        1818.322                       
         Slant range rate    (km/sec)             4.787604D+00                  
                                                                                
                                                                                
         Satellite latitude     (degrees)         38.638785                     
                                                                                
         Satellite longitude    (degrees)        302.468172                     
                                                                                
         Satellite altitude  (kilometers)         399.597                       
                                                                                
                        < press any key to continue >                           
                                                                                

                               Set Conditions                                   
                                                                                
         Satellite right ascension               08 h  39 m  57 s               
                                                                                
         Satellite declination  (degrees)          7.466022                     
                                                                                
                                                                                
         Shadow condition                          Sunlight                     
                                                                                
         Rise/set duration      (minutes)        5.685126                       
                                                                                
                        < press any key to continue >                           


The following is a typical data file generated by the RISESET program. It 
indicates that the user has input a five degree minimum elevation angle 
constraint. Azimuth is measured positive clockwise from north. For example, an
azimuth angle of 90 degrees is east, 180 degrees is south, and so forth. The
elevation angle is positive above the observer's local horizon, and the sub-
point of the satellite is indicated by the data in the columns labeled 
(geodetic) Latitude and (east) Longitude. The data is the Range column is the 
slant range from the observer to the satellite. The satellite's altitude is
also geodetic. The satellite's right ascension and declination are topocentric
coordinates. The shadow condition calculations include a 2% increase in the
radius of the earth to account for the thickness of the atmosphere.

Ground Site   38:00:00 N  077:00:00 W 
   
 Calendar   Universal   Azimuth      Az rate      Elevation     El rate         Range       Range-rate     Latitude    Longitude     Altitude      Rasc       Decl        Event     Duration     Shadow
   Date       Time     (degrees)    (deg/sec)     (degrees)    (deg/sec)         (km)        (km/sec)      (degrees)   (degrees)       (km)     (hh:mm:ss)  (degrees)     Type      (minutes)   Condition
08/06/1995, 03:15:48, 190.382420, -8.850147D-02,   0.000000,  5.325134D-02,  2.339297D+03, -6.055639D+00,  17.977429, 279.249277,  3.949334D+02, 09:02:46, -51.373882,    Rise,     0.000000,   Sunlight
08/06/1995, 03:20:31, 128.926772, -3.636857D-01,  14.383489, -2.632116D-05,  1.199311D+03,  3.148032D-02,  31.419719, 291.987673,  3.970905D+02, 09:02:47, -19.115657,    Max ,     0.000000,   Sunlight
08/06/1995, 03:25:15,  67.814990, -8.608974D-02,   0.000000, -5.289610D-02,  2.359982D+03,  6.085246D+00,  42.916441, 309.076014,  3.999888D+02, 09:02:47,  16.940018,    Set ,     9.462713,   Sunlight
08/06/1995, 04:51:07, 241.046893,  2.842539D-02,   0.000000,  6.018629D-02,  2.346866D+03, -6.855334D+00,  26.407721, 263.230917,  3.960937D+02, 09:03:01, -22.806379,    Rise,     0.000000,   Sunlight
08/06/1995, 04:56:29, 324.075579,  1.234938D+00,  48.804175, -3.987228D-04,  5.192319D+02,  1.507796D-02,  40.328181, 280.776675,  3.992641D+02, 09:03:02,  62.076370,    Max ,     0.000000,   Sunlight
08/06/1995, 05:01:54,  47.136876,  2.895587D-02,   0.000000, -5.960755D-02,  2.365063D+03,  6.842950D+00,  49.839296, 306.308938,  4.020906D+02, 09:03:03,  31.995352,    Set ,    10.795846,   Sunlight
08/06/1995, 06:28:48, 284.041107,  1.031253D-01,  -0.000000,  4.975494D-02,  2.357834D+03, -5.671465D+00,  40.078447, 256.864784,  3.991883D+02, 09:03:17,  10.661692,    Rise,     0.000000,   Sunlight
08/06/1995, 06:33:24, 342.370198,  3.173923D-01,  11.536888,  6.985870D-06,  1.357472D+03,  1.456294D-02,  48.702691, 277.842570,  4.017060D+02, 09:03:18,  59.129587,    Max ,     0.000000,   Sunlight
08/06/1995, 06:38:02,  40.694872,  1.026041D-01,  -0.000000, -4.945382D-02,  2.367228D+03,  5.669924D+00,  51.791231, 304.547041,  4.029718D+02, 09:03:18,  36.247017,    Set ,     9.233639,   Sunlight
08/06/1995, 08:06:49, 313.131068,  1.231453D-01,  -0.000000,  4.393342D-02,  2.365082D+03, -5.018220D+00,  49.922962, 259.755783,  4.021031D+02, 09:03:32,  32.177612,    Rise,     0.000000,   Sunlight
08/06/1995, 08:10:58,   3.062053,  2.627220D-01,   7.544132, -3.487572D-06,  1.620503D+03,  3.631864D-03,  51.705541, 284.168145,  4.030028D+02, 09:03:33,  59.301424,    Max ,     0.000000,   Sunlight
08/06/1995, 08:15:06,  52.966159,  1.229351D-01,  -0.000000, -4.391185D-02,  2.366830D+03,  5.022388D+00,  47.975614, 307.549760,  4.025637D+02, 09:03:34,  27.931665,    Set ,     8.290431,   Sunlight
08/06/1995, 09:43:29, 318.908275,  8.650383D-02,  -0.000000,  5.293856D-02,  2.367341D+03, -6.060830D+00,  51.676373, 261.327996,  4.030009D+02, 09:03:48,  35.993588,    Rise,     0.000000,   Sunlight
08/06/1995, 09:48:24,  23.279366,  3.793068D-01,  15.628444, -2.168430D-05,  1.155567D+03, -7.239617D-03,  46.581949, 288.407816,  4.023147D+02, 09:03:49,  59.603392,    Max ,     0.000000,   Sunlight
08/06/1995, 09:53:17,  87.588340,  8.648791D-02,   0.000000, -5.319194D-02,  2.361319D+03,  6.069510D+00,  36.059306, 308.470103,  4.003657D+02, 09:03:49,   1.546638,    Set ,     9.807045,   Sunlight
08/06/1995, 11:19:35, 308.601518, -5.507420D-04,   0.000000,  6.046087D-02,  2.366950D+03, -6.932596D+00,  48.487521, 258.741992,  4.026376D+02, 09:04:03,  29.041901,    Rise,     0.000000,   Sunlight
08/06/1995, 11:25:03, 220.641452, -8.755791D+00,  83.133792,  2.363672D-04,  4.033801D+02, -7.748788D-03,  37.689285, 282.664810,  4.006572D+02, 09:04:04,  32.665784,    Max ,     0.000000,   Sunlight
08/06/1995, 11:30:28, 132.470376, -1.663689D-03,  -0.000000, -6.088161D-02,  2.352524D+03,  6.938030D+00,  23.063559, 299.150871,  3.984457D+02, 09:04:05, -32.561976,    Set ,    10.893265,    Umbra  
08/06/1995, 12:56:50, 281.464306, -1.237034D-01,   0.000000,  4.354332D-02,  2.363010D+03, -5.008549D+00,  39.178241, 256.888553,  4.009281D+02, 09:04:19,   8.652934,    Rise,     0.000000,   Sunlight
08/06/1995, 13:00:46, 234.756140, -2.557137D-01,   6.846054, -1.517692D-05,  1.663602D+03, -2.876895D-02,  29.063433, 269.843771,  3.992126D+02, 09:04:19, -22.307566,    Max ,     0.000000,    Umbra  
08/06/1995, 13:04:41, 187.839129, -1.257712D-01,   0.000000, -4.367662D-02,  2.348265D+03,  4.962572D+00,  17.790243, 280.155627,  3.979894D+02, 09:04:20, -51.885046,    Set ,     7.850016,    Umbra  

******************************************************************************

C. David Eagle

November 6, 1995

(703) 815-8834

Internet  davidea@haven.ios.org

CompuServe 74561,606

******************************************************************************

Additional Science Software programs:

NPOE - Numerical Prediction of Orbital Events

Celestial Computing - A Journal and Companion Software for Computers and 
                      Celestial Mechanics

Thank you for using RISESET. Please call, write or e-mail for additional 
information and NPOE and Celestial Computing demo disks. I can also provide 
custom mission analysis and numerical analysis software written in either
Microsoft (tm) QuickBASIC or PowerStation FORTRAN.

******************************************************************************

NPOE Software System

NPOE is an interactive computer program for the IBM-PC and true compatible 
computers which can model important orbital events and predict the long term 
evolution of satellites in Earth orbits. Program NPOE implements a special 
perturbation solution of orbital motion using a variable step size Runge-
Kutta-Fehlberg integration method to numerically integrate Cowell's form of 
the system of differential equations. Orbital events are predicted using 
Brent's method for finding the root of a nonlinear equation, and the user can 
control both the integration and root-finding criteria.

Program NPOE can accurately predict the time, geometric and dynamic orbit 
characteristics for any physically realizable user-defined value of the 
following orbit parameters:

        True anomaly
        Argument of latitude
        Flight path angle
        Geocentric declination
        East longitude
        Geodetic altitude
        Geodetic latitude
        Orbital speed

The software can also determine the time and orbital characteristics of the 
following discrete events:

        Ascending node crossings
        Descending node crossings
        Rise and set conditions of a satellite relative to a ground site
        Visibility conditions of the Sun or Moon relative to a satellite
        Earth and lunar shadow entrance and exit conditions

The NPOE software can model one or more of the following types of orbit 
perturbations:

        Earth gravity - user-defined degree and order

        Solar gravity - point mass

        Lunar gravity - point mass

        Atmospheric drag

         - U.S. Standard 1976 density model
         - Jacchia 1970 density model
         - user-defined geometric and mass properties

        Solar radiation pressure

         - user-defined reflective and geometric properties

Please see the NPOE catalog for additional information about the contents of 
the NPOE software system. A catalog and demo disk can be obtained by 
contacting Science Software.

******************************************************************************

ORBLIB - the Science Software Orbital Mechanics Library

The following is a list of mission analysis computer programs available from 
Science Software.

    Orbit Propagation and Utility Programs

        Interpolation of Orbital State Vectors

        Intersection of Two Orbits

        SGP Utility Program

        Two body orbit propagation

        Kozai method of orbit propagation

        Brouwer-Lyddane method of orbit propagation

        Cowell method of orbit propagation

    Visualization

        Mercator, orthographic and true view satellite graphics

        Mercator and rectangular display of satellite ground tracks

        Three dimensional views of satellite orbits

        Two dimensional display of relative motion between two satellites

        Graphics display of three-body motion

        Graphics display of Earth-to-moon trajectories

        Graphics display of sun and moon visibility

        Create VERSAMAP plot files

    Orbital Event Prediction

        Rise and set of a satellite

        Mutual visibility between two satellites

        Closest approach between two satellites

        Closest approach between a satellite and ground site

        Orbital lifetime prediction

        Eclipse conditions of satellites

    Orbit Design

        Repeating ground track design

        Sun-synchronous orbit design

        Frozen orbit design

        Composite orbit design

    Orbital Transfer and Maneuvers

        Single impulse orbital maneuvers

        Two impulse Hohmann transfer

        Optimal two impulse orbital transfer

        Primer vector analysis and graphics

    Interplanetary Mission Analysis

        Interplanetary trajectory optimization

        Gravity assist flyby trajectories

    Symbolic Orbital Mechanics with Mercury

        Kepler's Equation
        Frozen Orbits
        Repeating Ground Track Orbits
        Two Impulse Hohmann Transfer
        Bielliptic Orbit Transfer
        Optimal Launching of a Rocket

    FORTRAN and QuickBASIC Source Code Library

        Kepler's equation
        Coordinate transformations
        Calendar and Julian dates
        Apparent sidereal time
        Lunar and solar ephemeris
        Goodyear's state transition matrix
        Orbital equations of motion
        Jacchia 1970 atmosphere model
        Lambert's problem
        Numerical Methods
         - Solution of systems of differential equations
         - Root of a nonlinear equation
         - One dimensional optimization
         - Trig, vector and matrix routines
        Solar activity data file
        Gravity coefficients data files

******************************************************************************
                        
                        WELCOME TO CELESTIAL COMPUTING

The use of personal computers in celestial mechanics seems only natural. The 
computer can help provide a vivid understanding of fundamental concepts of 
astronomy and celestial mechanics. We can also use the power of computers to 
predict unique celestial events and phenomena which we have yet to witness. 
Although celestial mechanics is the world's oldest science, it attracts our 
attention today perhaps even more than it did many centuries ago.

Celestial Computing was written for two types of computer users. It provides 
technical information and source code for the programmer who is interested in 
the math and physics required to solve problems in celestial mechanics, and it 
will also be useful for the person who simply wants reliable and accurate 
astronomical software.

The material in Celestial Computing focuses on computer applications in the 
following three areas of celestial mechanics:

  * Astronomy - the observation, calculation and interpretation of the 
                characteristics of celestial bodies and phenomena

  * Astrometry - the study of positions and motions of celestial bodies

  * Astrodynamics - the study of the motion and behavior of man-made spacecraft

The purpose of Celestial Computing is to provide efficient and accurate 
computer applications which will allow everyone to explore these areas of 
celestial mechanics. Each computer application includes a discussion of the 
mathematics and physics of a particular problem. We have also examined books, 
technical publications, and other computer programs about celestial mechanics. 
We have tried our best to provide material which is easy to understand and use.

Each issue contains a feature article, and regular columns in the areas of 
fundamental astronomy, applied astrodynamics, symbolic computing, and numerical 
methods. There is also a recreational computing column which emphasizes 
computer graphics to illustrate many fundamental concepts of celestial 
mechanics and astronomy. Each issue also contains a book and software review.

Individual issues of Celestial Computing consist of a written journal and 
companion floppy disk. The written journal contains a technical discussion 
about each article and instructions which explain how to use the software. The 
floppy disk contains the actual computer programs, symbolic computing 
documents, data files, etc. The Celestial Computing companion software is 
provided in both source code and executable form. The majority of the programs 
are written in Microsoft QuickBASIC. This compiler is inexpensive, about $90 
mail order, and offers a complete and easy to use programming environment. It 
is a highly structured language with extensive debugging features. The 
QuickBASIC compiler includes many of the constructs of PASCAL, the COMMON 
blocks of FORTRAN, and the simple I/O of BASIC. These programs will also run 
with the QBASIC interpreter included with MS-DOS versions 5.0 and 6.x.

FEATURE ARTICLE

Each issue of Celestial Computing includes a feature article of general 
interest. Some of the topics covered in Volumes 1 through 4 are as follows:

        *  The prediction of lunar eclipses
        *  The prediction of solar eclipses
        *  Tracking and observing Earth satellites
        *  Lunar occultations of stars and planets
        *  Calculating planetary positions and unique events
        *  Real-time orbit simulation of a space telescope
        *  Lambert's problem for interplanetary spaceflight
        *  Computer methods for orbit determination

FUNDAMENTAL ASTRONOMY

This column of Celestial Computing features interactive QuickBASIC computer 
programs which can be used to understand and study fundamental concepts of 
astronomy.

The following is a list of some of the topics discussed in this column:

        *  Julian and calendar dates
        *  The accurate calculation of sidereal time
        *  Precession and nutation in astronomy
        *  Astronomical coordinate systems and transformations
        *  The calculation of classical orbital elements
        *  The numerical solution of Kepler's equation
        *  Computing the apparent position of a star
        *  Predicting an accurate Earth and lunar ephemeris

APPLIED ASTRODYNAMICS

In this regular department of Celestial Computing, we provide computer 
solutions to classic and unique problems in the field of astrodynamics. This 
is an area where we can apply fundamental principles of celestial mechanics to 
solve problems related to manned and unmanned spaceflight. This column 
presents computer solutions in the following areas:

        *  Spacecraft trajectory analysis
        *  The prediction of orbital events
        *  Methods of orbit design
        *  Interplanetary spaceflight
        *  Optimal orbital transfer
        *  Perturbed orbital motion
        *  Earth and lunar shadow conditions of satellites

SYMBOLIC COMPUTING

This is a regular column of Celestial Computing which illustrates the use 
different symbolic computing programs such as MathCAD, Eureka: The Solver, 
Mathematica, Mercury, and Derive to solve fundamental and unique problems in 
celestial mechanics. Typical topics discussed in this column include the 
following:

        *  Symbolic computing solutions of Kepler's equation
        *  Symbolic computing solutions for the geodetic latitude and altitude 
           of an Earth orbiting spacecraft
        *  Symbolic computing solutions for the closest approach between a 
           satellite and an observer on an oblate Earth
        *  Symbolic computing solutions of lunar and planetary events

RECREATIONAL COMPUTING

This column of Celestial Computing is dedicated to computer applications which 
are both fun and entertaining. Many of these programs emphasize graphics to 
help the user visualize different types of astronomical concepts and celestial 
motions. Typical graphics applications which have appeared in this column 
include:

        *  A computer graphics display of the Galilean satellites
        *  A computer graphics simulation of the Three-Body problem
        *  Computer graphic displays of orbital motion and events
        *  Computer graphic displays of the Earth from space
        *  Computer graphic displays of Sun and Moon visibility contours

NUMERICAL METHODS

This column of Celestial Computing focuses on numerical methods which can be 
used to solve a variety of problems in celestial mechanics, astronomy and 
astrodynamics. Many of these methods are QuickBASIC computer programs and 
subroutines which you can use as modules in your own programs and computer 
applications. Each of these modules also includes a short program which 
demonstrates how to use the software correctly.

The following is a brief list of some of the algorithms which have been 
discussed:

        *  Computer programs for linear algebra
        *  Computer programs for numerical optimization
        *  A Least-squares curve fit program
        *  Computing the real and complex roots of a polynomial
        *  The Gauss-Radau method for solving differential equations
        *  Evaluating the ICE Chebyshev coefficients
        *  Computer programs for numerical interpolation


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but is necessary if you want to modify the source code. A shareware version of 
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                          CELESTIAL COMPUTING INDEX

The following is an index of the articles which have appeared in the four 
volumes of Celestial Computing. The articles are listed by volume and number.

FEATURE ARTICLE

    Vol. 1  No. 1   Symbolic Computing and Celestial Mechanics
    Vol. 1  No. 2   A Computer Program for Predicting Lunar Eclipses
    Vol. 1  No. 3   Uniform Extension of Gauss's Boundary Value Problem
    Vol. 1  No. 4   A Computer Program for Predicting Planetary Positions 
                    and Events

    Vol. 2  No. 1   The Stumpff/Weiss Solution of the Four-Body Problem
    Vol. 2  No. 2   A Computer Program for Predicting Solar Eclipses
    Vol. 2  No. 3   The Gauss Method of Orbit Determination
    Vol. 2  No. 4   A Computer Program for Predicting Lunar Occultations

    Vol. 3  No. 1   Calculating the Apparent Place of Celestial Objects
    Vol. 3  No. 2   A Computer Program for Predicting Comet Ephemerides and 
                    Events
    Vol. 3  No. 3   A Computer Program for Solving the Interplanetary 
                    Lambert Problem
    Vol. 3  No. 4   A Computer Program for Predicting Lunar Events

    Vol. 4  No. 1   Ephemerides for Physical Observations
    Vol. 4  No. 2   A Computer Implementation of the Brouwer-Lyddane Orbit 
                    Theory
    Vol. 4  No. 3   Celestial Mechanics with Mathematica
    Vol. 4  No. 4   Interplanetary Trajectory Optimization

FUNDAMENTAL ASTRONOMY

    Vol. 1  No. 1   Calculating Julian and Calendar Dates
    Vol. 1  No. 2   The Calculation of Sidereal Time
    Vol. 1  No. 3   A Computer Program for Precession
    Vol. 1  No. 4   Astronomical Coordinate Systems and Transformations

    Vol. 2  No. 1   A Computer Program for Predicting an Earth Ephemeris
    Vol. 2  No. 2   Calculating the Apparent Position of a Star
    Vol. 2  No. 3   Calculating a Lunar Ephemeris
    Vol. 2  No. 4   Calculating the Classical Orbital Elements

    Vol. 3  No. 1   The VSOP Planetary Ephemeris
    Vol. 3  No. 2   Converting Elliptic Elements from One Equinox to Another
    Vol. 3  No. 3   Predicting Transits of Mercury and Venus
    Vol. 3  No. 4   Calculating a Lunar Ephemeris with DE200

    Vol. 4  No. 1   A Computer Implementation of Newcomb's Solar Theory
    Vol. 4  No. 2   Predicting Rise, Transit and Set of Celestial Objects
    Vol. 4  No. 3   Computing a Physical Ephemeris of the Moon
    Vol. 4  No. 4   Spreadsheet Astronomy

APPLIED ASTRODYNAMICS

    Vol. 1  No. 1   Sun-synchronous, Repeating-groundtrack Orbits
    Vol. 1  No. 2   Optimal Impulsive Orbital Transfer
    Vol. 1  No. 3   Calculating Shadow Conditions of Satellites
    Vol. 1  No. 4   Calculating Visibility Conditions of Earth Satellites

    Vol. 2  No. 1   Calculating Mutual Visibility Between Two Earth 
                    Satellites
    Vol. 2  No. 2   An Amateur Space Telescope Real-Time Orbit Simulation
    Vol. 2  No. 3   Goodyear's Method of Orbit Propagation
    Vol. 2  No. 4   Predicting the Orbital Lifetime of Earth Satellites

    Vol. 3  No. 1   Lunar and Solar Perturbations of Earth Satellite Orbits
    Vol. 3  No. 2   Encke's Method of Orbit Propagation
    Vol. 3  No. 3   N-body Perturbations of Heliocentric Orbits
    Vol. 3  No. 4   Visibility Conditions of Lunar Satellites

    Vol. 4  No. 1   Predicting Lunar Eclipses of Earth Satellites
    Vol. 4  No. 2   Converting Between Osculating and Mean Orbital Elements
    Vol. 4  No. 3   Solar Radiation Pressure Perturbations of Earth 
                    Satellite Orbits
    Vol. 4  No. 4   The Method of Differential Corrections

SYMBOLIC COMPUTING

    Vol. 1  No. 1   Estimating the Time of Apogee and Perigee of the Moon
    Vol. 1  No. 2   Geodetic Latitude and Altitude of a Point in Space
    Vol. 1  No. 3   Closest Approach Distance Between Two Planets
    Vol. 1  No. 4   Closest Approach Between a Satellite and an Observer

    Vol. 2  No. 1   Symbolic Computer Solutions of Kepler's Equation
    Vol. 2  No. 2   Symbolic Computing with DERIVE
    Vol. 2  No. 3   Symbolic Computing with QUICK
    Vol. 2  No. 4   Closest Approach Conditions Between Two Earth Satellites

    Vol. 3  No. 1   Symbolic Curve-Fitting of Celestial Coordinates
    Vol. 3  No. 2   Time of Closest Approach Between a Comet and the Earth
    Vol. 3  No. 3   Calculating the Characteristics of Frozen Orbits
    Vol. 3  No. 4   Lunar Calculations with Mercury

    Vol. 4  No. 1   Symbolic Computing and Graphics with Mercury
    Vol. 4  No. 2   Designing Repeating Groundtrack Orbits with Mercury
    Vol. 4  No. 3   Solving the Bielliptic Orbit Transfer Problem with 
                    Mercury
    Vol. 4  No. 4   Optimal Launching of a Rocket

RECREATIONAL COMPUTING

    Vol. 1  No. 4   A Computer Graphics Display of the Galilean Satellites

    Vol. 2  No. 1   A Computer Graphics Simulation of the Three-Body Problem
    Vol. 2  No. 2   Computer Graphics Display of Orbital Motion
    Vol. 2  No. 3   Computer Graphics Display of Orbital Events
    Vol. 2  No. 4   A Computer Graphics Display of Zero-velocity Contours

    Vol. 3  No. 1   Computer Graphics Display of Astronomical Coordinates
    Vol. 3  No. 2   A Computer Graphics Display of Comet Motion
    Vol. 3  No. 3   A Computer Graphics Display of Earth Satellite Orbits
    Vol. 3  No. 4   A Computer Graphics Display of Earth-Moon Trajectories

    Vol. 4  No. 1   A Mercator Graphics Display of Earth Satellite 
                    Groundtracks
    Vol. 4  No. 2   Computer Graphic Displays of the Earth from Space
    Vol. 4  No. 3   A Computer Graphics Display of Relative Motion
    Vol. 4  No. 4   Computer Graphic Displays of Sun and Moon Visibility 
                    Contours

NUMERICAL METHODS

    Vol. 1  No. 1   Matrix, Vector and Trigonometry Utility Functions and 
                    Subroutines
    Vol. 1  No. 2   Computer Programs for Linear Algebra
    Vol. 1  No. 3   Computer Programs for Numerical Integration
    Vol. 1  No. 4   Computer Programs for Numerical Optimization

    Vol. 2  No. 1   Computer Programs for Solving Non-linear Equations
    Vol. 2  No. 2   A Least-squares Curve Fit Computer Program
    Vol. 2  No. 3   Computing the Real and Complex Roots of a Polynomial
    Vol. 2  No. 4   Numerical Integration of Algebraic Functions

    Vol. 3  No. 1   The Gauss-Radau Method for Solving Differential 
                    Equations
    Vol. 3  No. 2   Computer Methods for Numerical Differentiation
    Vol. 3  No. 3   A Computer Program for Multivariable Optimization
    Vol. 3  No. 4   Computer Programs for Numerical Interpolation

    Vol. 4  No. 1   A Computer Method for Solving Systems of Non-linear 
                    Equations
    Vol. 4  No. 2   Evaluating the ICE Chebyshev Coefficients
    Vol. 4  No. 3   Computer Routines for Chebyshev Approximations
    Vol. 4  No. 4   A Computer Program for Non-linear Curve-fitting
