		     ***********************************     
		     **        Program SATPLOT        **
		     **                               **
		     ** Graphics Display of Satellite **               
		     **   Ground Tracks and Orbits    **
		     **                               **
		     **      Copyright (c) 1995       **
		     **        by David Eagle         **
		     ***********************************

SATPLOT is an interactive computer program for the IBM-PC (tm) and true 
compatible personal computers which can be used to generate three dimensional 
orthographic displays of Earth satellite orbits, two dimensional Mercator 
displays of ground tracks, and polar plots of azimuth and elevation during
visibility passes.  The software can propagate a satellite's orbit using 
either the NORAD SGP4 algorithm, Kozai's secular perturbation method, a fast
analytic orbit propagator, or a seventh-order Runge-Kutta-Fehlberg (RKF) 
numerical integration technique. The Kozai, analytic and RKF options account 
for the effect of J2 (first order earth oblateness) on the motion of a 
satellite and its orbital plane.

For the SGP4 option, the software reads 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. 

For the Kozai, analytic and numerical integration method, the program prompts 
you for the name of an ASCII data file containing a satellite's classical 
orbital elements and the corresponding epoch, and an integration tolerance. 
This request is as follows:

      Please input the name of the orbital elements data file 
      (be sure to include the filename extension)

The following is a typical orbital elements data file:

      epoch - calendar date; month, day, year 
      (1 <= month <= 12; 1 <= day <= 31; all digits of the year!)
      10, 1, 1995

      epoch - Universal time; hours, minutes, seconds
      (0 <= hours <= 24; 0 <= minutes <= 60; 0 <= seconds <= 60)
      0, 0, 0

      RKF78 tolerance (try 1D-8 to 1D-10)
      1D-10

      semimajor axis (kilometers)
      6728.14
   
      orbital eccentricity (non-dimensional; 0 <= eccentricity < 1)
      0

      orbital inclination (degrees; 0 <= inclination <= 180)
      30

      argument of perigee (degrees; 0 <= argument of perigee <= 360)
      0

      RAAN (degrees; 0 <= RAAN <= 360)
      0

      true anomaly (degrees; 0 <= true anomaly <= 360)
      0

The epoch is the calendar date and time at which these classical orbital 
elements are valid. It is not necessarily the same as the initial simulation 
time described below. However, the epoch should be close to the initial 
SATPLOT simulation time. Please note the units and valid range for each entry. 
Do not delete any of the comment lines. RAAN is the right ascension of the 
ascending node. Smaller RKF tolerances will result in better orbit prediction
at the expense of longer run times. Values between 1D-8 and 1D-10 should be
adequate for SATPLOT simulations spanning several days. 

NOTE: SATPLOT assumes that these orbital elements are "Kozai mean elements" 
when using the Kozai orbit propagation option, and "osculating" orbital 
elements when using the analytic and RKF numerical integration method.

The values for the earth's gravitational constant (mu), gravity coefficient 
(j2), equatorial radius (req) and flattening factor (flat) used in SATPLOT are

     mu   = 398600.5 km^3/sec^2
     j2   = .00108263 (non-dimensional)
     req  = 6378.14 kilometers
     flat = 1/298.257 (non-dimensional)

You may know a satellite's perigee and apogee altitude instead of its 
semimajor axis and eccentricity. The equations which relate perigee and apogee 
altitudes, semimajor axis and orbital eccentricity are as follows:

     rp = req + hp
     ra = req + ha

     sma = (ra + rp) / 2
     ecc = (ra - rp) / (ra + rp)

     where

       hp  = perigee altitude (kilometers)
       ha  = apogee altitude (kilometers)
       rp  = perigee radius (kilometers)
       ra  = apogee radius (kilometers)
       sma = semimajor axis (kilometers)
       ecc = orbital eccentricity (non-dimensional)

Please note that these equations are valid for satellite altitudes specified 
with respect to a spherical Earth.

The SATPLOT software displays the satellite orbit or ground track only during 
periods of ground site to satellite visibility. The user can input a minimum 
elevation angle constraint and the viewpoint of the graphics display. Program 
SATPLOT requires a computer with 16 color VGA graphics capability, 300 KB of 
conventional memory and about one megabyte of hard drive space. A hardware 
coprocessor is highly recommended and will be used if present.

The SATPLOT program will ask you to input several items necessary for proper 
operation. If you give an invalid response, the program will repeat the prompt
and you can input a response again. The following is a short description of 
each program prompt. Please note that several of these inputs are only 
required for certain program options.

The program begins by displaying the following orbit propagation menu:

		    Orbit Propagation Menu

	< 1 > SGP4 propagator - Two-Line-Element data set

	< 2 > Analytic propagation - mean orbital elements

	< 3 > Analytic propagation - osculating orbital elements

	< 4 > Numerical integration - osculating orbital elements

      Selection (1, 2, 3 or 4)

Input the single digit 1, 2, 3 or 4 followed by the Enter key to make your 
selection.

The next prompt is the SATPLOT graphics menu which appears as follows:

	      SATPLOT Graphics Menu
      
	   < 1 > Orthographic display
      
	   < 2 > Mercator display
      
	   < 3 > Azimuth/elevation polar display

      Selection (1, 2 or 3)

Option < 1 > will create a three-dimensional orthographic display of orbits, 
menu option < 2 > will create a Mercator map of a satellite's ground track, 
and program option < 3 > will create a polar plot of azimuth and elevation.

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.

For options < 1 > and < 2 > the program will ask if you would like to display 
a world map on the Earth's surface. The prompt is a follows:

      Would you like to display a world map (y = yes, n = no)

If you choose "y" for yes, the ASCII data files XYZMAP.DAT and MLATLON.DAT
must be in the current directory in order for the SATPLOT program to find and 
plot them.

The user can define the interval at which the program plots lines of constant
latitude and longitude by responding to these two prompts:

      Please input the latitude lines plot interval (degrees)

      Please input the longitude lines plot interval (degrees)

The plot will be more pleasing if these inputs are numbers which divide evenly
into 90 (latitude) and 360 (longitude) degrees (inputs such as 15, 30, etc.).

The software will ask you to input the viewpoint coordinates. The othographic 
view created by the SATPLOT program is relative to a point very far from the 
Earth which is located above a user-defined geographic latitude and east or 
west longitude. The viewpoint rotates with the Earth as the satellite moves
in its (inertial) trajectory. For the Mercator display the viewpoint defines
the center of the map. The viewpoint prompts are as follows:

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

If you have selected the Mercator display option, the program will ask you to
input the width of the Mercator display in degrees with

      Please input the delta longitude of the map (degrees)
      (0 < delta longitude <= +360)

Please note that SATPLOT maintains the Mercator relationship by adjusting the
upper and lower latitude range based on this delta longitude number.

If have selected the SGP4 orbit propagation option, SATPLOT will ask you to 
enter the name of a Two-Line-Element (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)
      
The software will also ask for the name of the satellite of interest with this 
next prompt:

      Please input the name of the satellite

Please note that these two inputs are not case sensitive but both must be
spelled correctly.

SATPLOT 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.

If you select menu option < 2 > the SATPLOT program will ask you to manually
input the geographic coordinates of the ground site with the next three 
interactive 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)
      
Please note the sign conventions and valid ranges for each coordinate. For 
example, 77 degrees, 30 minutes and 45 seconds west longitude is input as 
-77,30,45.

The software will ask you for the initial calendar date of the simulation with
this next prompt.

      Please input the initial calendar date of the simulation
      (month [1 - 12], day [1 - 31], year [YYYY])
      
Please note the valid range of each data item. Be sure to include all four 
digits of the calendar year.

The total simulation time is defined in response to this next question:

      Please input the total simulation time (days)
      (total time must be greater than zero)
      
The step size for the orbit plot during visibility conditions is specified by 
responding to this question:

      Please input the plot display step size (minutes)
      
SATPLOT will allow you to enforce a minimum elevation angle constraint for
the visibility calculations. This prompt is as follows:

      Would you like to enforce a minimum elevation angle constraint
      (y = yes, n = no)
	 
If you choose "y" for yes, the program will ask you to input the value of the
minimum elevation angle constraint with

      Please input a minimum elevation angle constraint (degrees)

*****************************************************************************
*****************************************************************************
** PLEASE NOTE THAT A RESPONSE OF -90 DEGREES WILL CAUSE SATPLOT TO ALWAYS **
** PLOT THE SATELLITE'S ORBIT OR GROUND TRACK.                             **
**                                                                         **
** Note: A polar plot with a -90 degree elevation angle constraint will    **
** produce very strange (and invalid) graphics outside the horizon contour **
** (elevation = 0 degrees) of the polar display!                           **
*****************************************************************************
*****************************************************************************

In the orthographic display mode the software can zoom in and out when 
displaying the Earth and satellite orbit. The zoom factor is input in response 
to this next request:

      Please input the zoom factor (zoom > 0)
      (try zoom = 1; larger zoom factor gives larger field of view)

If you have selected the orthographic display option, the program will ask if 
you would like to display the ground track of the satellite with this next 
prompt:

      Would you like to plot the satellite's ground track (y = yes, n = no)

Finally, the program will ask if you would like to single step the graphics 
display during ground site to satellite visibility. This question is as 
follows:

      Would you like to single step the screen display (y = yes, n = no)

If you input "y" for yes, you can manually advance the orbit plot by pressing 
the Enter key after each point is plotted. Pressing the P key will pause the 
program and pressing the C key will resume the calculations and graphics. 

You can leave the SATPLOT program at any time by pressing the Escape key.

****************************
SATPLOT.CAL Calibration file
****************************

The software expects to find a SATPLOT "calibration" file called SATPLOT.CAL
in the current directory. The following are the contents of a typical file:

XY aspect ratio
1.32
X-axis calibration factor
10
Y-axis calibration factor
7.125

The XY aspect ratio is for the orthographic and polar plot displays and the 
X-axis and Y-axis calibration factors are for the Mercator display. Please 
note that the three comment lines can be changed but should not be eliminated. 
This XY aspect ratio and X-Y axes calibration factors are for typical VGA 
monitors but may have to be "tweaked" for your particular hardware. Tweaking 
of the XY aspect ratio is best done trial and error by measuring the height 
and width of the Earth on the screen. The screen is calibrated when they are 
both equal. The X-axis and Y-axis calibaration factors are determined by 
measuring the width and height of the Mercator image displayed on the screen. 
These measurements can be in any units as long as they are both in the same 
units (inches, etc.).

***********************
VIEWPCX UTILITY PROGRAM
***********************

The SATPLOT distribution disk also contains a utility program called VIEWPCX
which can be used to view and print several PCX images captured from the 
SATPLOT program (SATPLOT1.PCX, etc.). To use this utility simply type VIEWPCX 
at the DOS command line. The program will display a menu of file names with a 
.PCX extension and you can select one using the mouse. You can also scroll
through the list of files using the keyboard up and down arrows keys and make
a selection by pressing the Enter key.

If it exists, VIEWPCX will also automatically read a simple ASCII data file 
of printer parameters. This file must be named PRINTER.DAT and it must be 
located in the same directory as VIEWPCX. The following is a typical example 
of the information contained in this file. Do not add or delete any lines 
from this file. Simply modify the integer numbers for your printer and port 
configuration if necessary.

This simple data file defines the printer type, parallel port, print 
orientation and for LaserJets, the print resolution. If you set up this file 
it is not necessary to manually set the printer characteristics. The following
is a typical VIEWPCX printer data file:

**********************************
*** VIEWPCX Printer Data File ***
**********************************

PRINTING OPTIONS

Type of printer (1 = Epson, 2 = HP Laserjet)
2

Printer parallel port (1 = LPT1, 2 = LPT2, 3 = LPT3)
1

Laserjet printer resolution (1 = 75 DPI, 2 = 100 DPI, 3 = 150 DPI, 4 = 300 DPI)
3

Laserjet printer orientation (1 = portrait mode, 2 = landscape mode)
1

A PCX screen can be printed by pressing the P key after the complete image is
displayed on your monitor screen. The VIEWPCX program is exited by pressing 
the Enter key after printing or viewing the image.

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

November 7, 1995

C. David Eagle

Science Software
P.O. Box 2188
Reston, VA 22090-0188

(703) 815-8834

CompuServe 74561,606

Internet davidea@haven.ios.com

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

Additional Science Software programs:

NPOE - Numerical Prediction of Orbital Events

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

OrbLib - the Science Software library of orbital mechanics software.

Thank you for using SATPLOT. This program is freeware with no warranties or
liablilties of any kind. Please call, write or e-mail for additional technical
information and to request NPOE and Celestial Computing demo disks. I can also 
provide custom mission analysis software written in either Microsoft (tm) 
QuickBASIC, Turbo PASCAL 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 and data files
available from Science Software. Please call, write or e-mail for additional 
technical information.

    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
	Shadow Conditions of Satellites

    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


		  CELESTIAL COMPUTING ORDERING INFORMATION 

Each volume of Celestial Computing consists of four issues. Both bound volumes 
and individual journal and floppy disk issues are available for the IBM PC and 
true compatible computers. 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 companion computer programs are available on 3 1/2", 1.44 MB capacity 
floppy disks.  Both QuickBASIC source code and executable programs are 
provided on the floppy disks. QuickBASIC is not required to run these programs 
but is necessary if you want to modify the source code. A shareware version of 
Mercury is provided on the Vol. 3, No. 3 disk.

Please submit payment in the form of a personal check or money order (no credit 
cards please), in U.S. dollars and drawn on a U.S. bank, payable to Science 
Software. The costs to countries other than the United States are shown in 
parentheses. These prices include first class shipping within the United 
States and air mail shipping elsewhere. Please send all orders and written 
correspondence to:

       ********************************
       * Science Software             *
       * P.O. Box 2188                *
       * Reston, VA 22090-0188    USA *
       ********************************

    Technical questions - (703) 815-8834

    Compuserve --> 74561,606      
    
    Internet --> davidea@haven.ios.com

    BBS - (703) 815-8834  (6 p.m.-4 a.m. weekdays, 24 hours a day on weekends)

    << Celestial Computing individual journal and floppy disk back issues >>
  
    (please order by volume and issue number(s))

    * Journal 
      Price: $7.95 U.S. ($9.95 elsewhere)  __________________________________
    
    * Floppy Disk 
      Price: $5.95 U.S. ($6.95 elsewhere)  __________________________________
     

    << Celestial Computing bound volumes and companion floppy disk sets >>
  
    *  __ Bound copy of Volume 1          $29.95 U.S.  ($39.95 elsewhere)
    *  __ Floppy disks for Volume 1       $19.95 U.S.  ($29.95 elsewhere)
    
    *  __ Bound copy of Volume 2          $29.95 U.S.  ($39.95 elsewhere)
    *  __ Floppy disks for Volume 2       $19.95 U.S.  ($29.95 elsewhere)
    
    *  __ Bound copy of Volume 3          $29.95 U.S.  ($39.95 elsewhere)
    *  __ Floppy disks for Volume 3       $19.95 U.S.  ($29.95 elsewhere)
    
    *  __ Bound copy of Volume 4          $29.95 U.S.  ($39.95 elsewhere)
    *  __ Floppy disks for Volume 4       $19.95 U.S.  ($29.95 elsewhere)



    Name _______________________________________________________________

    Street address _____________________________________________________

    City, state, zip ___________________________________________________

    Telephone and/or e-mail address ____________________________________


			  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
