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Celestial Computing

A Journal for Personal Computers and Celestial Mechanics

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 that 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, 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 that 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 that 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 that emphasizes computer graphics to illustrate many fundamental concepts of celestial mechanics and astronomy. Each issue also contains a book and software review.

The written journal contains a technical discussion about each article and instructions that explain how to use the software. The Celestial Computing companion software is provided in both source code and executable form. The majority of the programs are written in Microsoft QuickBASIC. 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. You are encouraged to examine the Celestial Computing source code and modify it for your own needs. These programs will also run with the QBASIC interpreter included with MS-DOS 5.0/6.2 and the PowerBASIC compiler with minor changes.

Please note that Celestial Computing was published between 1988 and 1992 and future subscriptions are no longer available.

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 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 Mathematicaâ

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

Electronic (PDF) copies of the journal

Volume 1, Number 1 Volume 1, Number 2

Volume 1, Number 3 Volume 1, Number 4

Volume 2, Number 1 Volume 2, Number 2

Volume 2, Number 3 Volume 2, Number 4

Volume 3, Number 1 Volume 3, Number 2

Volume 3, Number 3 Volume 3, Number 4

Volume 4, Number 1 Volume 4, Number 2

Volume 4, Number 3 Volume 4, Number 4

Example Executable Programs

A Computer Program for Predicting Solar Eclipses

A Computer Program for Predicting Lunar Eclipses

A Computer Program for Predicting Planetary Events

A Computer Program for Predicting Transits

Companion Celestial Computing software (source code and executable programs)

The cost of the companion software is $99. The software can be purchased using the secure and flexible e-commerce services provided by PayPal. After placing your order, you will receive an email, within 24 hours, with a password that can be used to extract the zipped source code and executable programs.

Click here to order.

Click here to download the Zipped companion software file (password protected)