Orbital Mechanics with MATLAB


Welcome

This web site describes a collection of MATLAB scripts and functions called Orbital Mechanics with MATLAB.  This software can be used to solve a variety of practical problems in orbital mechanics, applied astrodynamics and astrometry.  MATLAB scripts and functions are provided for solving spaceflight problems in the areas of orbit design, event prediction and trajectory optimization.

 

These MATLAB scripts and support functions are available in the File Exchange area of the Mathworks website located at www.mathworks.com/matlabcentral/fileexchange/authors/30927 (author name: David Eagle).

 

Please be sure to read any special script requirements posted on the File Exchange description page.

 

Several Orbital Mechanics with MATLAB scripts also use the SNOPT nonlinear programming algorithm.  Platform specific versions of the SNOPT mex file and MATLAB support functions can be downloaded at https://ccom.ucsd.edu/~optimizers.  Please use the versions of SNOPT dated 6.15.2013 located in the DOWNLOADS section.

 

This website also contains links for several binary ephemeris files which are required for several MATLAB scripts.  They can be found in the DOWNLOADS section of this website.  The DOWNLOADS section also includes MATLAB scripts and companion PDF documents that are not posted in the Mathworks File Exchange area.

 

 

Last updated  April 16, 2014

 

Thanks for visiting.


The following is a list of the analysis scripts and functions included in the Orbital Mechanics with MATLAB software suite.

Astrodynamic Coordinates

 

·       A MATLAB Script for Time and Coordinate Calculations

·       Geodetic and Geocentric Coordinates

·       Terrestrial and Celestial Coordinate Conversion

·       Mean Local Time of the Ascending Node

·       A MATLAB Script for Greenwich Sidereal Time with NOVAS

·       True-of-Date and EME2000 Coordinate Conversion (NOVAS)

 

Orbital Periods of a Satellite

 

·       Keplerian – the unperturbed or two-body period

·       Nodal – the time interval from one ascending (or descending) node to the next

·       Anomalistic – the time interval from one perigee to the next

·       Sidereal – the time interval from one value of argument of latitude to the next identical value

 

Cowell's Method

 

·       Cowell’s Method for Earth Satellites

·       Cowell’s Method - MICE routines

 

Encke's Method

 

·       Geocentric orbits

·       Heliocentric orbits

 

Methods of Orbit Design

 

·       Sun-synchronous Orbit Design

·       Frozen Orbit Design

·       Repeating Ground Track Orbit Design

·       Composite Orbit Design

 

Orbital Maneuvers

 

·       Circular Orbit Plane Change

·       Optimal Impulsive Orbital Transfer

·       Bi-elliptic Transfer Between Coplanar Circular Orbits

·       Aero-assist Orbital Transfer

·       Low thrust orbit transfer using solar-electric propulsion

·       Single impulse De-orbit

·       A MATLAB Script for Optimal Single Impulse De-orbit From Earth Orbits

·       Aero-assisted co-planar orbital transfer

·       Hohmann two impulse orbital transfer

·       Gravity Perturbed Hohmann Transfer

·       Bi-elliptic transfer between coplanar circular orbits

·       A MATLAB Script for Designing Low-thrust Spiral trajectories with Constant Periapsis Radius

·       Low-thrust Transfer Between Non-coplanar Circular Orbits

·       Two Impulse Phasing Analysis

 

Lambert's Problem

 

·       Earth orbit solution

·       Interplanetary solution

·       Earth orbit solution – perturbed orbital motion – shooting method

·       Earth orbit solution – perturbed orbital motion – NLP method

 

Circular-Restricted Three-Body Problem

 

·       Coordinates and energy of the libration points

·       Graphics display of three-body motion

·       Graphics display of zero velocity curves

·       Graphics display of user-defined zero relative velocity

 

Numerical Methods and Trajectory Modeling

 

·       Kepler’s Equation

·       A MATLAB Implementation of the Jacchia Atmosphere Model

·       Trajectory Modeling in the Flight Path System

·       Modeling Aero-assist Flight Mechanics with MATLAB

·       Long-term Evolution of Geosynchronous Transfer Orbits

 

Ephemeris and Astrometry

 

·       Low precision Ephemeris

·       Precision Sun Ephemeris

·       Orbital Elements of the Moon

·       Apparent Position of a Star

·       Ephemeris Calculations with MICE

·       MATLAB Versions of NOVAS

·       A MATLAB Implementation of the IAU 2000A Nutation Theory

·       A MATLAB Implementation of the IAU 2000B Nutation Theory

·       A MATLAB Implementation of the IAU 1980 Nutation Theory

·       A MATLAB Implementation of the SLP96 Ephemeris

·       A MATLAB Implementation of the JPL Ephemeris

·       Apparent Coordinates of the Moon, Sun and Planets

·       Rise and Set of the Sun, Moon and Planets

·       A MATLAB Script for Predicting Lunar Occultations

·       A MATLAB Script for Predicting Lunar Eclipses

·       A MATLAB Script for Predicting Transits of Mercury and Venus

·       Predicting Equinoxes and Solstices

·       A MATLAB Script for Predicting Solar Eclipses

·       Closest Approach Between the Earth and Heliocentric Objects

·       Predicting Apogee and Perigee of the Moon

·       A MATLAB Script for Predicting Orbital Events of the Moon

·       Graphics Display of the Orbital Characteristics of the Moon

·       Graphics Display of the Orbital Characteristics of the Planets

·       Predicting Orbital Events of the Planets

 

Lunar Mission Analysis

 

·       Parametric Analysis of Minimum TLI Delta-v, Lunar Transfer Trajectories

·       A MATLAB Script for Propagating Trajectories from the Earth to the Moon

·       A MATLAB Script for Predicting the Evolution of Lunar Orbits

·       Lunar Free-Return Trajectory Analysis with MATLAB

·       Selenocentric Coordinates and Transformations

 

Interplanetary Mission Analysis

 

·       Interplanetary Pork Chop Plots

·       Impulsive Hyperbolic Injection from a Circular Park Orbit

·       Impulsive Hyperbolic Injection from a Circular Park Orbit – NLP Solution

·       Optimal Finite-burn Interplanetary Injection from Earth Orbit

·       A MATLAB Script for Designing Interplanetary Launch Trajectories

·       Ballistic Interplanetary Trajectory Design and Optimization

·       Gravity-assist Trajectory Design and Analysis

·       A MATLAB Script for Earth-to-Mars Mission Design

·       Two-dimensional, Low-thrust Earth-to-Mars Trajectory Analysis with MATLAB

·       Solar Sail Trajectory Analysis with MATLAB

·       A MATLAB Script for Propagating Interplanetary Trajectories from Earth to Mars

·       A MATLAB Script for Computing the Energy and Orientation of a Hyperbolic Orbit

·       B-Plane Coordinates

 

DOWNLOADS

 

Binary Ephemeris Data Files

 

Please note that these binary ephemeris files are compatible with Windows computers.  The JPL DE binary files have also been tested on an Intel-based MacBook Pro.

 

SLP96 ephemeris binary data file (~6 MB)

JPL DE405 ephemeris binary data file (~6 MB)

JPL DE421 ephemeris binary data file (~14 MB)

JPL DE424 ephemeris binary data file (~18 MB)

JPL DE430 ephemeris binary data file (~27 MB)

INPOP06c ephemeris binary data file (~17 MB)

INPOP08a ephemeris binary data file (~17 MB)

 

Additional MATLAB scripts and companion PDF documents (zipped files)

 

Shadow Conditions of Earth Satellites

Numerical Prediction of Orbital Events

Rise and Set of Earth Satellites

The Design and Analysis of Geosynchronous Orbits

Coverage Characteristics of Earth Satellites

Graphics Display of Satellite Ground Tracks and Orbits

Mutual Visibility Between Two Earth Satellites

Closest Approach Between Two Earth Satellites

 


Web site contents copyright © 1996-2014 by C. David Eagle.  All rights reserved.

cdeaglejr@yahoo.com          www.cdeagle.com