org.vizzini.math.orbit
Class OrbitMechanic

java.lang.Object
  org.vizzini.math.orbit.OrbitMechanic

public class OrbitMechanic
extends Object

Provides a helper class for orbit mechanics calculations.

Classical Orbital Elements

Symbol	Description	Units
mu	gravitational parameter	km^3 sec^-2
a	semi-major axis	km
ecc	eccentricity	N/A
i	inclination	radians
omega	longitude of the ascending node	radians
w	argument of periapsis	radians
nu	true anomaly	radians

Additional parameters

Symbol	Description	Units
P	period	sec
n	mean motion	radians/sec
M	mean anomaly	radians
E	eccentric anomaly	radians
t	time	sec
tp	time of periapsis passage	sec

Since:

v0.3

Version:

v0.3

Author:

Jeffrey M. Thompson

Method Summary

protected double	acos(double numerator, double denominator) Compute the arc cosine using the given numerator and denominator.
protected double	checkAngleBounds(double angle) Make the given angle in [0.0, 2*PI].
Vector	computeE(double mu, Vector r, Vector v) Compute the eccentricity vector E.
double	computeEcc(double mu, Vector r, Vector v) Compute the eccentricity.
double	computeEccentricAnomalyFromEccM(double ecc, double meanAnomaly) Compute the eccentric anomaly from the given parameters.
double	computeEccentricAnomalyFromEccM(double ecc, double meanAnomaly, double delta) Compute the eccentric anomaly from the given parameters.
double	computeEccentricAnomalyFromEccNu(double ecc, double trueAnomaly) Compute the eccentric anomaly from the given parameters.
Vector	computeH(Vector r, Vector v) Compute the angular momentum vector H.
double	computeMeanAnomalyFromEccE(double ecc, double eccentricAnomaly) Compute mean anomaly from the given parameters.
double	computeMeanAnomalyFromT(double mu, double a, double m0, double t, double t0) Compute mean anomaly from the given parameters.
double	computeMeanMotion(double mu, double a) Compute mean motion from the given parameters.
Vector	computeN(Vector h) Compute the node vector N.
double	computeOmega(Vector n) Compute the longitude of the ascending node.
double	computePeriod(double mu, double a) Compute period of orbit from the given parameter.
Vector	computeR(double mu, double a, double ecc, double i, double omega, double w, double nu) Compute the position vector for the given orbit elements.
Vector[]	computeRAndV(double mu, double a, double ecc, double i, double omega, double w, double nu) Compute the position and velocity vectors for the given orbit elements.
double	computeSemiLatusRectum(double a, double ecc) Compute the semi-latus rectum.
double	computeSemiMajorAxis(double p, double ecc) Compute the semi-major axis.
double	computeT(double mu, double a, double meanAnomaly, double meanAnomaly0, double t0) Compute time from the given paramters.
double	computeTimeOfPeriapsisPassage(double mu, double a, double ecc, double meanAnomaly0, double t0) Return the time of periapsis passage.
double	computeTrueAnomaly(double ecc, double eccentricAnomaly) Compute the true anomaly from the given parameters.
double	computeTrueAnomaly(Vector e, Vector n, Vector r, Vector v) Compute the true anomaly from the given parameters.
Vector	computeV(double mu, double a, double ecc, double i, double omega, double w, double nu) Compute the velocity vector for the given orbit elements.
double	computeW(Vector e, Vector n) Compute the argument of periapsis.
static OrbitMechanic	getInstance() Return the singleton instance.
boolean	isCircularOrbit(double ecc) Return true if the given eccentricity indicates a circular orbit.
boolean	isEllipticOrbit(double ecc) Return true if the given eccentricity indicates an elliptic orbit.
boolean	isHyperbolicOrbit(double ecc) Return true if the given eccentricity indicates a hyperbolic orbit.
boolean	isParabolicOrbit(double ecc) Return true if the given eccentricity indicates a parabolic orbit.
protected double	quadrantCheck(double angle, double factor) Perform a quadrant check on the given angle.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

getInstance

public static OrbitMechanic getInstance()

Return the singleton instance.

Since:

v0.3

computeE

public Vector computeE(double mu,
                       Vector r,
                       Vector v)

Compute the eccentricity vector E.

Parameters:

mu - Gravitational parameter of central body. (km^3 sec^-2)

r - Position vector. (km)

v - Velocity vector. (km/sec)

Since:

v0.3

computeEcc

public double computeEcc(double mu,
                         Vector r,
                         Vector v)

Compute the eccentricity.

Parameters:

mu - Gravitational parameter of central body. (km^3 sec^-2)

r - Position vector. (km)

v - Velocity vector. (km/sec)

Since:

v0.3

computeEccentricAnomalyFromEccM

public double computeEccentricAnomalyFromEccM(double ecc,
                                              double meanAnomaly)

Compute the eccentric anomaly from the given parameters.

Parameters:

ecc - Eccentricity.

meanAnomaly - Mean anomaly. (radians)

Since:

v0.3

computeEccentricAnomalyFromEccM

public double computeEccentricAnomalyFromEccM(double ecc,
                                              double meanAnomaly,
                                              double delta)

Compute the eccentric anomaly from the given parameters.

Parameters:

ecc - Eccentricity.

meanAnomaly - Mean anomaly. (radians)

delta - Allowable error in mean anomaly.

Since:

v0.3

computeEccentricAnomalyFromEccNu

public double computeEccentricAnomalyFromEccNu(double ecc,
                                               double trueAnomaly)

Compute the eccentric anomaly from the given parameters.

Parameters:

ecc - Eccentricity.

trueAnomaly - True anomaly. (radians)

Since:

v0.3

computeH

public Vector computeH(Vector r,
                       Vector v)

Compute the angular momentum vector H.

Parameters:

r - Position vector. (km)

v - Velocity vector. (km/sec)

Since:

v0.3

computeMeanAnomalyFromEccE

public double computeMeanAnomalyFromEccE(double ecc,
                                         double eccentricAnomaly)

Compute mean anomaly from the given parameters. This method uses Kepler's Equation.

Parameters:

ecc - Eccentricity.

Since:

v0.3

computeMeanAnomalyFromT

public double computeMeanAnomalyFromT(double mu,
                                      double a,
                                      double m0,
                                      double t,
                                      double t0)

Compute mean anomaly from the given parameters.

Parameters:

mu - Gravitational parameter of central body. (km^3 sec^-2)

Since:

v0.3

computeMeanMotion

public double computeMeanMotion(double mu,
                                double a)

Compute mean motion from the given parameters.

Parameters:

mu - Gravitational parameter of central body. (km^3 sec^-2)

a -

Since:

v0.3

computeN

public Vector computeN(Vector h)

Compute the node vector N.

Parameters:

h - Angular momentum vector.

Since:

v0.3

computeOmega

public double computeOmega(Vector n)

Compute the longitude of the ascending node.

Since:

v0.3

computePeriod

public double computePeriod(double mu,
                            double a)

Compute period of orbit from the given parameter.

Parameters:

mu - Gravitational parameter of central body. (km^3 sec^-2)

a - Semi-major axis. (km)

Returns:

orbital period. (sec)

Since:

v0.3

computeR

public Vector computeR(double mu,
                       double a,
                       double ecc,
                       double i,
                       double omega,
                       double w,
                       double nu)

Compute the position vector for the given orbit elements.

Parameters:

mu - Gravitational parameter of central body. (km^3 sec^-2)

a - Semi-major axis. (km)

ecc - Eccentricity.

i - Inclination. (radians)

omega - Longitude of the ascending node. (radians)

w - Argument of periapsis. (radians)

nu - True anomaly at epoch. (radians)

Since:

v0.3

computeRAndV

public Vector[] computeRAndV(double mu,
                             double a,
                             double ecc,
                             double i,
                             double omega,
                             double w,
                             double nu)

Compute the position and velocity vectors for the given orbit elements.

Parameters:

mu - Gravitational parameter of central body. (km^3 sec^-2)

a - Semi-major axis. (km)

ecc - Eccentricity.

i - Inclination. (radians)

omega - Longitude of the ascending node. (radians)

w - Argument of periapsis. (radians)

nu - True anomaly at epoch. (radians)

Since:

v0.3

computeSemiLatusRectum

public double computeSemiLatusRectum(double a,
                                     double ecc)

Compute the semi-latus rectum.

Parameters:

ecc - Eccentricity.

Since:

v0.3

computeSemiMajorAxis

public double computeSemiMajorAxis(double p,
                                   double ecc)

Compute the semi-major axis.

Parameters:

p - Semi-latus rectum. (km)

ecc - Eccentricity.

Since:

v0.3

computeT

public double computeT(double mu,
                       double a,
                       double meanAnomaly,
                       double meanAnomaly0,
                       double t0)

Compute time from the given paramters.

Parameters:

mu - Gravitational parameter of central body. (km^3 sec^-2)

a - Semi-major axis. (km)

meanAnomaly - Mean anomaly at desired time. (radians)

meanAnomaly0 - Mean anomaly at t0. (radians)

t0 - Time of epoch. (sec)

Since:

v0.3

computeTimeOfPeriapsisPassage

public double computeTimeOfPeriapsisPassage(double mu,
                                            double a,
                                            double ecc,
                                            double meanAnomaly0,
                                            double t0)

Return the time of periapsis passage.

Parameters:

mu - Gravitational parameter of central body. (km^3 sec^-2)

a - Semi-major axis. (km)

meanAnomaly0 - Mean anomaly at t0. (radians)

t0 - Time of epoch. (sec)

Since:

v0.3

computeTrueAnomaly

public double computeTrueAnomaly(double ecc,
                                 double eccentricAnomaly)

Compute the true anomaly from the given parameters.

Parameters:

ecc - Eccentricity.

eccentricAnomaly - Eccentric anomaly at time of interest. (radians)

Since:

v0.3

computeTrueAnomaly

public double computeTrueAnomaly(Vector e,
                                 Vector n,
                                 Vector r,
                                 Vector v)

Compute the true anomaly from the given parameters.

Parameters:

e - Eccentricity vector.

n - Normal vector.

r - Position vector. (km)

v - Velocity vector. (km/sec)

Since:

v0.3

computeV

public Vector computeV(double mu,
                       double a,
                       double ecc,
                       double i,
                       double omega,
                       double w,
                       double nu)

Compute the velocity vector for the given orbit elements.

Parameters:

mu - Gravitational parameter of central body. (km^3 sec^-2)

a - Semi-major axis. (km)

ecc - Eccentricity.

i - Inclination. (radians)

omega - Longitude of the ascending node. (radians)

w - Argument of periapsis. (radians)

nu - True anomaly at epoch. (radians)

Since:

v0.3

computeW

public double computeW(Vector e,
                       Vector n)

Compute the argument of periapsis.

Parameters:

e - Eccentricity vector.

n - Normal vector.

Since:

v0.3

isCircularOrbit

public boolean isCircularOrbit(double ecc)

Return true if the given eccentricity indicates a circular orbit.

Parameters:

ecc - Eccentricity.

Since:

v0.3

isEllipticOrbit

public boolean isEllipticOrbit(double ecc)

Return true if the given eccentricity indicates an elliptic orbit.

Parameters:

ecc - Eccentricity.

Since:

v0.3

isHyperbolicOrbit

public boolean isHyperbolicOrbit(double ecc)

Return true if the given eccentricity indicates a hyperbolic orbit.

Parameters:

ecc - Eccentricity.

Since:

v0.3

isParabolicOrbit

public boolean isParabolicOrbit(double ecc)

Return true if the given eccentricity indicates a parabolic orbit.

Parameters:

ecc - Eccentricity.

Since:

v0.3

acos

protected double acos(double numerator,
                      double denominator)

Compute the arc cosine using the given numerator and denominator.

Since:

v0.3

checkAngleBounds

protected double checkAngleBounds(double angle)

Make the given angle in [0.0, 2*PI].

Parameters:

angle - Angle. (radians)

Since:

v0.3

quadrantCheck

protected double quadrantCheck(double angle,
                               double factor)

Perform a quadrant check on the given angle.

Parameters:

angle - Angle.

factor - Factor which determines if the angle should be less than PI radians.

Since:

v0.3