Table of Contents

Class OrbitalMotionLibrary

Namespace
NominalSystems.Universe
Assembly
NominalSystems.Universe.dll

Helper library for Orbital motion functions. These include Classical (Keplerian) elements, Vector Elements, Two Line Elements, Hill Frame and general orbital motion. All methods are public and can be used by any class at any point in time.

public static class OrbitalMotionLibrary
Inheritance
OrbitalMotionLibrary

Methods

CalculateClassicalAtTime(ClassicElements, double, double) 

public static ClassicElements CalculateClassicalAtTime(ClassicElements initial, double mu, double time)

Parameters

initial ClassicElements
mu double
time double

Returns

ClassicElements

ClassicalElem2VectorElem(double, ClassicElements)

Converts a classic elements to a vector elements based on the MU of the body

public static VectorElements ClassicalElem2VectorElem(double mu, ClassicElements classicElements)

Parameters

mu double

[-] Gravitational MU parameter

classicElements ClassicElements

[-] A classical elements struct

Returns

VectorElements

[-] A vector element struct

CreateFrozenOrbit(GravityBody, SpiceTimeMessage, double, double)

Creates a frozen orbit based on some parameters. This assumes that the orbit will pass over the same ground location at the same local time of day each time.

public static ClassicElements CreateFrozenOrbit(GravityBody planet, SpiceTimeMessage time, double semiMajorAxis, double timeOfDay = 0)

Parameters

planet GravityBody

[-] The orbiting planet to orbit around

time SpiceTimeMessage

[-] The SPICE time message of the current epoch

semiMajorAxis double

[m] The SMA of the orbit

timeOfDay double

[h] The time of day between 0 and 24 hours

Returns

ClassicElements

[-] The classical elements of the orbit for the SSO

CreateSunSynchronousOrbit(GravityBody, SpiceTimeMessage, double, double, double)

Creates a sun synchronous orbit based on some parameters. This will return the classical elements associated with a sun synchronous orbit. An SSO will pass the Earth's equator at a fixed time of day, which is defined by the timeOfDay parameter.

public static ClassicElements CreateSunSynchronousOrbit(GravityBody planet, SpiceTimeMessage time, double semiMajorAxis, double eccentricity = 0, double timeOfDay = 0)

Parameters

planet GravityBody

[-] The orbiting planet to orbit around

time SpiceTimeMessage

[-] The SPICE time message of the current epoch

semiMajorAxis double

[m] The SMA of the orbit

eccentricity double

[-] The eccentricity of the orbit

timeOfDay double

[h] The time of day between 0 and 24 hours

Returns

ClassicElements

[-] The classical elements of the orbit for the SSO

Eccentric2MeanAnom(double, double)

Maps the eccentric anomaly angle into the corresponding mean elliptic anomaly angle. Both 2D and 1D elliptic orbit are allowed.

public static double Eccentric2MeanAnom(double eccentricAnom, double eccentricity)

Parameters

eccentricAnom double

[rad] Eccentric anomaly

eccentricity double

[-] Eccentricity(0 <= e > 1)

Returns

double

[rad] Mean elliptic anomaly

Eccentric2TrueAnom(double, double)

Converts the Eccentric Anomaly to the True Anomaly

public static double Eccentric2TrueAnom(double eccentricAnom, double eccentricity)

Parameters

eccentricAnom double

[rad] The Eccentric Anomaly

eccentricity double

[-] The eccentricity of the orbit (0 <= e > 1)

Returns

double

[rad] The True Anomaly

GetMeanMotion(double, double)

Calculates the mean motion of a particular orbit with some semi major axis.

public static double GetMeanMotion(double mu, double semiMajorAxis)

Parameters

mu double

[m^3 s^-2] The gravitational MU parameter of the planet orbiting

semiMajorAxis double

[m] The SMA of the orbit

Returns

double

[s^-2] The mean motion for the orbit

GetSMAFromPeriod(double, double)

Returns the Semi Major Axis (SMA) from an Orbital Period in seconds.

public static double GetSMAFromPeriod(double mu, double period)

Parameters

mu double

The primary body gravitational parameter

period double

[s] The orbital period

Returns

double

[m] The semi major axis of the orbit

GetSemiLactusRectum(double, double)

Calculates the cross section of the semi-major lactus of the orbit.

public static double GetSemiLactusRectum(double semiMajorAxis, double eccentricity)

Parameters

semiMajorAxis double

[m] The SMA of the orbit

eccentricity double

[-] The eccentricity of the orbit

Returns

double

[m] The Semi Lactus Rectum parameter

GetSunSynchronousInclination(GravityBody, double, double)

Returns the inclination in radians of a defined SSO orbit based on the semi major axis and desired eccentricity of the orbit.

public static double GetSunSynchronousInclination(GravityBody planet, double semiMajorAxis, double eccentricity = 0)

Parameters

planet GravityBody

[-] The orbiting planet to orbit around

semiMajorAxis double

[m] The SMA of the orbit

eccentricity double

[-] The eccentricity of the orbit

Returns

double

[rad] The inclination angle of the orbit

GetSunSynchronousInclinationEstimate(double, double, double, double, double, double)

Calculates the sun synchronous inclination estimate based on the position of the planet relative to the sun and the mean and peturbed motion of the orbit.

public static double GetSunSynchronousInclinationEstimate(double meanMotion, double perturbedMotion, double bodyRadius, double bodyOrbit, double bodyJ2, double bodyParentMu)

Parameters

meanMotion double

[s^-2] The mean motion of the orbit

perturbedMotion double

[s^-2] The perturbed motion of the orbit

bodyRadius double

[m] The radius of the orbting body

bodyOrbit double

[m] The sun-body radius of the orbit of the orbiting body

bodyJ2 double

[-] The orbiting body J2 value

bodyParentMu double

[m^3 s^-2] The gravitational Mu parameter of the parent of the orbital body

Returns

double

[rad] The estimated inclination of the orbit

Hill2VectorElem(Vector3, Vector3, Vector3, Vector3)

Maps Hill frame deputy states to inertial inertial position and velocity vectors

public static VectorElements Hill2VectorElem(Vector3 rc_N, Vector3 vc_N, Vector3 rho_H, Vector3 rhoPrime_H)

Parameters

rc_N Vector3

[m] Chief inertial position vector

vc_N Vector3

[m/s] Chief inertial velocity vector

rho_H Vector3

[m] Deputy Hill position vector

rhoPrime_H Vector3

[m/s] Deputy Hill velocity vector

Returns

VectorElements

[-] The vector elements of the other body

InertialFrameToHillFrame(Vector3, Vector3)

Maps inertial position and velocity vectors in the Hill frame DCM HN

public static Matrix3 InertialFrameToHillFrame(Vector3 rc_N, Vector3 vc_N)

Parameters

rc_N Vector3

[m] Inertial position vector

vc_N Vector3

[m/s] Inertial velocity vector

Returns

Matrix3

[-] Hill frame DCM relative to inertial frame

Mean2EccentricAnom(double, double)

Converts the Mean Anomaly to the Eccentric Anomaly

public static double Mean2EccentricAnom(double meanAnom, double eccentricity)

Parameters

meanAnom double

[rad] The Mean Anomaly

eccentricity double

[-] The eccentricity of the orbit (0 <= e > 1)

Returns

double

[rad] The Eccentric Anomaly

Mean2OscElem(double, double, ClassicElements, bool)

First-order J2 Mapping Between Mean and Osculating Orbital Elements Analytical Mechanics of Space Systems, Hanspeter Schaub, John L. Junkins, 4th edition. [m] or [km] should be the same both for req and elements.

public static ClassicElements Mean2OscElem(double Req, double J2, ClassicElements OE, bool MeanToOsc)

Parameters

Req double

[-] Equatorial radius or the orbital body

J2 double

[-] J2 parameter for the orbital body of interest

OE ClassicElements

[-] Classical orbit element set

MeanToOsc bool

[-] Sgn=True:mean to osc, Sgn=False:osc to mean

Returns

ClassicElements

[-] A classical element struct

Period(double, double)

Calculate the period of the orbit

public static double Period(double mu, double semiMajorAxis)

Parameters

mu double

The primary body gravitational parameter

semiMajorAxis double

[m] The orbit semi-major axis

Returns

double

[s] The orbit time in seconds

Exceptions

Exception

An error in the SMA or Mu will throw an error

ProgressByTime(VectorElements, double, double)

Progresses some Vector Elements that are about some orbital body with a Mu by some time. This will predict where the orbit will be after a specific amount of seconds.

public static VectorElements ProgressByTime(VectorElements initial, double mu, double delta)

Parameters

initial VectorElements

[m] The initial vector elements to start with

mu double

[m3 s−2] The orbiting planet's Mu

delta double

[s] The time to progress by

Returns

VectorElements

[m] The final vector elements that have been progressed by a certain amount of time

TLE2ClassicElements(TwoLineElements)

Converts The TLE to Classic Elements

public static ClassicElements TLE2ClassicElements(TwoLineElements tle)

Parameters

tle TwoLineElements

The Two Line Elements data

Returns

ClassicElements

The Classic Elements data

True2EccentricAnom(double, double)

Maps true anomaly angles into eccentric anomaly angles. This function requires the orbit to be either circular or non - rectilinear elliptic orbit.

public static double True2EccentricAnom(double trueAnom, double eccentricity)

Parameters

trueAnom double

[rad] True anomaly angle

eccentricity double

[-] Eccentricity (0 <= e > 1)

Returns

double

[rad] Eccentric anomaly

True2MeanAnom(double, double)

Calculate the mean anomaly from the true anomaly

public static double True2MeanAnom(double trueAnom, double eccentricity)

Parameters

trueAnom double

[rad] The true anomaly of the orbit

eccentricity double

[-] The eccentricity of the orbit (0 <= e > 1)

Returns

double

[rad] Mean elliptic anomaly

VectorElem2ClassicalElem(double, VectorElements)

Converts a vector elements to a classic elements based on the MU of the body

public static ClassicElements VectorElem2ClassicalElem(double mu, VectorElements rv)

Parameters

mu double

[-] Gravitational MU parameter

rv VectorElements

[-] A vector elements struct

Returns

ClassicElements

[-] A classic element struct