Orbital utilities relating to classical orbital elements (COE) and converting between (r,v) <=> COE. More...

Classes
class	COE
	Classical orbit elements. More...

struct	COEStruct
	Light weight struct to hold COE core data for the job system and propagators. More...

Public Types
enum	OrbitPoint { APOAPSIS , PERIAPSIS , ASC_NODE , DESC_NODE , TRUEANOM_DEG }

enum	OrbitType { UNKNOWN , CIRCULAR_EQUATORIAL , CIRCULAR_INCLINED , ELLIPSE_EQUATORIAL , ELLIPSE_INCLINED , HYPERBOLA , FREEFALL }

Static Public Member Functions
static bool	CheckHitPlanet (double planetRadius, double planetMass, double3 r1c, double3 v1tc, double3 r2c, double3 v2tc, int nrev)

static bool	COEEqual (COE coe1, COE coe2, bool includePhase, double sizeTol=1E-2, double angleRadTol=1E-3)
	Determine if two COEs are equal within the indicated tolerances.

static double3 double3 v	COEStructWithPhasetoRVRelative (COEStruct coe, double phaseRad)

static double3 double3 v	COEtoRVatTime (COE coe, double time)

static double3 double3 v	COEtoRVRelative (COE oe)

static double3 double3 v	COEWithPhasetoRVRelative (COE oe, double phaseRad)

static double	ConvertEtoMeanAnomoly (double eValue, double ecc)

static double	ConvertEtoTrueAnomoly (double eValue, double ecc)
	Convert the eccentric anomaly (angle from center of ellipse wrt x-axis) to the true anomoly (angle from focus wrt periapsis/x-axis if e=0).

static double	ConvertMeanAnomolyToE (double M, double ecc)

static double	ConvertMeanToTrueAnomoly (double M, double ecc)

static double	ConvertTrueAnomolytoE (double nu, double ecc)

static void	FindC2C3 (double znew, out double c2new, out double c3new)
	Taken from Vallado source code site. (Also used in LambertUniversal) Internal use only.

static double	FlightPathAngle (double3 r, double3 v)

static double	GreenwichSiderealTime (double jdut1)

static double3	LaunchPlane (double targetInclDeg, double3 r, double latitudeDeg)
	Determine the orbit normal for a launch from an point at the given latitude into an orbit of specified inclination.

static double3	OrbitAxis (COE coe)
	Determine the orbit axis (normalized)

static double	PhaseAngleRadiansForDirection (double3 pos, COE coe)
	Determine the phase in radians for the specified direction. This can be a point on the orbit but this is not required as only the direction of the given vector is used.

static double	PhaseForOrbitPoint (COE coe, OrbitPoint point, double deg=0)
	Determine the phase for a specific OrbitPoint in an orbit (e.g. APOAPSIS)

static double	PhaseForRadius (COE coe, double radius)
	Determine phase for a given radius. There are two valid responses, phase and -phase (or 2 Pi - phase). This return +phase.

static double3	PositionForCOE (COE coe, double phaseRad)
	Given a COE and phase (radians) determine the relative position in the orbit. The length scale used will match the length scale used in the COE initialization.

static double3	PositionsForR (COE coe, double r)

static double3	RotateToOrbitFrame (COE coe, double3 r)
	Rotate a 3D vector specified with respect to the default orbit frame (XY orbital plane) into the 3D space where the orientation is adjusted by inclination, omegaU and omegaL.

static void	RSWState (ref GEBodyState ship, ref GEBodyState planet, double3 orbitNormal, ref GEBodyState rswState)
	Given the state of a ship and planet determine the state info in the RSW frame in which: R is the radial vector to the planet S is along track W is cross track (see Vallado 3.3 p159 (5th ed))

static double3	RVForOrbitPoint (COE coe, OrbitPoint point, double deg=0)

static COE	RVtoCOE (double3 r, double3 v, double mu, double small=1e-6)
	Given state information (r,v) and mu=GM determine the classical orbital elements (COE).

static double	TimeOfFlight (double3 r0, double3 r1, COE coe)
	Determine the time of flight in COE relevant units that it takes for the body in orbit to go from position r0 to position r1 in an orbit with given COE.

static double3	VDirFromFPAandRR (double fpa, double3 r1, double3 r2)
	Given a FPA and two position vectors, return the velocity vector direction.

static double3	VelocityForCircularOrbitRelative (GEBodyState body, double mu)
	Compute the 3D velocity for a circular velocity for the given 3D body state (r, v) around a mass with specified mu (=GM)

static double3	VelocityForCOE (COE coe, double phaseRad)
	Determine the 3D velocity vector for a COE at the specified phase.

static bool	VelocityIsPrograde (double3 r, double3 v_now, double3 v_next)
	Determine if the given velocities v_now and v_next are both oriented in the same direction around the orbit.

static double	VelocityMagnitudeForCircular (double r, double mu)
	Determine the magnitude of a circular orbit for a given radius around a body of given mu.

Static Public Attributes
static	double3
	Determine the two possible 3D positions in an orbit that are at the specified radius.

static double3	r
	Determine the relative R and V for a specified set of classical orbital elements and a GM (mu) for the body at the center of the orbit.

const double	SMALL_ANGLE = 1E-3

const double	SMALL_E = 1E-3

const double	SMALL_P = 1E-6

const double	SMALL_SME = 1E-6

Detailed Description

Orbital utilities relating to classical orbital elements (COE) and converting between (r,v) <=> COE.

A number of these algorithms originate with Vallado's excellent "Fundamentals of Astrodynamics and Applications" (Microcosm Press) and their adaptations in the original Gravity Engine asset.

There are also some other useful algorithms.

Member Function Documentation

◆ COEEqual()

static bool GravityEngine2.Orbital.COEEqual	(	COE	coe1,
		COE	coe2,
		bool	includePhase,
		double	sizeTol = 1E-2,
		double	angleRadTol = 1E-3 )

static

Determine if two COEs are equal within the indicated tolerances.

Phase comparison can be excluded (Useful when getting COE for display orbit, where the phase does not matter)

Parameters

coe1
coe2
includePhase
sizeTol
angleRadTol

Returns

◆ ConvertEtoTrueAnomoly()

static double GravityEngine2.Orbital.ConvertEtoTrueAnomoly	(	double	eValue,
		double	ecc )

static

Convert the eccentric anomaly (angle from center of ellipse wrt x-axis) to the true anomoly (angle from focus wrt periapsis/x-axis if e=0).

Equations from front cover of Vallado.

Parameters

eValue
ecc

Returns

◆ FindC2C3()

static void GravityEngine2.Orbital.FindC2C3	(	double	znew,
		out double	c2new,
		out double	c3new )

static

Taken from Vallado source code site. (Also used in LambertUniversal) Internal use only.

Parameters

znew
c2new
c3new

◆ LaunchPlane()

static double3 GravityEngine2.Orbital.LaunchPlane	(	double	targetInclDeg,
		double3	r,
		double	latitudeDeg )

static

Determine the orbit normal for a launch from an point at the given latitude into an orbit of specified inclination.

This assumes that a check that inclination > latitude has already been done.

Parameters

targetInclDeg
r
latitudeDeg

Returns: normal to orbit plane

◆ OrbitAxis()

static double3 GravityEngine2.Orbital.OrbitAxis ( COE coe )

static

Determine the orbit axis (normalized)

Parameters

coe

Returns: orbit axis

◆ PhaseAngleRadiansForDirection()

static double GravityEngine2.Orbital.PhaseAngleRadiansForDirection	(	double3	pos,
		COE	coe )

static

Determine the phase in radians for the specified direction. This can be a point on the orbit but this is not required as only the direction of the given vector is used.

Parameters

pos	direction relative to the orbit center
coe	orbital elements for the orbit

Returns: phase in the specified direction (radians)

◆ PhaseForOrbitPoint()

static double GravityEngine2.Orbital.PhaseForOrbitPoint	(	COE	coe,
		OrbitPoint	point,
		double	deg = 0 )

static

Determine the phase for a specific OrbitPoint in an orbit (e.g. APOAPSIS)

Parameters

coe
point
deg

Returns: phase in radians

◆ PhaseForRadius()

static double GravityEngine2.Orbital.PhaseForRadius	(	COE	coe,
		double	radius )

static

Determine phase for a given radius. There are two valid responses, phase and -phase (or 2 Pi - phase). This return +phase.

Parameters

coe
radius

Returns: phase in radians

◆ PositionForCOE()

static double3 GravityEngine2.Orbital.PositionForCOE	(	COE	coe,
		double	phaseRad )

static

Given a COE and phase (radians) determine the relative position in the orbit. The length scale used will match the length scale used in the COE initialization.

Parameters

coe
phaseRad

Returns: relative position in orbit

◆ RotateToOrbitFrame()

static double3 GravityEngine2.Orbital.RotateToOrbitFrame	(	COE	coe,
		double3	r )

static

Rotate a 3D vector specified with respect to the default orbit frame (XY orbital plane) into the 3D space where the orientation is adjusted by inclination, omegaU and omegaL.

Parameters

coe
r

Returns: rotated vector

◆ RSWState()

static void GravityEngine2.Orbital.RSWState	(	ref GEBodyState	ship,
		ref GEBodyState	planet,
		double3	orbitNormal,
		ref GEBodyState	rswState )

static

Given the state of a ship and planet determine the state info in the RSW frame in which: R is the radial vector to the planet S is along track W is cross track (see Vallado 3.3 p159 (5th ed))

The position vector defines R The orbit normal is used to define the axis for cross track. The cross of R and W defines S.

Parameters

ship
planet
rswState

◆ RVtoCOE()

static COE GravityEngine2.Orbital.RVtoCOE	(	double3	r,
		double3	v,
		double	mu,
		double	small = 1e-6 )

static

Given state information (r,v) and mu=GM determine the classical orbital elements (COE).

Classical orbital elements have inherent singularities for: circular orbits (e=0) flat orbits (i=0 or Pi radians)

In this case the sense of how small is zero is set by the optional parameter small.

In the case of circular orbits there is no closest approach point from which to measure phase nu. For circular orbits the X-axis defines nu=0.

In the case of a flat orbit, there is no ascending node to provide a reference for omegaU. It is set to zero.

See the discussion in the Orbits section of the documentation for other information.

Parameters

r
v
mu
small (optional) threshold for detecting circular/flat orbits

Returns: COE (struct containing orbit elements)

◆ TimeOfFlight()

static double GravityEngine2.Orbital.TimeOfFlight	(	double3	r0,
		double3	r1,
		COE	coe )

static

Determine the time of flight in COE relevant units that it takes for the body in orbit to go from position r0 to position r1 in an orbit with given COE.

Parameters

r0	from position in orbit
r1	to position in orbit
coe	COE struct describing the orbit

Returns: time to move from r0 to r1

◆ VDirFromFPAandRR()

static double3 GravityEngine2.Orbital.VDirFromFPAandRR	(	double	fpa,
		double3	r1,
		double3	r2 )

static

Given a FPA and two position vectors, return the velocity vector direction.

Parameters

fpa
r1
r2

Returns

◆ VelocityForCircularOrbitRelative()

static double3 GravityEngine2.Orbital.VelocityForCircularOrbitRelative	(	GEBodyState	body,
		double	mu )

static

Compute the 3D velocity for a circular velocity for the given 3D body state (r, v) around a mass with specified mu (=GM)

Parameters

body	struct with r, v state
mu	center body mass

Returns: 3D circular velocity vector

◆ VelocityForCOE()

static double3 GravityEngine2.Orbital.VelocityForCOE	(	COE	coe,
		double	phaseRad )

static

Determine the 3D velocity vector for a COE at the specified phase.

Parameters

coe
phaseRad

Returns: 3D velocity

◆ VelocityIsPrograde()

static bool GravityEngine2.Orbital.VelocityIsPrograde	(	double3	r,
		double3	v_now,
		double3	v_next )

static

Determine if the given velocities v_now and v_next are both oriented in the same direction around the orbit.

This is used in Lambert transfer calculations to select the transfer option that matches the current direction in the orbit

Parameters

r	position in the orbit
v_now	current velocity
v_next	velocity after possible maneuver

Returns: true if v_next is in same direction as v_now

◆ VelocityMagnitudeForCircular()

static double GravityEngine2.Orbital.VelocityMagnitudeForCircular	(	double	r,
		double	mu )

static

Determine the magnitude of a circular orbit for a given radius around a body of given mu.

Parameters

r	agnitude of radius
mu	mu of center body (GM)

Returns

Member Data Documentation

◆ double3

static GravityEngine2.Orbital.double3

static

Determine the two possible 3D positions in an orbit that are at the specified radius.

Determine the 3D position and velocity (relative to the center) for the specified type of OrbitPoint.

Parameters

coe
r

Returns: (pos1, pos2) two 3D positions

Parameters

coe
point
deg

Returns: (pos, vel) relative 3D position and velocity

◆ r

static double3 GravityEngine2.Orbital.r

static

Determine the relative R and V for a specified set of classical orbital elements and a GM (mu) for the body at the center of the orbit.

Determine state from COE and a time from current phase in COE. This used a KeplerPropagator and it might be better to use this approach directly if this will be used more than once.

COEStruct version to determine relative position and velocity for a given COE and phase.

Determine the relative position and velocity for the point in an orbit specified by the COE at the given phase in radians.

Parameters

oe
mu

Returns

Parameters

oe
phaseRad

Returns: (pos, vel) relative position and velocity

Used in job system (PKEPLER) to determine R, V

Parameters

coe
phaseRad

Returns: (pos, vel) relative position and velocity

Parameters

coe
time

Returns

The documentation for this class was generated from the following file:

ge2/GE2/Assets/GravityEngine2/Runtime/Core/Orbital.cs

Classes

Public Types

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Function Documentation

◆ COEEqual()

◆ ConvertEtoTrueAnomoly()

◆ FindC2C3()

◆ LaunchPlane()

◆ OrbitAxis()

◆ PhaseAngleRadiansForDirection()

◆ PhaseForOrbitPoint()

◆ PhaseForRadius()

◆ PositionForCOE()

◆ RotateToOrbitFrame()

◆ RSWState()

◆ RVtoCOE()

◆ TimeOfFlight()

◆ VDirFromFPAandRR()

◆ VelocityForCircularOrbitRelative()

◆ VelocityForCOE()

◆ VelocityIsPrograde()

◆ VelocityMagnitudeForCircular()

Member Data Documentation

◆ double3

◆ r