Detailed Description

class EarthOrientation encapsulates the Earth orientation parameters or EOPs, which consist of the polar motion angle xp and yp and the time offset UT1-UTC. These three parameters are determined by interpolating measured values managed by class EOPStore. Also, this class includes several static functions that implement the models in the IERS Conventions (1996, 2003 or 2010), many of which involve the EOPs. This includes the frame transformation between the conventional terrestrial (i.e. ECEF) frame and the conventional celestial (inertial) frame. The class implements models of precession and nutation of Earth's axis, as well as the precise rotation of Earth and its 'wobble' as given by the EOPs. The class requires time to be in one of two systems: UTC or TT; class EphTime is a simple class that enforces this requirement (plus TDB), transformation to and from CommonTime should be automatic. (TT is terrestrial and TDB is barycentric dynamic time, which is the time of SolarSystemEphemeris.) Also cf. classes EOPStore and SolarSystem. References: IERS1996: IERS Technical Note 21, "IERS Conventions (1996)," Dennis D. McCarthy, U.S. Naval Observatory, 1996. IERS2003: IERS Technical Note 32, "IERS Conventions (2003)," Dennis D. McCarthy and Gerard Petit eds., U.S. Naval Observatory and Bureau International des Poids et Mesures, 2004. IERS2010: IERS Technical Note 36, "IERS Conventions (2010)," Gerard Petit and Brian Luzum eds., Bureau International des Poids et Mesures and U.S. Naval Observatory, 2010.

Definition at line 93 of file EarthOrientation.hpp.

#include <EarthOrientation.hpp>

Public Member Functions
	EarthOrientation ()
	Constructor. More...

Matrix< double >	ECEFtoInertial (const EphTime &t, bool reduced=false)

Matrix< double >	ECEFtoJ2000 (const EphTime &t, bool reduced=false)

double	GAST (const EphTime &t, bool reduced=false)

double	GMST (const EphTime &t, bool reduced=false)

void	interpolateEOP (const EphTime &ttag, const std::vector< double > &time, const std::vector< double > &X, const std::vector< double > &Y, std::vector< double > &dT, const IERSConvention &conv)

Matrix< double >	nutationMatrix (const EphTime &t)

double	obliquity (double T)

Matrix< double >	polarMotionMatrix (const EphTime &t)

Matrix< double >	precessionMatrix (const EphTime &t)

Matrix< double >	preciseEarthRotation (const EphTime &t)

Static Public Member Functions
static double	coordTransTime (EphTime t)

static double	D (double T)

static double	F (double T)

static double	L (double T)

static double	LE (double T)

static double	LJ (double T)

static double	LMa (double T)

static double	LMe (double T)

static double	LN (double T)

static double	Lp (double T)

static double	LS (double T)

static double	LU (double T)

static double	LV (double T)

static double	Omega (double T)

static double	Omega2003 (double T)

static double	Pa (double T)

Public Attributes
IERSConvention	convention
	IERS convention appropriate for this data. More...

double	UT1mUTC
	Time offset UT1 minus UTC, in seconds. More...

double	xp
	Polar motion angle xp, in arcseconds. More...

double	yp
	Polar motion angle yp, in arcseconds. More...

Static Public Attributes
static const double	ARCSEC_PER_CIRCLE = 1296000.0
	how many arcseconds in 360 degrees? More...

static const double	ARCSEC_TO_RAD = 4.848136811095359935899141e-6
	convert arc seconds to radians More...

static const double	DEG_TO_RAD = 0.0174532925199432957692369
	convert degrees to radians and back More...

static const double	HALFPI = (TWOPI / 4.)

static const int	intJulianEpoch = 51544

static const double	JulianEpoch = 51544.5

static const double	PI = (TWOPI / 2.)
	pi, 2*pi and pi/2 More...

static const double	RAD_TO_DEG = 57.29577951308232087679815

static const double	TWOPI = 6.283185307179586476925287

Private Member Functions
Matrix< double >	ECEFtoInertial1996 (EphTime t, double xp, double yp, double UT1mUTC, bool reduced=false)

Matrix< double >	ECEFtoInertial2003 (EphTime t, double xp, double yp, double UT1mUTC)

Matrix< double >	ECEFtoInertial2010 (EphTime t, double xp, double yp, double UT1mUTC)

Static Private Member Functions
static Matrix< double >	biasMatrix2010 ()

static double	EarthRotationAngle (const EphTime &t, double &UT1mUTC)

static double	equationOfEquinoxes2003 (EphTime t)

static Matrix< double >	FukushimaWilliams (double gamb, double phib, double psib, double epsa)

static void	FukushimaWilliams (double T, double &gamb, double &phib, double &psib, double &eps)

static double	gast1996 (EphTime t, double om, double eps, double dpsi, double UT1mUTC)

static double	GAST1996 (EphTime t, double UT1mUTC, bool reduced=false)

static double	GAST2003 (EphTime t, double UT1mUTC)

static double	GAST2010 (EphTime t, double UT1mUTC)

static double	GMST1996 (EphTime t, double UT1mUTC, bool reduced=false)

static double	GMST2003 (EphTime t, double UT1mUTC)

static double	GMST2010 (EphTime t, double UT1mUTC)

static void	nutationAngles1996 (double T, double &deps, double &dpsi, double &om)

static void	nutationAngles2003 (double T, double &deps, double &dpsi)

static void	nutationAngles2010 (double T, double &deps, double &dpsi)

static Matrix< double >	nutationMatrix (double eps, double dpsi, double deps)

static Matrix< double >	nutationMatrix1996 (double T)

static Matrix< double >	nutationMatrix2003 (double T)

static Matrix< double >	nutationMatrix2010 (double T)

static double	obliquity1996 (double T)

static double	obliquity2010 (double T)

static Matrix< double >	polarMotionMatrix1996 (double xp, double yp)

static Matrix< double >	polarMotionMatrix2003 (EphTime t, double xp, double yp)

static Matrix< double >	precessionMatrix1996 (double T)

static Matrix< double >	precessionMatrix2003 (double T)

static Matrix< double >	precessionMatrix2010 (double T)

static void	precessionRateCorrections2003 (double T, double &dpsi, double &deps)

static Matrix< double >	preciseEarthRotation2003 (double T)

static Matrix< double >	preciseEarthRotation2010 (double T)

static double	S (double T, double &X, double &Y, IERSConvention which=IERSConvention::IERS2003)

static double	Sprime (double T)

static double	Sprime (EphTime t)
	Sprime with EphTime input; cf. Sprime(double T == coordTransTime(t)) More...

static void	UT1mUTCTidalCorrections (double T, double &UT1mUTR, double &dlodR, double &domegaR)

static void	XYCIO (double &T, double &X, double &Y)

Friends
std::ostream &	operator<< (std::ostream &s, const EarthOrientation &)
	append to output stream More...

Constructor & Destructor Documentation

◆ EarthOrientation()

gnsstk::EarthOrientation::EarthOrientation ( )

inline

Constructor.

Definition at line 109 of file EarthOrientation.hpp.

Member Function Documentation

◆ biasMatrix2010()

Matrix< double > gnsstk::EarthOrientation::biasMatrix2010 ( )

staticprivate

IERS2010 frame bias matrix, a 3x3 rotation matrix; cf. FukushimaWilliams().

Returns: frame bias matrix Matrix<double>(3,3)

Definition at line 2764 of file EarthOrientation.cpp.

◆ coordTransTime()

double gnsstk::EarthOrientation::coordTransTime ( EphTime t )

static

'coordinate transformation time', which is used throughout the class, defined as the terrestrial time (TT) since J2000, in centuries. Valid for IERS1996, IERS2003, IERS2010

Parameters

t	EphTime time of interest.

Returns: coordinate transformation time at t.

Exceptions

Exception if the TimeSystem conversion fails (if TimeSystem is Unknown)

Definition at line 805 of file EarthOrientation.cpp.

◆ D()

double gnsstk::EarthOrientation::D ( double T )

static

mean elongation of the moon from the sun, in radians, given T, the coordTransTime at the time of interest. Valid for IERS1996, IERS2003, IERS2010

Parameters

T	coordinate transformation time.

Returns: D in radians.

Definition at line 874 of file EarthOrientation.cpp.

◆ EarthRotationAngle()

double gnsstk::EarthOrientation::EarthRotationAngle	(	const EphTime &	t,
		double &	UT1mUTC
	)

staticprivate

Starting with 2003 conventions a new method for computing the transformation fron ITRS to GCRS is provided by the Celestial Ephemeris Origin (CEO) which is based on the Earth Rotation Angle, which depends on time(UT1). Ref. IERS Tech Note 32 Chap 5 Eqn 14

Parameters

t	EphTime time of interest
UT1mUTC	offset UT1-UTC

Returns: Earth rotation angle in radians

Exceptions

Exception if the TimeSystem conversion fails (if TimeSystem is Unknown)

Definition at line 1719 of file EarthOrientation.cpp.

◆ ECEFtoInertial()

Matrix< double > gnsstk::EarthOrientation::ECEFtoInertial	(	const EphTime &	t,
		bool	reduced = `false`
	)

Generate the full transformation matrix (3x3 rotation) relating the ECEF frame to the conventional inertial frame. Input is the time of interest; use this object's EOPs - the polar motion angles xp and yp (arcseconds), and UT1-UTC (seconds) (xp,yp and UT1-UTC are as found in the IERS bulletin).

Parameters

t	epoch of the rotation.
reduced	true when UT1mUTC is 'reduced', meaning assumes 'no tides', as is the case with the NGA EOPs (default=F).

Returns: 3x3 rotation matrix

Exceptions

Exception	if the TimeSystem conversion fails (if TimeSystem is Unknown)
Exception	if convention is not defined

Definition at line 1247 of file EarthOrientation.cpp.

◆ ECEFtoInertial1996()

Matrix< double > gnsstk::EarthOrientation::ECEFtoInertial1996	(	EphTime	t,
		double	xp,
		double	yp,
		double	UT1mUTC,
		bool	reduced = `false`
	)

private

Generate the full transformation matrix (3x3 rotation) relating the ECEF frame to the conventional inertial frame, using IERS 1996 conventions. Input is the time of interest, the polar motion angles xp and yp (arcsecs), and UT1-UTC (sec) (xp,yp and UT1-UTC are just as found in the IERS bulletin)

Parameters

t	EphTime epoch of the rotation.
xp	Earth wobble in arcseconds, as found in the IERS bulletin.
yp	Earth wobble in arcseconds, as found in the IERS bulletin.
UT1mUTC	UT1-UTC in seconds, as found in the IERS bulletin.
reduced	bool true when UT1mUTC is 'reduced', meaning assumes 'no tides', as is the case with the NGA EOPs (default=F).

Returns: 3x3 rotation matrix

Exceptions

Exception if the TimeSystem conversion fails (if TimeSystem is Unknown)

Definition at line 2854 of file EarthOrientation.cpp.

◆ ECEFtoInertial2003()

Matrix< double > gnsstk::EarthOrientation::ECEFtoInertial2003	(	EphTime	t,
		double	xp,
		double	yp,
		double	UT1mUTC
	)

private

Generate the full transformation matrix (3x3 rotation) relating the ECEF frame to the conventional inertial frame, using IERS 2003 conventions. Input is the time of interest, the polar motion angles xp and yp (arcsecs), and UT1-UTC (sec) (xp,yp and UT1-UTC are just as found in the IERS bulletin)

Parameters

t	EphTime epoch of the rotation.
xp	Earth wobble in arcseconds, as found in the IERS bulletin.
yp	Earth wobble in arcseconds, as found in the IERS bulletin.
UT1mUTC	UT1-UTC in seconds, as found in the IERS bulletin.

Returns: 3x3 rotation matrix

Exceptions

Exception if the TimeSystem conversion fails (if TimeSystem is Unknown)

Definition at line 2925 of file EarthOrientation.cpp.

◆ ECEFtoInertial2010()

Matrix< double > gnsstk::EarthOrientation::ECEFtoInertial2010	(	EphTime	t,
		double	xp,
		double	yp,
		double	UT1mUTC
	)

private

Generate the full transformation matrix (3x3 rotation) relating the ECEF frame to the conventional inertial frame, using IERS 2010 conventions. Input is the time of interest, the polar motion angles xp and yp (arcsecs), and UT1-UTC (sec) (xp,yp and UT1-UTC are just as found in the IERS bulletin)

Parameters

t	EphTime epoch of the rotation.
xp	Earth wobble in arcseconds, as found in the IERS bulletin.
yp	Earth wobble in arcseconds, as found in the IERS bulletin.
UT1mUTC	UT1-UTC in seconds, as found in the IERS bulletin.

Returns: 3x3 rotation matrix

Exceptions

Exception if TimeSystem conversion fails (if TimeSystem is Unknown)

Definition at line 3002 of file EarthOrientation.cpp.

◆ ECEFtoJ2000()

Matrix<double> gnsstk::EarthOrientation::ECEFtoJ2000	(	const EphTime &	t,
		bool	reduced = `false`
	)

Compute the transformation from ECEF to the J2000 dynamical (inertial) frame. This differs from the ECEFtoInertial transformation only by the frame bias matrix. Only available in IERS2010. NB currently not tested. ***

Exceptions

Exception

◆ equationOfEquinoxes2003()

double gnsstk::EarthOrientation::equationOfEquinoxes2003 ( EphTime t )

staticprivate

Equation of the equinoxes complementary terms, IAU 2000 (IERS 2003) Note that GAST = GMST + equationOfEquinoxes

Parameters

t	EphTime epoch of interest

Returns: the ee in radians

Exceptions

Exception if the TimeSystem conversion fails (if TimeSystem is Unknown)

Definition at line 1770 of file EarthOrientation.cpp.

◆ F()

double gnsstk::EarthOrientation::F ( double T )

static

mean longitude of the moon minus Omega, in radians, given T, the coordTransTime at the time of interest. Valid for IERS1996, IERS2003, IERS2010

Parameters

T	coordinate transformation time.

Returns: F in radians.

Definition at line 860 of file EarthOrientation.cpp.

◆ FukushimaWilliams() [1/2]

Matrix< double > gnsstk::EarthOrientation::FukushimaWilliams	(	double	gamb,
		double	phib,
		double	psib,
		double	epsa
	)

staticprivate

For IERS 2010, generate any of B = frame bias matrix PB = Precession*Bias matrix NPB = Nutation*Precession*Bias matrix given the four F-W angles with caviats, as follows. Get B by passing the full F-W angles at J2000. Get PB by passing the full F-W angles at time time of interest. Get NPB by passing the full F-W angles at time time of interest with nutation angle corrections (nutationAngles2010()). Specifically, FukushimaWilliams(T, gamb, phib, psib, eps); nutationAngles2010(T, deps, dpsi); NPB = FukushimaWilliams(gamb, phib, psib+dpsi, eps+deps); Thus the precession matrix is computed as PB * transpose(B), and the nutation matrix is computed as N = NPB * transpose(PB).

Parameters

gamb	F-W angle
phib	F-W angle
psib	F-W angle
epsa	F-W angle, the obliquity

Returns: 3x3 rotation matrix B, PB or NPB

Definition at line 2355 of file EarthOrientation.cpp.

◆ FukushimaWilliams() [2/2]

void gnsstk::EarthOrientation::FukushimaWilliams	(	double	T,
		double &	gamb,
		double &	phib,
		double &	psib,
		double &	eps
	)

staticprivate

Compute Fukushima-Williams angles for computing nutation, frame bias and precession matrices in IERS2010; cf. FukushimaWilliams(). NB. fourth angle is obliquity.

Definition at line 2305 of file EarthOrientation.cpp.

◆ GAST()

double gnsstk::EarthOrientation::GAST	(	const EphTime &	t,
		bool	reduced = `false`
	)

Compute Greenwich Apparent Sidereal Time, or the Greenwich hour angle of the true vernal equinox (radians), given the coordinate time of interest, and this object's UT1-UTC (sec), which comes from the IERS bulletin.

Parameters

t	epoch of the rotation.
reduced	true when UT1mUTC is 'reduced', meaning assumes 'no tides', as is the case with the NGA EOPs (default=F).

Returns: GAST in radians

Exceptions

Exception	if the TimeSystem conversion fails (if TimeSystem is Unknown)
Exception	if convention is not defined

Definition at line 1078 of file EarthOrientation.cpp.

◆ gast1996()

double gnsstk::EarthOrientation::gast1996	(	EphTime	t,
		double	om,
		double	eps,
		double	dpsi,
		double	UT1mUTC
	)

staticprivate

Helper to compute the Greenwich hour angle of the true vernal equinox, or Greenwich Apparent Sidereal Time, in radians, for IERS1996, given the (UT) time of interest t, and, where T = coordTransTime(t), om = Omega(T) = mean longitude of lunar ascending node, in radians, ep = obliquity(T) = the obliquity of the ecliptic, in radians, dp = nutation in longitude (counted in the ecliptic), in seconds of arc.

GAST = Greenwich hour angle of the true vernal equinox = Greenwich apparent sidereal time = GMST + dpsi*cos(eps) + 0.00264"*sin(Omega) + 0.000063"*sin(2*Omega) (these terms account for the accumulated precession and nutation in right ascension and minimize any discontinuity in UT1)

GMST = Greenwich hour angle of the mean vernal equinox = Greenwich mean sidereal time = GMST0 + r*[UTC + (UT1-UTC)] r = is the ratio of universal to sidereal time = 1.002737909350795 + 5.9006E-11*T' - 5.9e-15*T'^2 T' = days'/36525 days'= number of days elapsed since t0 = +/-(integer+0.5) and (UT1-UTC) (seconds) is taken from the IERS bulletin

GMST0 = GMST at 0h UT1 = 6h 41m (50.54841+8640184.812866*T'+0.093104*T'^2-6.2E-6*T'^3)s

Parameters

t	EphTime time of interest.
om	Omega(T), mean longitude of lunar ascending node, in radians,
eps	obliquity(T), the obliquity of the ecliptic, in radians,
dpsi	nutation in longitude (counted in the ecliptic), in seconds of arc
UT1mUTC	UT1-UTC in seconds, as found in the IERS bulletin.

Returns: gast in radians

Exceptions

Exception

Definition at line 2089 of file EarthOrientation.cpp.

◆ GAST1996()

double gnsstk::EarthOrientation::GAST1996	(	EphTime	t,
		double	UT1mUTC,
		bool	reduced = `false`
	)

staticprivate

Compute Greenwich Apparent Sidereal Time, or the Greenwich hour angle of the true vernal equinox (radians), given the coordinate time of interest, and UT1-UTC (sec), which comes from the IERS bulletin.

Parameters

t	EphTime epoch of the rotation.
UT1mUTC	UT1-UTC in seconds, as found in the IERS bulletin.

Returns: GAST in radians

Exceptions

Exception if the TimeSystem conversion fails (if TimeSystem is Unknown)

Definition at line 2142 of file EarthOrientation.cpp.

◆ GAST2003()

double gnsstk::EarthOrientation::GAST2003	(	EphTime	t,
		double	UT1mUTC
	)

staticprivate

Compute Greenwich Apparent Sidereal Time, or the Greenwich hour angle of the true vernal equinox (radians), given the coordinate time of interest, and UT1-UTC (sec), which comes from the IERS bulletin.

Parameters

t	EphTime epoch of the rotation.
UT1mUTC	UT1-UTC in seconds, as found in the IERS bulletin.

Returns: GAST in radians

Exceptions

Exception if the TimeSystem conversion fails (if TimeSystem is Unknown)

Definition at line 2178 of file EarthOrientation.cpp.

◆ GAST2010()

double gnsstk::EarthOrientation::GAST2010	(	EphTime	t,
		double	UT1mUTC
	)

staticprivate

Compute Greenwich Apparent Sidereal Time, or the Greenwich hour angle of the true vernal equinox (radians), given the coordinate time of interest, and UT1-UTC (sec), which comes from the IERS bulletin.

Parameters

t	EphTime epoch of the rotation
UT1mUTC	UT1-UTC in seconds, as found in the IERS bulletin

Returns: GAST in radians

Exceptions

Exception if the TimeSystem conversion fails (if TimeSystem is Unknown)

Definition at line 2218 of file EarthOrientation.cpp.

◆ GMST()

double gnsstk::EarthOrientation::GMST	(	const EphTime &	t,
		bool	reduced = `false`
	)

Compute Greenwich Mean Sidereal Time, or the Greenwich hour angle of the mean vernal equinox (radians), given the coordinate time of interest, using this->UT1mUTC (sec), which comes from the IERS bulletin.

Parameters

t	epoch of the rotation.
reduced	true when UT1mUTC is 'reduced', meaning assumes 'no tides', as is the case with the NGA EOPs (default=F).

Returns: GMST in radians

Exceptions

Exception	if the TimeSystem conversion fails (if TimeSystem is Unknown)
Exception	if convention is not defined

Definition at line 1042 of file EarthOrientation.cpp.

◆ GMST1996()

double gnsstk::EarthOrientation::GMST1996	(	EphTime	t,
		double	UT1mUTC,
		bool	reduced = `false`
	)

staticprivate

Compute Greenwich Mean Sidereal Time, or the Greenwich hour angle of the mean vernal equinox (radians), given the coordinate time of interest, and UT1-UTC (sec), which comes from the IERS bulletin. For IERS1996,03

Parameters

t	EphTime epoch of the rotation.
UT1mUTC	UT1-UTC in seconds, as found in the IERS bulletin.
reduced	true when UT1mUTC is 'reduced', meaning assumes 'no tides', as is the case with the NGA EOPs (default=F).

Returns: GMST in radians

Exceptions

Exception if the TimeSystem conversion fails (if TimeSystem is Unknown)

Definition at line 1960 of file EarthOrientation.cpp.

◆ GMST2003()

double gnsstk::EarthOrientation::GMST2003	(	EphTime	t,
		double	UT1mUTC
	)

staticprivate

Compute Greenwich Mean Sidereal Time, or the Greenwich hour angle of the mean vernal equinox (radians), given the coordinate time of interest, and UT1-UTC (sec), which comes from the IERS bulletin. For IERS2003

Parameters

t	EphTime epoch of the rotation.
UT1mUTC	UT1-UTC in seconds, as found in the IERS bulletin.

Returns: GMST in radians

Exceptions

Exception if the TimeSystem conversion fails (if TimeSystem is Unknown)

Definition at line 2025 of file EarthOrientation.cpp.

◆ GMST2010()

double gnsstk::EarthOrientation::GMST2010	(	EphTime	t,
		double	UT1mUTC
	)

staticprivate

Compute Greenwich Mean Sidereal Time, or the Greenwich hour angle of the mean vernal equinox (radians), given the coordinate time of interest, and UT1-UTC (sec), which comes from the IERS bulletin. For IERS2010

Parameters

t	EphTime epoch of the rotation.
UT1mUTC	UT1-UTC in seconds, as found in the IERS bulletin.

Returns: GMST in radians

Exceptions

Exception if the TimeSystem conversion fails (if TimeSystem is Unknown)

Definition at line 2054 of file EarthOrientation.cpp.

◆ interpolateEOP()

void gnsstk::EarthOrientation::interpolateEOP	(	const EphTime &	ttag,
		const std::vector< double > &	time,
		const std::vector< double > &	X,
		const std::vector< double > &	Y,
		std::vector< double > &	dT,
		const IERSConvention &	conv
	)

Given parallel arrays of length four containing the values from EOPStore for time (int MJD) and EOPs xp, yp, and UT1mUTC, where the time of interest ttag lies within the values of the time array, interpolate and apply corrections to determine the EOPs at ttag, using the algorithm prescribed by the given IERS convention.

Parameters

ttag	EphTime at which to compute EOPs
time	vector of length 4 of consecutive MJDs from EOPStore; ttag must lie within this timespan.
X	vector of length 4 of consecutive xp from EOPStore.
Y	vector of length 4 of consecutive yp from EOPStore.
dT	vector of length 4 of consecutive UT1mUTC from EOPStore.
conv	the IERSConvention to be used.

Exceptions

InvalidRequest

Definition at line 158 of file EarthOrientation.cpp.

◆ L()

double gnsstk::EarthOrientation::L ( double T )

static

mean anomaly of the moon, in radians, given T, the coordTransTime at the time of interest. Valid for IERS1996, IERS2003, IERS2010

Parameters

T	coordinate transformation time.

Returns: L in radians.

Definition at line 888 of file EarthOrientation.cpp.

◆ LE()

double gnsstk::EarthOrientation::LE ( double T )

static

mean longitude of Earth, in radians, given T, the coordTransTime at the time of interest. Valid for IERS2003, IERS2010

Parameters

T	coordinate transformation time.

Returns: LE in radians.

Definition at line 937 of file EarthOrientation.cpp.

◆ LJ()

double gnsstk::EarthOrientation::LJ ( double T )

static

mean longitude of Jupiter, in radians, given T, the coordTransTime at the time of interest. Valid for IERS2003, IERS2010

Parameters

T	coordinate transformation time.

Returns: LE in radians.

Definition at line 958 of file EarthOrientation.cpp.

◆ LMa()

double gnsstk::EarthOrientation::LMa ( double T )

static

mean longitude of Mars, in radians, given T, the coordTransTime at the time of interest. Valid for IERS2003, IERS2010

Parameters

T	coordinate transformation time.

Returns: LE in radians.

Definition at line 947 of file EarthOrientation.cpp.

◆ LMe()

double gnsstk::EarthOrientation::LMe ( double T )

static

mean longitude of Mercury, in radians, given T, the coordTransTime at the time of interest. Valid for IERS2003, IERS2010

Parameters

T	coordinate transformation time.

Returns: LMe in radians.

Definition at line 917 of file EarthOrientation.cpp.

◆ LN()

double gnsstk::EarthOrientation::LN ( double T )

static

mean longitude of Neptune, in radians, given T, the coordTransTime at the time of interest. Valid for IERS2003, IERS2010

Parameters

T	coordinate transformation time.

Returns: LE in radians.

Definition at line 991 of file EarthOrientation.cpp.

◆ Lp()

double gnsstk::EarthOrientation::Lp ( double T )

static

mean anomaly of the sun, in radians, given T, the coordTransTime at the time of interest. Valid for IERS1996, IERS2003, IERS2010

Parameters

T	coordinate transformation time.

Returns: Lp in radians.

Definition at line 901 of file EarthOrientation.cpp.

◆ LS()

double gnsstk::EarthOrientation::LS ( double T )

static

mean longitude of Saturn, in radians, given T, the coordTransTime at the time of interest. Valid for IERS2003, IERS2010

Parameters

T	coordinate transformation time.

Returns: LE in radians.

Definition at line 969 of file EarthOrientation.cpp.

◆ LU()

double gnsstk::EarthOrientation::LU ( double T )

static

mean longitude of Uranus, in radians, given T, the coordTransTime at the time of interest. Valid for IERS2003, IERS2010

Parameters

T	coordinate transformation time.

Returns: LE in radians.

Definition at line 980 of file EarthOrientation.cpp.

◆ LV()

double gnsstk::EarthOrientation::LV ( double T )

static

mean longitude of Venus, in radians, given T, the coordTransTime at the time of interest. Valid for IERS2003, IERS2010

Parameters

T	coordinate transformation time.

Returns: LV in radians.

Definition at line 927 of file EarthOrientation.cpp.

◆ nutationAngles1996()

void gnsstk::EarthOrientation::nutationAngles1996	(	double	T,
		double &	deps,
		double &	dpsi,
		double &	om
	)

staticprivate

Nutation of the obliquity (deps) and of the longitude (dpsi), IERS 1996 model (ref pg 26), given

Parameters

T	the coordinate transformation time at the time of interest
deps	nutation of the obliquity (output) in radians
dpsi	nutation of the longitude (output) in radians
om	longitude mean ascending node of lunar orbit, from mean equinox

Definition at line 2372 of file EarthOrientation.cpp.

◆ nutationAngles2003()

void gnsstk::EarthOrientation::nutationAngles2003	(	double	T,
		double &	deps,
		double &	dpsi
	)

staticprivate

Nutation of the obliquity (deps) and of the longitude (dpsi), IERS 2003

Parameters

T	the coordinate transformation time at the time of interest
deps	nutation of the obliquity (output) in radians
dpsi	nutation of the longitude (output) in radians

Definition at line 2447 of file EarthOrientation.cpp.

◆ nutationAngles2010()

void gnsstk::EarthOrientation::nutationAngles2010	(	double	T,
		double &	deps,
		double &	dpsi
	)

staticprivate

Nutation of the obliquity (deps) and of the longitude (dpsi), IERS 2010

Parameters

T	the coordinate transformation time at the time of interest
deps	nutation of the obliquity (output) in radians
dpsi	nutation of the longitude (output) in radians

Definition at line 2572 of file EarthOrientation.cpp.

◆ nutationMatrix() [1/2]

Matrix< double > gnsstk::EarthOrientation::nutationMatrix ( const EphTime & t )

Generate an Earth Nutation Matrix (3X3 rotation) at the given EphTime.

Parameters

t	EphTime epoch of the rotation.

Returns: nutation matrix Matrix<double>(3,3)

Exceptions

Exception if convention is not defined

Definition at line 1184 of file EarthOrientation.cpp.

◆ nutationMatrix() [2/2]

Matrix< double > gnsstk::EarthOrientation::nutationMatrix	(	double	eps,
		double	dpsi,
		double	deps
	)

staticprivate

nutation matrix, a 3x3 rotation matrix, given

Parameters

eps	obliquity(T), the obliquity of the ecliptic, in radians,
dpsi	the nutation in longitude (counted in the ecliptic) in radians.
deps	the nutation in obliquity, in radians.

Returns: nutation matrix Matrix<double>(3,3)

Definition at line 2586 of file EarthOrientation.cpp.

◆ nutationMatrix1996()

Matrix< double > gnsstk::EarthOrientation::nutationMatrix1996 ( double T )

staticprivate

IERS1996 nutation matrix, a 3x3 rotation matrix, given

Parameters

T	the coordinate transformation time at the time of interest

Returns: nutation matrix Matrix<double>(3,3)

Definition at line 2599 of file EarthOrientation.cpp.

◆ nutationMatrix2003()

Matrix< double > gnsstk::EarthOrientation::nutationMatrix2003 ( double T )

staticprivate

IERS2003 nutation matrix, a 3x3 rotation matrix (including the frame bias matrix), given

Parameters

T	the coordinate transformation time at the time of interest

Returns: nutation matrix Matrix<double>(3,3)

Definition at line 2612 of file EarthOrientation.cpp.

◆ nutationMatrix2010()

Matrix< double > gnsstk::EarthOrientation::nutationMatrix2010 ( double T )

staticprivate

IERS2010 nutation matrix, a 3x3 rotation matrix, given

Parameters

T	the coordinate transformation time at the time of interest; cf. FukushimaWilliams().

Returns: nutation matrix Matrix<double>(3,3)

Definition at line 2630 of file EarthOrientation.cpp.

◆ obliquity()

double gnsstk::EarthOrientation::obliquity ( double T )

obliquity of the ecliptic, in radians, given T, the coordTransTime at the time of interest. Valid for IERS1996 IERS2003 IERS2010

Parameters

T	coordinate transformation time.

Returns: eps in radians.

Exceptions

Exception if convention is not defined

Definition at line 1013 of file EarthOrientation.cpp.

◆ obliquity1996()

double gnsstk::EarthOrientation::obliquity1996 ( double T )

staticprivate

obliquity of the ecliptic, in radians, given T, the coordTransTime at the time of interest, for IERS1996 (also 03)

Parameters

T	coordinate transformation time.

Returns: eps in radians.

Definition at line 1923 of file EarthOrientation.cpp.

◆ obliquity2010()

double gnsstk::EarthOrientation::obliquity2010 ( double T )

staticprivate

obliquity of the ecliptic, in radians, given T, the coordTransTime at the time of interest, for IERS2010

Parameters

T	coordinate transformation time.

Returns: eps in radians.

Definition at line 1938 of file EarthOrientation.cpp.

◆ Omega()

double gnsstk::EarthOrientation::Omega ( double T )

static

mean longitude of lunar ascending node, in radians, given T, the coordTransTime at the time of interest. Valid for IERS1996, IERS2003, IERS2010

Parameters

T	coordinate transformation time.

Returns: Omega in radians.

Definition at line 832 of file EarthOrientation.cpp.

◆ Omega2003()

double gnsstk::EarthOrientation::Omega2003 ( double T )

static

mean longitude of lunar ascending node, in radians, given T, the coordTransTime at the Epoch of interest. valid for IERS 2003, 2010

Parameters

T	coordinate transformation time.

Returns: Omega in radians.

Definition at line 846 of file EarthOrientation.cpp.

◆ Pa()

double gnsstk::EarthOrientation::Pa ( double T )

static

general precession in longitude, in radians, given T, the coordTransTime at the time of interest. Valid for IERS2003, IERS2010

Parameters

T	coordinate transformation time.

Returns: Pa in radians.

Definition at line 1003 of file EarthOrientation.cpp.

◆ polarMotionMatrix()

Matrix< double > gnsstk::EarthOrientation::polarMotionMatrix ( const EphTime & t )

Generate transformation matrix (3X3 rotation) due to this object's EOPs polar motion angles xp and yp (arcseconds), as found in the IERS bulletin;

Parameters

t	EphTime epoch of the rotation.

Exceptions

Exception if convention is not defined

Definition at line 1111 of file EarthOrientation.cpp.

◆ polarMotionMatrix1996()

Matrix< double > gnsstk::EarthOrientation::polarMotionMatrix1996	(	double	xp,
		double	yp
	)

staticprivate

Generate transformation matrix (3X3 rotation) due to the polar motion angles xp and yp (arcseconds), as found in the IERS bulletin;

Parameters

xp	Earth wobble in arcseconds, as found in the IERS bulletin.
yp	Earth wobble in arcseconds, as found in the IERS bulletin.

Returns: Matrix<double>(3,3) rotation matrix

Definition at line 2266 of file EarthOrientation.cpp.

◆ polarMotionMatrix2003()

Matrix< double > gnsstk::EarthOrientation::polarMotionMatrix2003	(	EphTime	t,
		double	xp,
		double	yp
	)

staticprivate

Generate transformation matrix (3X3 rotation) due to the polar motion angles xp and yp (arcseconds), as found in the IERS bulletin; The returned matrix R transforms the CIP into TRS: V(TRS) = R * V(CIP). see sofa pom00. Also valid for IERS2010.

Parameters

t	EphTime epoch of the rotation.
xp	Earth wobble in arcseconds, as found in the IERS bulletin.
yp	Earth wobble in arcseconds, as found in the IERS bulletin.

Returns: Matrix<double>(3,3) rotation matrix CIP -> TRS

Definition at line 2286 of file EarthOrientation.cpp.

◆ precessionMatrix()

Matrix< double > gnsstk::EarthOrientation::precessionMatrix ( const EphTime & t )

Generate an Earth Precession Matrix (3X3 rotation) at the given EphTime.

Parameters

t	EphTime epoch of the rotation.

Returns: precession matrix Matrix<double>(3,3)

Exceptions

Exception if convention is not defined

Definition at line 1136 of file EarthOrientation.cpp.

◆ precessionMatrix1996()

Matrix< double > gnsstk::EarthOrientation::precessionMatrix1996 ( double T )

staticprivate

IERS1996 precession matrix, a 3x3 rotation matrix, given

Parameters

T	the coordinate transformation time at the time of interest

Returns: precession matrix Matrix<double>(3,3)

Definition at line 2659 of file EarthOrientation.cpp.

◆ precessionMatrix2003()

Matrix< double > gnsstk::EarthOrientation::precessionMatrix2003 ( double T )

staticprivate

IERS2003 precession matrix, a 3x3 rotation matrix (including the frame bias matrix), given

Parameters

T	the coordinate transformation time at the time of interest

Returns: precession matrix Matrix<double>(3,3)

Definition at line 2681 of file EarthOrientation.cpp.

◆ precessionMatrix2010()

Matrix< double > gnsstk::EarthOrientation::precessionMatrix2010 ( double T )

staticprivate

IERS2010 precession matrix, a 3x3 rotation matrix, given

Parameters

T	the coordinate transformation time at the time of interest Does not include the frame bias matrix; cf. FukushimaWilliams().

Returns: precession matrix Matrix<double>(3,3)

Definition at line 2779 of file EarthOrientation.cpp.

◆ precessionRateCorrections2003()

void gnsstk::EarthOrientation::precessionRateCorrections2003	(	double	T,
		double &	dpsi,
		double &	deps
	)

staticprivate

IERS2003 precession and obliquity rate corrections, IAU 2000

Parameters

T	the coordinate transformation time at the time of interest

Returns: precession, obliquity corrections in radians

Definition at line 2752 of file EarthOrientation.cpp.

◆ preciseEarthRotation()

Matrix< double > gnsstk::EarthOrientation::preciseEarthRotation ( const EphTime & t )

Generate precise transformation matrix (3X3 rotation) for Earth motion due to precession, nutation and frame bias, at the given time of interest.

Parameters

t	EphTime epoch of the rotation.

Returns: 3x3 rotation matrix

Exceptions

Exception	if the TimeSystem conversion fails (if TimeSystem is Unknown)
Exception	if convention is not defined

Definition at line 1220 of file EarthOrientation.cpp.

◆ preciseEarthRotation2003()

Matrix< double > gnsstk::EarthOrientation::preciseEarthRotation2003 ( double T )

staticprivate

Generate precise transformation matrix (3X3 rotation) for Earth motion due to precession, nutation and frame bias, at the given time of interest. Valid only for 2010

Parameters

T	coordTransTime(EphTime t) for time of interest

Returns: 3x3 rotation matrix

Exceptions

Exception if the TimeSystem conversion fails (if TimeSystem is Unknown)

Definition at line 2801 of file EarthOrientation.cpp.

◆ preciseEarthRotation2010()

Matrix< double > gnsstk::EarthOrientation::preciseEarthRotation2010 ( double T )

staticprivate

Generate precise transformation matrix (3X3 rotation) for Earth motion due to precession, nutation and frame bias, at the given time of interest. Valid only for 2010

Parameters

T	coordTransTime(EphTime t) for time of interest

Returns: 3x3 rotation matrix

Exceptions

Exception if the TimeSystem conversion fails (if TimeSystem is Unknown)

Definition at line 2826 of file EarthOrientation.cpp.

◆ S()

double gnsstk::EarthOrientation::S	(	double	T,
		double &	X,
		double &	Y,
		IERSConvention	which = `IERSConvention::IERS2003`
	)

staticprivate

locator s which gives the position of the CIO on the equator of the CIP, given the coordinate transformation time T and the coordinates X,Y of the CIP. Consistent with IAU 2000A (IERS2003) precession-nutation, and P03 precession (IERS2010). Derived in part from SOFA routine s00.c for IERS2003 and s06.c for IERS2010. Used for both IERS2003 and IERS2010, but not for IERS1996

Parameters

T	the coordinate transformation time at the time of interest
X	the X coordinate of the CIP (input)
Y	the Y coordinate of the CIP (input)
which	the IERS convention to be used (input)

Returns: S, the parameter that positions the CIO on the CIP equator.

Definition at line 1327 of file EarthOrientation.cpp.

◆ Sprime() [1/2]

double gnsstk::EarthOrientation::Sprime ( double T )

staticprivate

The position of the Terrestrial Ephemeris Origin (TEO) on the equator of the Celestial Intermediate Pole (CIP), as given by the quantity s'. Also called the Terrestrial Intermediate Origin (TIO). Ref. IERS Tech Note 32 Chap 5 Eqn 12

Parameters

T	Coordinate transformation time T.

Returns: angle 's prime' in radians

Definition at line 1587 of file EarthOrientation.cpp.

◆ Sprime() [2/2]

static double gnsstk::EarthOrientation::Sprime ( EphTime t )

inlinestaticprivate

Sprime with EphTime input; cf. Sprime(double T == coordTransTime(t))

Definition at line 471 of file EarthOrientation.hpp.

◆ UT1mUTCTidalCorrections()

void gnsstk::EarthOrientation::UT1mUTCTidalCorrections	(	double	T,
		double &	UT1mUTR,
		double &	dlodR,
		double &	domegaR
	)

staticprivate

Zonal tide terms for corrections of UT1mUTC when that quantity does not include tides (e.g. NGA EOP), ref. IERS 1996 Ch. 8, table 8.1 pg 74.

Parameters

T	the coordinate transformation time at the time of interest
UT1mUTR	the correction to UT1mUTC (seconds)
dlodR	the correction to the length of day (seconds)
domegaR	the correction to the Earth rotation rate, rad/second.

Definition at line 1903 of file EarthOrientation.cpp.

◆ XYCIO()

void gnsstk::EarthOrientation::XYCIO	(	double &	T,
		double &	X,
		double &	Y
	)

staticprivate

coordinates X,Y of the Celestial Intermediate Origin (CIO) using a series based on IAU 2006 precession and IAU 2000A nutation (IERS 2010). The coordinates form a unit vector that points towards the CIO; they include the effects of frame bias, precession and nutation. cf. sofa xy06

Parameters

T	the coordinate transformation time at the time of interest
X	x coordinate of CIO
Y	y coordinate of CIO

Definition at line 1601 of file EarthOrientation.cpp.

Friends And Related Function Documentation

◆ operator<<

std::ostream& operator<<	(	std::ostream &	s,
		const EarthOrientation &
	)

friend

append to output stream

Member Data Documentation

◆ ARCSEC_PER_CIRCLE

const double gnsstk::EarthOrientation::ARCSEC_PER_CIRCLE = 1296000.0

static

how many arcseconds in 360 degrees?

Definition at line 143 of file EarthOrientation.hpp.

◆ ARCSEC_TO_RAD

const double gnsstk::EarthOrientation::ARCSEC_TO_RAD = 4.848136811095359935899141e-6

static

convert arc seconds to radians

Definition at line 140 of file EarthOrientation.hpp.

◆ convention

IERSConvention gnsstk::EarthOrientation::convention

IERS convention appropriate for this data.

Definition at line 106 of file EarthOrientation.hpp.

◆ DEG_TO_RAD

const double gnsstk::EarthOrientation::DEG_TO_RAD = 0.0174532925199432957692369

static

convert degrees to radians and back

Definition at line 137 of file EarthOrientation.hpp.

◆ HALFPI

const double gnsstk::EarthOrientation::HALFPI = (TWOPI / 4.)

static

Definition at line 134 of file EarthOrientation.hpp.

◆ intJulianEpoch

const int gnsstk::EarthOrientation::intJulianEpoch = 51544

static

integer MJD J2000 epoch for use in maximizing precision of coordTransTime()

Definition at line 131 of file EarthOrientation.hpp.

◆ JulianEpoch

const double gnsstk::EarthOrientation::JulianEpoch = 51544.5

static

Epoch for the coordinate transformation time, used throughout the formulas = J2000 = January 1 2000 12h UT but use MJD for this constant

Definition at line 125 of file EarthOrientation.hpp.

◆ PI

const double gnsstk::EarthOrientation::PI = (TWOPI / 2.)

static

pi, 2*pi and pi/2

Definition at line 134 of file EarthOrientation.hpp.

◆ RAD_TO_DEG

const double gnsstk::EarthOrientation::RAD_TO_DEG = 57.29577951308232087679815

static

Definition at line 137 of file EarthOrientation.hpp.

◆ TWOPI

const double gnsstk::EarthOrientation::TWOPI = 6.283185307179586476925287

static

Definition at line 134 of file EarthOrientation.hpp.

◆ UT1mUTC

double gnsstk::EarthOrientation::UT1mUTC

Time offset UT1 minus UTC, in seconds.

Definition at line 103 of file EarthOrientation.hpp.

◆ xp

double gnsstk::EarthOrientation::xp

Polar motion angle xp, in arcseconds.

Definition at line 97 of file EarthOrientation.hpp.

◆ yp

double gnsstk::EarthOrientation::yp

Polar motion angle yp, in arcseconds.

Definition at line 100 of file EarthOrientation.hpp.

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

Detailed Description

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Private Member Functions

Static Private Member Functions

Friends

Constructor & Destructor Documentation

◆ EarthOrientation()

Member Function Documentation

◆ biasMatrix2010()

◆ coordTransTime()

◆ D()

◆ EarthRotationAngle()

◆ ECEFtoInertial()

◆ ECEFtoInertial1996()

◆ ECEFtoInertial2003()

◆ ECEFtoInertial2010()

◆ ECEFtoJ2000()

◆ equationOfEquinoxes2003()

◆ F()

◆ FukushimaWilliams() [1/2]

◆ FukushimaWilliams() [2/2]

◆ GAST()

◆ gast1996()

◆ GAST1996()

◆ GAST2003()

◆ GAST2010()

◆ GMST()

◆ GMST1996()

◆ GMST2003()

◆ GMST2010()

◆ interpolateEOP()

◆ L()

◆ LE()

◆ LJ()

◆ LMa()

◆ LMe()

◆ LN()

◆ Lp()

◆ LS()

◆ LU()

◆ LV()

◆ nutationAngles1996()

◆ nutationAngles2003()

◆ nutationAngles2010()

◆ nutationMatrix() [1/2]

◆ nutationMatrix() [2/2]

◆ nutationMatrix1996()

◆ nutationMatrix2003()

◆ nutationMatrix2010()

◆ obliquity()

◆ obliquity1996()

◆ obliquity2010()

◆ Omega()

◆ Omega2003()

◆ Pa()

◆ polarMotionMatrix()

◆ polarMotionMatrix1996()

◆ polarMotionMatrix2003()

◆ precessionMatrix()

◆ precessionMatrix1996()

◆ precessionMatrix2003()

◆ precessionMatrix2010()

◆ precessionRateCorrections2003()

◆ preciseEarthRotation()

◆ preciseEarthRotation2003()

◆ preciseEarthRotation2010()

◆ S()

◆ Sprime() [1/2]

◆ Sprime() [2/2]

◆ UT1mUTCTidalCorrections()

◆ XYCIO()

Friends And Related Function Documentation

◆ operator<<

Member Data Documentation

◆ ARCSEC_PER_CIRCLE

◆ ARCSEC_TO_RAD

◆ convention