Procedures

Decompose radians into degrees, arcminutes, arcseconds, fraction.

Decompose radians into hours, minutes, seconds, fraction.

Apply aberration to transform natural direction into proper direction.

Horizon to equatorial coordinates: transform azimuth and altitude to hour angle and declination.

Convert degrees, arcminutes, arcseconds to radians.

Normalize angle into the range 0 <= A < 2pi.

Normalize angle into the range -pi <= A < +pi.

For a geocentric observer, prepare star-independent astrometry parameters for transformations between ICRS and GCRS coordinates. The Earth ephemeris is supplied by the caller.

For a geocentric observer, prepare star-independent astrometry parameters for transformations between ICRS and GCRS coordinates. The caller supplies the date, and SOFA models are used to predict the Earth ephemeris.

For a terrestrial observer, prepare star-independent astrometry parameters for transformations between ICRS and geocentric CIRS coordinates. The Earth ephemeris and CIP/CIO are supplied by the caller.

For a terrestrial observer, prepare star-independent astrometry parameters for transformations between ICRS and geocentric CIRS coordinates. The caller supplies the date, and SOFA models are used to predict the Earth ephemeris and CIP/CIO.

For a terrestrial observer, prepare star-independent astrometry parameters for transformations between ICRS and observed coordinates. The caller supplies the Earth ephemeris, the Earth rotation information and the refraction constants as well as the site coordinates.

For a terrestrial observer, prepare star-independent astrometry parameters for transformations between ICRS and observed coordinates. The caller supplies UTC, site coordinates, ambient air conditions and observing wavelength, and SOFA models are used to obtain the Earth ephemeris, CIP/CIO and refraction constants.

For an observer whose geocentric position and velocity are known, prepare star-independent astrometry parameters for transformations between ICRS and GCRS. The Earth ephemeris is supplied by the caller.

For an observer whose geocentric position and velocity are known, prepare star-independent astrometry parameters for transformations between ICRS and GCRS. The Earth ephemeris is from SOFA models.

In the star-independent astrometry parameters, update only the Earth rotation angle, supplied by the caller explicitly.

In the star-independent astrometry parameters, update only the Earth rotation angle. The caller provides UT1 (n.b. not UTC).

For a terrestrial observer, prepare star-independent astrometry parameters for transformations between CIRS and observed coordinates. The caller supplies the Earth orientation information and the refraction constants as well as the site coordinates.

For a terrestrial observer, prepare star-independent astrometry parameters for transformations between CIRS and observed coordinates. The caller supplies UTC, site coordinates, ambient air conditions and observing wavelength.

Transform ICRS star data, epoch J2000.0, to CIRS.

Quick ICRS, epoch J2000.0, to CIRS transformation, given precomputed star-independent astrometry parameters.

Quick ICRS, epoch J2000.0, to CIRS transformation, given precomputed star-independent astrometry parameters plus a list of light- deflecting bodies.

Quick ICRS to CIRS transformation, given precomputed star-independent astrometry parameters, and assuming zero parallax and proper motion.

ICRS RA,Dec to observed place. The caller supplies UTC, site coordinates, ambient air conditions and observing wavelength.

Transform star RA,Dec from geocentric CIRS to ICRS astrometric.

Quick CIRS RA,Dec to ICRS astrometric place, given the star- independent astrometry parameters.

Quick CIRS to ICRS astrometric place transformation, given the star-independent astrometry parameters plus a list of light- deflecting bodies.

CIRS RA,Dec to observed place. The caller supplies UTC, site coordinates, ambient air conditions and observing wavelength.

Quick CIRS to observed place transformation.

Observed place at a groundbased site to to ICRS astrometric RA,Dec. The caller supplies UTC, site coordinates, ambient air conditions and observing wavelength.

Observed place to CIRS. The caller supplies UTC, site coordinates, ambient air conditions and observing wavelength.

Quick observed place to CIRS, given the star-independent astrometry parameters.

Frame bias components of IAU 2000 precession-nutation models (part of MHB2000 with additions).

Frame bias and precession, IAU 2000.

Frame bias and precession, IAU 2006.

Extract from the bias-precession-nutation matrix the X,Y coordinates of the Celestial Intermediate Pole.

Form the celestial-to-intermediate matrix for a given date using the IAU 2000A precession-nutation model.

Form the celestial-to-intermediate matrix for a given date using the IAU 2000B precession-nutation model.

Form the celestial-to-intermediate matrix for a given date using the IAU 2006 precession and IAU 2000A nutation models.

Form the celestial-to-intermediate matrix for a given date given the bias-precession-nutation matrix. IAU 2000.

Form the celestial to intermediate-frame-of-date matrix for a given date when the CIP X,Y coordinates are known. IAU 2000.

Form the celestial to intermediate-frame-of-date matrix given the CIP X,Y and the CIO locator s.

P-vector to spherical coordinates.

Form the celestial to terrestrial matrix given the date, the UT1 and the polar motion, using the IAU 2000A nutation model.

Form the celestial to terrestrial matrix given the date, the UT1 and the polar motion, using the IAU 2000B nutation model.

Form the celestial to terrestrial matrix given the date, the UT1 and the polar motion, using the IAU 2006 precession and IAU 2000A nutation models.

Assemble the celestial to terrestrial matrix from CIO-based components (the celestial-to-intermediate matrix, the Earth Rotation Angle and the polar motion matrix).

Assemble the celestial to terrestrial matrix from CIO-based components (the celestial-to-intermediate matrix, the Earth Rotation Angle and the polar motion matrix).

Assemble the celestial to terrestrial matrix from equinox-based components (the celestial-to-true matrix, the Greenwich Apparent Sidereal Time and the polar motion matrix).

Form the celestial to terrestrial matrix given the date, the UT1, the nutation and the polar motion. IAU 2000.

Form the celestial to terrestrial matrix given the date, the UT1, the CIP coordinates and the polar motion. IAU 2000.

Gregorian Calendar to Julian Date.

Copy a p-vector.

Copy a position/velocity vector.

Copy an r-matrix.

Format for output a 2-part Julian Date (or in the case of UTC a quasi-JD form that includes special provision for leap seconds).

Decompose days to hours, minutes, seconds, fraction.

For a given UTC date, calculate Delta(AT) = TAI-UTC.

An approximation to TDB-TT, the difference between barycentric dynamical time and terrestrial time, for an observer on the Earth.

Encode date and time fields into 2-part Julian Date (or in the case of UTC a quasi-JD form that includes special provision for leap seconds).

Transformation from ecliptic coordinates (mean equinox and ecliptic of date) to ICRS RA,Dec, using the IAU 2006 precession model.

ICRS equatorial to ecliptic rotation matrix, IAU 2006.

The equation of the equinoxes, compatible with IAU 2000 resolutions, given the nutation in longitude and the mean obliquity.

Equation of the equinoxes, compatible with IAU 2000 resolutions.

Equation of the equinoxes, compatible with IAU 2000 resolutions but using the truncated nutation model IAU 2000B.

Equation of the equinoxes, compatible with IAU 2000 resolutions and IAU 2006/2000A precession-nutation.

Equation of the equinoxes complementary terms, consistent with IAU 2000 resolutions.

Earth reference ellipsoids.

Equation of the origins, IAU 2006 precession and IAU 2000A nutation.

Equation of the origins, given the classical NPB matrix and the quantity s.

Julian Date to Besselian Epoch.

Besselian Epoch to Julian Date.

Julian Date to Julian Epoch.

Julian Epoch to Julian Date.

Earth position and velocity, heliocentric and barycentric, with respect to the Barycentric Celestial Reference System.

Transformation from ICRS equatorial coordinates to ecliptic coordinates (mean equinox and ecliptic of date) using IAU 2006 precession model.

Equation of the equinoxes, IAU 1994 model.

Earth rotation angle (IAU 2000 model).

Fundamental argument, IERS Conventions (2003): mean elongation of the Moon from the Sun.

Fundamental argument, IERS Conventions (2003): mean longitude of Earth.

Fundamental argument, IERS Conventions (2003): mean longitude of the Moon minus mean longitude of the ascending node.

Fundamental argument, IERS Conventions (2003): mean longitude of Jupiter.

Fundamental argument, IERS Conventions (2003): mean anomaly of the Moon.

Fundamental argument, IERS Conventions (2003): mean anomaly of the Sun.

Fundamental argument, IERS Conventions (2003): mean longitude of Mars.

Fundamental argument, IERS Conventions (2003): mean longitude of Mercury.

Fundamental argument, IERS Conventions (2003): mean longitude of Neptune.

Fundamental argument, IERS Conventions (2003): mean longitude of the Moon's ascending node.

Fundamental argument, IERS Conventions (2003): general accumulated precession in longitude.

Fundamental argument, IERS Conventions (2003): mean longitude of Saturn.

Fundamental argument, IERS Conventions (2003): mean longitude of Uranus.

Fundamental argument, IERS Conventions (2003): mean longitude of Venus.

Convert B1950.0 FK4 star catalog data to J2000.0 FK5.

Convert a B1950.0 FK4 star position to J2000.0 FK5, assuming zero proper motion in the FK5 system.

Convert J2000.0 FK5 star catalog data to B1950.0 FK4.

Transform FK5 (J2000.0) star data into the Hipparcos system.

Convert a J2000.0 FK5 star position to B1950.0 FK4, assuming zero proper motion in FK5 and parallax.

FK5 to Hipparcos rotation and spin.

Transform an FK5 (J2000.0) star position into the system of the Hipparcos catalogue, assuming zero Hipparcos proper motion.

Form rotation matrix given the Fukushima-Williams angles.

CIP X,Y given Fukushima-Williams bias-precession-nutation angles.

Transformation from Galactic Coordinates to ICRS.

Transform geocentric coordinates to geodetic using the specified reference ellipsoid.

Transform geocentric coordinates to geodetic for a reference ellipsoid of specified form.

Transform geodetic coordinates to geocentric using the specified reference ellipsoid.

Transform geodetic coordinates to geocentric for a reference ellipsoid of specified form.

Greenwich Mean Sidereal Time (model consistent with IAU 2000 resolutions).

Greenwich mean sidereal time (consistent with IAU 2006 precession).

Universal Time to Greenwich Mean Sidereal Time (IAU 1982 model).

Greenwich Apparent Sidereal Time (consistent with IAU 2000 resolutions).

Greenwich Apparent Sidereal Time (consistent with IAU 2000 resolutions but using the truncated nutation model IAU 2000B).

Greenwich apparent sidereal time, IAU 2006, given the NPB matrix.

Greenwich apparent sidereal time (consistent with IAU 2000 and 2006 resolutions).

Greenwich Apparent Sidereal Time (consistent with IAU 1982/94 resolutions).

Transform Hipparcos star data into the FK5 (J2000.0) system.

Equatorial to horizon coordinates: transform hour angle and declination to azimuth and altitude.

Parallactic angle for a given hour angle and declination.

Transform a Hipparcos star position into FK5 J2000.0, assuming zero Hipparcos proper motion.

Transformation from ICRS to Galactic Coordinates.

Initialize an r-matrix to the identity matrix.

Julian Date to Gregorian year, month, day, and fraction of a day.

Julian Date to Gregorian Calendar, expressed in a form convenient for formatting messages: rounded to a specified precision, and with the fields stored in a single array.

Apply light deflection by a solar-system body, as part of transforming coordinate direction into natural direction.

For a star, apply light deflection by multiple solar-system bodies, as part of transforming coordinate direction into natural direction.

Deflection of starlight by the Sun.

Transformation from ecliptic coordinates (mean equinox and ecliptic of date) to ICRS RA,Dec, using a long-term precession model.

ICRS equatorial to ecliptic rotation matrix, long-term.

Transformation from ICRS equatorial coordinates to ecliptic coordinates (mean equinox and ecliptic of date), using a long-term precession model.

Long-term precession matrix.

Long-term precession matrix, including ICRS frame bias.

Long-term precession of the ecliptic.

Long-term precession of the equator.

Form the matrix of nutation for a given date, IAU 2000A model.

Form the matrix of nutation for a given date, IAU 2000B model.

Form the matrix of nutation for a given date, IAU 2006/2000A model.

Form the matrix of nutation.

Nutation, IAU 2000A model (MHB2000 luni-solar and planetary nutation with free core nutation omitted).

Nutation, IAU 2000B model.

IAU 2000A nutation with adjustments to match the IAU 2006 precession.

Nutation, IAU 1980 model.

Form the matrix of nutation for a given date, IAU 1980 model.

Mean obliquity of the ecliptic, IAU 2006 precession model.

Mean obliquity of the ecliptic, IAU 1980 model.

Precession angles, IAU 2006, equinox based.

Extend a p-vector to a pv-vector by appending a zero velocity.

P-vector to spherical polar coordinates.

Position-angle from two p-vectors.

Position-angle from spherical coordinates.

This routine forms three Euler angles which implement general precession from epoch J2000.0, using the IAU 2006 model. Frame bias (the offset between ICRS and mean J2000.0) is included.

p-vector inner (=scalar=dot) product.

Precession angles, IAU 2006 (Fukushima-Williams 4-angle formulation).

Approximate heliocentric position and velocity of a nominated major planet: Mercury, Venus, EMB, Mars, Jupiter, Saturn, Uranus or Neptune (but not the Earth itself).

Modulus of p-vector.

Precession matrix (including frame bias) from GCRS to a specified date, IAU 2000 model.

Precession matrix (including frame bias) from GCRS to a specified date, IAU 2006 model.

Precession matrix from J2000.0 to a specified date, IAU 1976 model.

P-vector subtraction.

Proper motion and parallax.

Star proper motion: update star catalog data for space motion, with special handling to handle the zero parallax case.

Convert a p-vector into modulus and unit vector.

Precession-nutation, IAU 2000 model: a multi-purpose routine, supporting classical (equinox-based) use directly and CIO-based use indirectly.

Precession-nutation, IAU 2000A model: a multi-purpose routine, supporting classical (equinox-based) use directly and CIO-based use indirectly.

Precession-nutation, IAU 2000B model: a multi-purpose routine, supporting classical (equinox-based) use directly and CIO-based use indirectly.

Precession-nutation, IAU 2006 model: a multi-purpose routine, supporting classical (equinox-based) use directly and CIO-based use indirectly.

Precession-nutation, IAU 2006/2000A models: a multi-purpose routine, supporting classical (equinox-based) use directly and CIO-based use indirectly.

Form the matrix of precession-nutation for a given date (including frame bias), equinox-based, IAU 2000A model.

Form the matrix of precession-nutation for a given date (including frame bias), equinox-based, IAU 2000B model.

Form the matrix of precession-nutation for a given date (including frame bias), IAU 2006 precession and IAU 2000A nutation models.

Form the matrix of precession/nutation for a given date, IAU 1976 precession model, IAU 1980 nutation model.

Form the matrix of polar motion for a given date, IAU 2000.

P-vector addition.

P-vector plus scaled p-vector.

Precession-rate part of the IAU 2000 precession-nutation models (part of MHB2000).

IAU 1976 precession model.

Discard velocity component of a pv-vector.

Convert position/velocity from Cartesian to spherical coordinates.

Inner (=scalar=dot) product of two pv-vectors.

Modulus of pv-vector.

Subtract one pv-vector from another.

Add one pv-vector to another.

Convert star position+velocity vector to catalog coordinates.

Position and velocity of a terrestrial observing station.

Update a pv-vector.

Update a pv-vector, discarding the velocity component.

Outer (=vector=cross) product of two pv-vectors.

p-vector outer (=vector=cross) product.

Determine the constants A and B in the atmospheric refraction model dZ = A tan Z + B tan^3 Z.

Express an r-matrix as an r-vector.

Form the r-matrix corresponding to a given r-vector.

Rotate an r-matrix about the x-axis.

Multiply a p-vector by an r-matrix.

Multiply a pv-vector by an r-matrix.

Multiply two r-matrices.

Rotate an r-matrix about the y-axis.

Rotate an r-matrix about the z-axis.

The CIO locator s, positioning the Celestial Intermediate Origin on the equator of the Celestial Intermediate Pole, given the CIP's X,Y coordinates. Compatible with IAU 2000A precession-nutation.

The CIO locator s, positioning the Celestial Intermediate Origin on the equator of the Celestial Intermediate Pole, using the IAU 2000A precession-nutation model.

The CIO locator s, positioning the Celestial Intermediate Origin on the equator of the Celestial Intermediate Pole, using the IAU 2000B precession-nutation model.

The CIO locator s, positioning the Celestial Intermediate Origin on the equator of the Celestial Intermediate Pole, given the CIP's X,Y coordinates. Compatible with IAU 2006/2000A precession-nutation.

The CIO locator s, positioning the Celestial Intermediate Origin on the equator of the Celestial Intermediate Pole, using the IAU 2006 precession and IAU 2000A nutation models.

Convert spherical coordinates to Cartesian.

Convert spherical polar coordinates to p-vector.

Convert position/velocity from spherical to Cartesian coordinates.

Multiply a pv-vector by two scalars.

Angular separation between two p-vectors.

Angular separation between two sets of spherical coordinates.

The TIO locator s', positioning the Terrestrial Intermediate Origin on the equator of the Celestial Intermediate Pole.

Star proper motion: update star catalog data for space motion.

Convert star catalog coordinates to position+velocity vector.

Multiply a p-vector by a scalar.

Multiply a pv-vector by a scalar.

Time scale transformation: International Atomic Time, TAI, to Terrestrial Time, TT.

Time scale transformation: International Atomic Time, TAI, to Universal Time, UT1.

Time scale transformation: International Atomic Time, TAI, to Coordinated Universal Time, UTC.

Time scale transformation: Barycentric Coordinate Time, TCB, to Barycentric Dynamical Time, TDB.

Time scale transformation: Geocentric Coordinate Time, TCG, to Terrestrial Time, TT.

Time scale transformation: Barycentric Dynamical Time, TDB, to Barycentric Coordinate Time, TCB.

Time scale transformation: Barycentric Dynamical Time, TDB, to Terrestrial Time, TT.

Convert hours, minutes, seconds to radians.

Convert hours, minutes, seconds to days.

In the tangent plane projection, given the rectangular coordinates of a star and its spherical coordinates, determine the spherical coordinates of the tangent point.

In the tangent plane projection, given the rectangular coordinates of a star and its direction cosines, determine the direction cosines of the tangent point.

In the tangent plane projection, given the star's rectangular coordinates and the spherical coordinates of the tangent point, solve for the spherical coordinates of the star.

In the tangent plane projection, given the star's rectangular coordinates and the direction cosines of the tangent point, solve for the direction cosines of the star.

In the tangent plane projection, given celestial spherical coordinates for a star and the tangent point, solve for the star's rectangular coordinates in the tangent plane.

In the tangent plane projection, given celestial direction cosines for a star and the tangent point, solve for the star's rectangular coordinates in the tangent plane.

Transpose an r-matrix.

Multiply a p-vector by the transpose of an r-matrix.

Multiply a pv-vector by the transpose of an r-matrix.

Time scale transformation: Terrestrial Time, TT, to International Atomic Time, TAI.

Time scale transformation: Terrestrial Time, TT, to Geocentric Coordinate Time, TCG.

Time scale transformation: Terrestrial Time, TT, to Barycentric Dynamical Time, TDB.

Time scale transformation: Terrestrial Time, TT, to Universal Time, UT1.

Time scale transformation: Universal Time, UT1, to International Atomic Time, TAI.

Time scale transformation: Universal Time, UT1, to Terrestrial Time, TT.

Time scale transformation: Universal Time, UT1, to Coordinated Universal Time, UTC.

Time scale transformation: Coordinated Universal Time, UTC, to International Atomic Time, TAI.

Time scale transformation: Coordinated Universal Time, UTC, to Universal Time, UT1.

X,Y coordinates of celestial intermediate pole from series based on IAU 2006 precession and IAU 2000A nutation.

For a given TT date, compute the X,Y coordinates of the Celestial Intermediate Pole and the CIO locator s, using the IAU 2000A precession-nutation model.

For a given TT date, compute the X,Y coordinates of the Celestial Intermediate Pole and the CIO locator s, using the IAU 2000B precession-nutation model.

For a given TT date, compute the X,Y coordinates of the Celestial Intermediate Pole and the CIO locator s, using the IAU 2006 precession and IAU 2000A nutation models.

Zero a p-vector.

Zero a pv-vector.

Initialize an r-matrix to the null matrix.