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SuperNOVAS: src/frames.c File Reference

Date

Created on Jun 23, 2024

Since

1.1

SuperNOVAS routines for higher-level and efficient repeat coordinate transformations using observer frames. Observer frames represent an observer location at a specific astronomical time (instant), which can be re-used again and again to calculate or transform positions of celestial sources in a a range of astronomical coordinate systems.

See also

timescale.c

Converts an observed apparent sky position of a source to an ICRS geometric position, by undoing the gravitational deflection and aberration corrections.

Parameters

frame The observer frame, defining the location and time of observation sys The reference system in which the observed position is specified. ra [h] Observed ICRS right-ascension of the source dec [deg] Observed ICRS declination of the source dist [AU] Observed distance from observer. A value of <=0 will translate to 10¹⁵ AU (around 5 Gpc). [out] geom_icrs [AU] The corresponding geometric position for the source, in ICRS.

Returns

0 if successful, or else an error from grav_undef2(), or -1 (errno will indicate the type of error).

See also

novas_geom_to_app()

novas_hor_to_app()

novas_geom_to_hor()

novas_transform_vector()

Since

1.1

Author

Attila Kovacs

References grav_undo_planets(), NOVAS_CIRS, NOVAS_ITRS, NOVAS_J2000, NOVAS_MOD, NOVAS_REFERENCE_SYSTEMS, NOVAS_TIRS, NOVAS_TOD, radec2vector(), spin(), wobble(), and WOBBLE_ITRS_TO_TIRS.

Converts an observed apparent position vector in the specified coordinate system to local horizontal coordinates in the specified observer frame. The observer must be located on the surface of Earth, or else the call will return with an error. The caller may optionally supply a refraction model of choice to calculate an appropriate elevation angle that includes a refraction correction for Earth's atmosphere. If no such model is provided the calculated elevation will be the astrometric elevation without a refraction correction.

Parameters

frame Observer frame, defining the time and place of observation (on Earth). sys Astronomical coordinate system in which the observed position is given. ra [h] Observed apparent right ascension (R.A.) coordinate dec [deg] Observed apparent declination coordinate ref_model An appropriate refraction model, or NULL to calculate unrefracted elevation. Depending on the refraction model, you might want to make sure that the weather parameters were set when the observing frame was defined. [out] az [deg] Calculated azimuth angle. It may be NULL if not required. [out] el [deg] Calculated elevation angle. It may be NULL if not required.

Returns

0 if successful, or else an error from tod_to_itrs() or cirs_to_itrs(), or -1 (errno will indicate the type of error).

See also

novas_hor_to_app()

novas_app_to_geom()

novas_standard_refraction()

novas_optical_refraction()

novas_radio_refraction()

novas_wave_refraction()

Since

1.1

Author

Attila Kovacs

References novas_timespec::fjd_tt, novas_timespec::ijd_tt, itrs_to_hor(), NOVAS_AIRBORNE_OBSERVER, NOVAS_CIRS, NOVAS_GCRS, NOVAS_ICRS, NOVAS_ITRS, NOVAS_J2000, NOVAS_MOD, NOVAS_OBSERVER_ON_EARTH, NOVAS_REFRACT_ASTROMETRIC, NOVAS_TIRS, NOVAS_TOD, radec2vector(), spin(), wobble(), WOBBLE_PEF_TO_ITRS, and WOBBLE_TIRS_TO_ITRS.

Change the observer location for an observing frame.

Parameters

orig Pointer to original observing frame obs New observer location [out] out Observing frame to populate with a original frame data and new observer location. It can be the same as the input.

Returns

0 if successfule or else an an error code from geo_posvel() (errno will also indicate the type of error).

See also

novas_make_frame()

Since

1.1

Author

Attila Kovacs

References novas_frame::accuracy, grav_bodies_full_accuracy, grav_bodies_reduced_accuracy, NOVAS_FULL_ACCURACY, novas_get_time(), NOVAS_TDB, obs_planets(), novas_frame::obs_pos, novas_frame::observer, novas_frame::planets, novas_frame::state, and novas_frame::time.

Calculates equatorial tracking position and motion (first and second time derivatives) for the specified source in the given observing frame. The position and its derivatives are calculated via the more precise IAU2006 method, and CIRS.

Parameters

source Observed source frame Observing frame, defining the observer location and astronomical time of observation. dt [s] Time step used for calculating derivatives. [out] track Output tracking parameters to populate

Returns

0 if successful, or else -1 if any of the pointer arguments are NULL, or else an error code from cio_ra() or from novas_sky_pos().

Since

1.3

Author

Attila Kovacs

See also

novas_hor_track()

novas_track_pos()

References cio_ra(), sky_pos::dec, sky_pos::dis, novas_timespec::fjd_tt, NOVAS_CIRS, novas_make_frame(), novas_sky_pos(), novas_v2z(), sky_pos::ra, sky_pos::rv, and SKY_POS_INIT.

Returns the Local (apparent) Sidereal Time for an observing frame of an Earth-bound observer.

Parameters

frame Observer frame, defining the location and time of observation

Returns

[h] The LST for an Earth-bound observer [0.0–24.0), or NAN otherwise. If NAN is returned errno will indicate the type of error.

Since

1.3

Author

Attila Kovacs

References NOVAS_AIRBORNE_OBSERVER, and NOVAS_OBSERVER_ON_EARTH.

Calculates the geometric position and velocity vectors, relative to the observer, for a source in the given observing frame, in the specified coordinate system of choice. The geometric position includes proper motion, and for solar-system bodies it is antedated for light travel time, so it effectively represents the geometric position as seen by the observer. However, the geometric does not include aberration correction, nor gravitational deflection.

If you want apparent positions, which account for aberration and gravitational deflection, use novas_skypos() instead.

You can also use novas_transform_vector() to convert the output position and velocity vectors to a dfferent coordinate system of choice afterwards if you want the results expressed in more than one coordinate system.

It implements the same geometric transformations as place() but at a reduced computational cost. See place() for references.

NOTES:

1. If sys is NOVAS_TOD (true equator and equinox of date), the less precise old (pre IAU 2006) method is used, with the Lieske et al. 1977 nutation model, matching the behavior of the original NOVAS C place() for that system. To obtain more precise TOD coordinates, set sys to NOVAS_CIRS here, and follow with cirs_to_tod() after.
2. As of SuperNOVAS v1.3, the returned velocity vector is a proper observer-based velocity measure. In prior releases, and in NOVAS C 3.1, this was inconsistent, with pseudo LSR-based measures being returned for catalog sources.

Parameters

source Pointer to a celestial source data structure that is observed. Catalog sources should have coordinates and properties in ICRS. You can use transform_cat() to convert catalog entries to ICRS as necessary. frame Observer frame, defining the location and time of observation sys The coordinate system in which to return positions and velocities. [out] pos [AU] Calculated geometric position vector of the source relative to the observer location, in the designated coordinate system. It may be NULL if not required. [out] vel [AU/day] The calculated velocity vector of the source relative to the observer in the designated coordinate system. It must be distinct from the pos output vector, and may be NULL if not required.

Returns

0 if successful, or else -1 if any of the arguments is invalid, 50–70 error is 50 + error from light_time2().

See also

novas_geom_to_app()

novas_sky_pos()

novas_transform_vector()

place()

cirs_to_tod()

Since

1.1

Author

Attila Kovacs

References bary2obs(), d_light(), light_time2(), NOVAS_CATALOG_OBJECT, NOVAS_FULL_ACCURACY, novas_get_time(), NOVAS_JD_J2000, NOVAS_PLANET, NOVAS_REDUCED_ACCURACY, NOVAS_TDB, proper_motion(), and starvectors().

Converts an geometric position in ICRS to an apparent position on sky, by applying appropriate corrections for aberration and gravitational deflection for the observer's frame. Unlike place() the output reports the distance calculated from the parallax for sidereal sources. The radial velocity of the output is set to NAN (if needed use novas_sky_pos() instead).

Parameters

frame The observer frame, defining the location and time of observation pos [AU] Geometric position of source in ICRS coordinates sys The coordinate system in which to return the apparent sky location [out] out Pointer to the data structure which is populated with the calculated apparent location in the designated coordinate system. It may be the same pounter as the input position.

Returns

0 if successful, or an error from grav_def2(), or else -1 (errno will indicate the type of error).

See also

novas_sky_pos()

novas_app_to_geom()

novas_app_to_hor()

novas_geom_posvel()

Since

1.1

Author

Attila Kovacs

References grav_planets(), NOVAS_FULL_ACCURACY, NOVAS_REDUCED_ACCURACY, novas_vlen(), and vector2radec().

Converts an observed azimuth and elevation coordinate to right ascension (R.A.) and declination coordinates expressed in the coordinate system of choice. The observer must be located on the surface of Earth, or else the call will return with an error. The caller may optionally supply a refraction model of choice to calculate an appropriate elevation angle that includes a refraction correction for Earth's atmosphere. If no such model is provided, the provided elevation value will be assumed to be an astrometric elevation without a refraction correction.

Parameters

frame Observer frame, defining the time and place of observation (on Earth). az [deg] Observed azimuth angle. It may be NULL if not required. el [deg] Observed elevation angle. It may be NULL if not required. ref_model An appropriate refraction model, or NULL to assume unrefracted elevation. Depending on the refraction model, you might want to make sure that the weather parameters were set when the observing frame was defined. sys Astronomical coordinate system in which the output is R.A. and declination values are to be calculated. [out] ra [h] Calculated apparent right ascension (R.A.) coordinate [out] dec [deg] Calculated apparent declination coordinate

Returns

0 if successful, or else an error from itrs_to_tod() or itrs_to_cirs(), or -1 (errno will indicate the type of error).

See also

novas_app_to_hor()

novas_app_to_geom()

novas_standard_refraction()

novas_optical_refraction()

novas_radio_refraction()

novas_wave_refraction()

Since

1.1

Author

Attila Kovacs

References novas_timespec::fjd_tt, hor_to_itrs(), novas_timespec::ijd_tt, NOVAS_AIRBORNE_OBSERVER, NOVAS_CIRS, NOVAS_GCRS, NOVAS_ICRS, NOVAS_ITRS, NOVAS_J2000, NOVAS_MOD, NOVAS_OBSERVER_ON_EARTH, NOVAS_REFRACT_OBSERVED, NOVAS_TIRS, NOVAS_TOD, spin(), vector2radec(), wobble(), WOBBLE_ITRS_TO_PEF, and WOBBLE_ITRS_TO_TIRS.

Calculates horizontal tracking position and motion (first and second time derivatives) for the specified source in the given observing frame. The position and its derivatives are calculated via the more precise IAU2006 method, and CIRS, and then converted to local horizontal coordinates using the specified refraction model (if any).

Parameters

source Observed source frame Observing frame, defining the observer location and astronomical time of observation. ref_model Refraction model to use, or NULL for an unrefracted track. [out] track Output tracking parameters to populate

Returns

0 if successful, or else -1 if any of the pointer arguments are NULL, or else an error code from cio_ra() or from novas_sky_pos(), or from novas_app_hor().

Since

1.3

Author

Attila Kovacs

See also

novas_equ_track()

novas_track_pos()

References cio_ra(), sky_pos::dec, sky_pos::dis, novas_timespec::fjd_tt, NOVAS_AIRBORNE_OBSERVER, novas_app_to_hor(), NOVAS_CIRS, novas_make_frame(), NOVAS_OBSERVER_ON_EARTH, novas_sky_pos(), NOVAS_TOD, novas_v2z(), sky_pos::ra, sky_pos::rv, and SKY_POS_INIT.

Inverts a novas coordinate transformation matrix.

Parameters

transform Pointer to a coordinate transformation matrix. [out] inverse Pointer to a coordinate transformation matrix to populate with the inverse transform. It may be the same as the input.

Returns

0 if successful, or else -1 if the was an error (errno will indicate the type of error).

See also

novas_make_transform()

Since

1.1

Author

Attila Kovacs

References novas_transform::matrix.

Sets up a observing frame for a specific observer location, time of observation, and accuracy requirement. The frame is initialized using the currently configured planet ephemeris provider function (see set_planet_provider() and set_planet_provider_hp()), and in case of reduced accuracy mode, the currently configured IAU nutation model provider (see set_nutation_lp_provider()).

Note, that to construct full accuracy frames, you will need a high-precision ephemeris provider for the major planets (not just the default Earth/Sun), as without it, gravitational bending around massive plannets cannot be accounted for, and therefore μas accuracy cannot be ensured, in general. Attempting to construct a high-accuracy frame without a high-precision ephemeris provider for the major planets will result in an error in the 10–40 range from the required ephemeris() call.

NOTES:

1. This function expects the Earth polar wobble parameters to be defined on a per-frame basis and will not use the legacy global (undated) orientation parameters set via cel_pole().

Parameters

accuracy Accuracy requirement, NOVAS_FULL_ACCURACY (0) for the utmost precision or NOVAS_REDUCED_ACCURACY (1) if ~1 mas accuracy is sufficient. obs Observer location time Time of observation dx [mas] Earth orientation parameter, polar offset in x, e.g. from the IERS Bulletins. (The global, undated value set by cel_pole() is not not used here.) You can use 0.0 if sub-arcsecond accuracy is not required. dy [mas] Earth orientation parameter, polar offset in y, e.g. from the IERS Bulletins. (The global, undated value set by cel_pole() is not not used here.) You can use 0.0 if sub-arcsecond accuracy is not required. [out] frame Pointer to the observing frame to configure.

Returns

0 if successful, 10–40: error is 10 + the error from ephemeris(), 40–50: error is 40 + the error from geo_posvel(), 50–80: error is 50 + the error from sidereal_time(), 80–90 error is 80 + error from cio_location(), 90–100 error is 90 + error from cio_basis(). or else -1 if there was an error (errno will indicate the type of error).

See also

novas_change_observer()

novas_sky_pos()

novas_geom_posvel()

novas_make_transform()

set_planet_provider()

set_planet_provider_hp()

set_nutation_lp_provider()

Since

1.1

Author

Attila Kovacs

References novas_frame::accuracy, novas_frame::deps0, novas_frame::dpsi0, novas_frame::dx, novas_frame::dy, novas_frame::earth_pos, novas_frame::earth_vel, novas_frame::ee, ee_ct(), ephemeris(), novas_frame::era, era(), EROT_GST, novas_timespec::fjd_tt, novas_frame::gst, novas_timespec::ijd_tt, mean_obliq(), novas_frame::mobl, NOVAS_BARYCENTER, novas_change_observer(), NOVAS_EARTH_INIT, novas_get_split_time(), NOVAS_JD_J2000, NOVAS_OBSERVER_PLACES, NOVAS_REDUCED_ACCURACY, NOVAS_SUN_INIT, NOVAS_TRUE_EQUINOX, NOVAS_UT1, nutation_angles(), sidereal_time(), novas_frame::state, novas_frame::sun_pos, novas_frame::sun_vel, novas_frame::time, novas_frame::tobl, tt2tdb(), novas_timespec::ut1_to_tt, and observer::where.

Calculates a transformation matrix that can be used to convert positions and velocities from one coordinate reference system to another.

Parameters

frame Observer frame, defining the location and time of observation from_system Original coordinate reference system to_system New coordinate reference system [out] transform Pointer to the transform data structure to populate.

Returns

0 if successful, or else -1 if there was an error (errno will indicate the type of error).

See also

novas_transform_vector()

novas_transform_sky_pos()

novas_invert_transform()

novas_geom_posvel()

novas_app_to_geom()

Since

1.1

Author

Attila Kovacs

References novas_frame::era, novas_transform::frame, novas_transform::from_system, novas_frame::gcrs_to_cirs, novas_frame::icrs_to_j2000, novas_matrix::M, novas_transform::matrix, NOVAS_CIRS, NOVAS_GCRS, NOVAS_ICRS, NOVAS_ITRS, NOVAS_J2000, NOVAS_MOD, NOVAS_REFERENCE_SYSTEMS, NOVAS_TIRS, NOVAS_TOD, novas_frame::nutation, novas_frame::precession, and novas_transform::to_system.

Returns the apparent angular distance of a source from the Moon from the observer's point of view.

Parameters

source An observed source frame Observing frame, defining the observer location and astronomical time of observation.

Returns

[deg] Apparent angular distance between the source an the Moon, from the observer's point of view

Since

1.3

Author

Attila Kovacs

See also

novas_sun_angle()

References NOVAS_MOON_INIT, and novas_object_sep().

Returns the angular separation of two objects from the observer's point of view. The calculated separation includes light-time corrections, aberration and gravitational deflection for both sources, and thus represents a precise observed separation between the two sources.

Parameters

source1 An observed source source2 Another observed source frame Observing frame, defining the observer location and astronomical time of observation.

Returns

[deg] Apparent angular separation between the two observed sources from the observer's point-of-view.

Since

1.3

Author

Attila Kovacs

See also

novas_sun_angle()

novas_moon_angle()

novas_sep()

References sky_pos::dec, sky_pos::dis, novas_equ_sep(), NOVAS_GCRS, novas_sky_pos(), sky_pos::ra, and SKY_POS_INIT.

Returns the UTC date at which a distant source appears to rise above the specified elevation angle. The calculated time will account for the (slow) motion for Solar-system bodies, and optionally for atmospheric refraction also.

NOTES:

1. The current implementation is not suitable for calculating the nearest successive rise times for near-Earth objects, at or within the geostationary orbit.
2. This function calculates the time when the center (not the limb!) of the source rises above the specified elevation threshold. Something to keep in mind for calculating Sun/Moon rise times.

Parameters

el [deg] Elevation angle. source Observed source frame Observing frame, defining the observer location and astronomical time of observation. ref_model Refraction model, or NULL to calculate unrefracted rise time.

Returns

[day] UTC-based Julian date at which the object rises above the specified elevation next after the specified date, or else NAN if the source stays above or below the given elevation for the entire 24-hour period.

Since

1.3

Author

Attila Kovacs

See also

novas_sets_below()

novas_transit_time()

Returns the UTC date at which a distant source appears to set below the specified elevation angle. The calculated time will account for the (slow) motion of Solar-system bodies, and optionally for atmopsheric refraction also.

NOTES:

1. The current implementation is not suitable for calculating the nearest successive set times for near-Earth objects, at or within the geostationary orbit.
2. This function calculates the time when the center (not the limb!) of the source sets below the specified elevation threshold. Something to keep in mind for calculating Sun/Moon rise times.

Parameters

el [deg] Elevation angle. source Observed source frame Observing frame, defining the observer location and astronomical time of observation. ref_model Refraction model, or NULL to calculate unrefracted setting time.

Returns

[day] UTC-based Julian date at which the object sets below the specified elevation next after the specified date, or else NAN if the source stays above or below the given elevation for the entire 24-hour day..

Since

1.3

Author

Attila Kovacs

See also

novas_rises_above()

novas_transit_time()

Calculates an apparent location on sky for the source. The position takes into account the proper motion (for sidereal source), or is antedated for light-travel time (for Solar-System bodies). It also applies an appropriate aberration correction and gravitational deflection of the light.

To calculate corresponding local horizontal coordinates, you can pass the output RA/Dec coordinates to novas_app_to_hor(). Or to calculate apparent coordinates in other systems, you may pass the result to novas_transform_sy_pos() after.

And if you want geometric positions instead (not corrected for aberration or gravitational deflection), you may want to use novas_geom_posvel() instead.

The approximate 'inverse' of this function is novas_app_to_geom().

This function implements the same aberration and gravitational deflection corrections as place(), but at reduced computational cost. See place() for references. Unlike place(), however, the output always reports the distance calculated from the parallax for sidereal sources. Note also, that while place() does not apply aberration and gravitational deflection corrections when sys is NOVAS_ICRS (3), this routine will apply those corrections consistently for all coordinate systems (and you can use novas_geom_posvel() instead to get positions without aberration or deflection in any system).

NOTES:

1. If sys is NOVAS_TOD (true equator and equinox of date), the less precise old (pre IAU 2006) method is used, with the Lieske et al. 1977 nutation model, matching the behavior of the original NOVAS C place() for that system. To obtain more precise TOD coordinates, set sys to NOVAS_CIRS here, and follow with cirs_to_tod() / cirs_to_app_ra() on the out->r_hat / out->ra respectively after (or you can use just convert one of the quantities, and use radec2vector() or vector2radec() to get the other even faster).
2. As of SuperNOVAS v1.3, the returned radial velocity component is a proper observer-based spectroscopic measure. In prior releases, and in NOVAS C 3.1, this was inconsistent, with LSR-based measures being returned for catalog sources.

Parameters

object Pointer to a celestial object data structure that is observed. Catalog sources should have coordinates and properties in ICRS. You can use transform_cat() to convert catalog entries to ICRS as necessary. frame The observer frame, defining the location and time of observation. sys The coordinate system in which to return the apparent sky location. [out] out Pointer to the data structure which is populated with the calculated apparent location in the designated coordinate system.

Returns

0 if successful, 50–70 error is 50 + error from light_time2(), 70–80 error is 70 + error from grav_def(), or else -1 (errno will indicate the type of error).

See also

novas_geom_to_app()

novas_app_to_hor()

place()

cirs_to_tod()

cirs_to_app_ra()

Since

1.1

Author

Attila Kovacs

References grav_planets(), NOVAS_CATALOG_OBJECT, NOVAS_FULL_ACCURACY, novas_geom_posvel(), novas_geom_to_app(), NOVAS_ICRS, NOVAS_REDUCED_ACCURACY, novas_vlen(), rad_vel2(), and object::type.

Returns the Solar illumination fraction of a source, assuming a spherical geometry for the observed body.

Parameters

source Observed source. Usually a Solar-system source. (For other source types, 1.0 is returned by default.) frame Observing frame, defining the observer location and astronomical time of observation.

Returns

Solar illumination fraction [0.0:1.0] of a spherical body observed at the source location from the given observer location, or NAN if there was an error (errno will indicate the type of error).

Since

1.3

Author

Attila Kovacs

References NOVAS_CATALOG_OBJECT, novas_geom_posvel(), NOVAS_ICRS, and novas_vlen().

Returns the apparent angular distance of a source from the Sun from the observer's point of view.

Parameters

source An observed source frame Observing frame, defining the observer location and astronomical time of observation.

Returns

[deg] the apparent angular distance between the source an the Sun, from the observer's point of view

Since

1.3

Author

Attila Kovacs

See also

novas_moon_angle()

References novas_object_sep(), and NOVAS_SUN_INIT.

Calculates a projected position and redshift for a source, given the available tracking position and derivatives. Using 'tracks' to project positions can be much faster than the repeated full recalculation of the source position over some short period.

In SuperNOVAS terminology a 'track' is a 2nd order Taylor series expansion of the observed position and redshift in time. For most but the fastest moving sources, horizontal (Az/El) tracks are sufficiently precise on minute timescales, whereas depending on the type of source equatorial tracks can be precise for up to days.

Parameters

track Tracking position and motion (first and second derivatives) time Astrometric time of observation [out] lon [deg] projected observed Eastward longitude in tracking coordinate system [out] lat [deg] projected observed latitude in tracking coordinate system [out] dist [AU] projected apparent distance to source from observer [out] z projected observed redshift

Returns

0 if successful, or else -1 if either input pointer is NULL (errno is set to EINVAL).

Since

1.3

Author

Attila Kovacs

See also

novas_equ_track()

novas_hor_track()

novas_z2v()

References novas_track::accel, novas_observable::dist, novas_observable::lat, novas_observable::lon, novas_diff_time(), novas_track::pos, novas_track::rate, novas_track::time, and novas_observable::z.

Transforms a position or velocity 3-vector from one coordinate reference system to another.

Parameters

in Input apparent position on sky in the original coordinate reference system transform Pointer to a coordinate transformation matrix [out] out Output apparent position on sky in the new coordinate reference system. It may be the same as the input.

Returns

0 if successful, or else -1 if there was an error (errno will indicate the type of error).

See also

novas_make_transform()

novas_transform_vector()

Since

1.1

Author

Attila Kovacs

References sky_pos::dec, sky_pos::r_hat, sky_pos::ra, and vector2radec().

Transforms a position or velocity 3-vector from one coordinate reference system to another.

Parameters

in Input 3-vector in the original coordinate reference system transform Pointer to a coordinate transformation matrix [out] out Output 3-vector in the new coordinate reference system. It may be the same as the input.

Returns

0 if successful, or else -1 if there was an error (errno will indicate the type of error).

See also

novas_make_transform()

novas_transform_skypos()

Since

1.1

Author

Attila Kovacs

Returns the UTC date at which a source transits the local meridian. The calculated time will account for the (slow) motion of Solar-system bodies.

NOTES:

1. The current implementation is not suitable for calculating the nearest successive transit times for near-Earth objects, at or within the geostationary orbit.

Parameters

source Observed source frame Observing frame, defining the observer location and astronomical time of observation.

Returns

[day] UTC-based Julian date at which the object transits the local meridian next after the specified date, or NAN if either input pointer is NULL.

Since

1.3

Author

Attila Kovacs

See also

novas_rises_above()

novas_sets_below()

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