[astrom, pmt, eb, eh, em, v, bm1, bpn, along, xpl, ypl, sphi, cphi, diurab, eral, refa, refb] = ERFA.apco(date1, date2, ebpv, ehp, x, y, s, theta, elong, phi, hm, xp, yp, sp, refa, refb)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.
date1 double TDB as a 2-part...
date2 double ...Julian Date (Note 1)
ebpv double[2][3] Earth barycentric PV (au, au/day, Note 2)
ehp double[3] Earth heliocentric P (au, Note 2)
x,y double CIP X,Y (components of unit vector)
s double the CIO locator s (radians)
theta double Earth rotation angle (radians)
elong double longitude (radians, east +ve, Note 3)
phi double latitude (geodetic, radians, Note 3)
hm double height above ellipsoid (m, geodetic, Note 3)
xp,yp double polar motion coordinates (radians, Note 4)
sp double the TIO locator s' (radians, Note 4)
refa double refraction constant A (radians, Note 5)
refb double refraction constant B (radians, Note 5)
astrom ASTROM* star-independent astrometry parameters:
pmt double PM time interval (SSB, Julian years)
eb double[3] SSB to observer (vector, au)
eh double[3] Sun to observer (unit vector)
em double distance from Sun to observer (au)
v double[3] barycentric observer velocity (vector, c)
bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor
bpn double[3][3] bias-precession-nutation matrix
along double adjusted longitude (radians)
xpl double polar motion xp wrt local meridian (radians)
ypl double polar motion yp wrt local meridian (radians)
sphi double sine of geodetic latitude
cphi double cosine of geodetic latitude
diurab double magnitude of diurnal aberration vector
eral double "local" Earth rotation angle (radians)
refa double refraction constant A (radians)
refb double refraction constant B (radians)
- The TDB date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TDB)=2450123.7 could be expressed in any of these ways, among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience. For most applications of this function the choice will not be at all critical.
TT can be used instead of TDB without any significant impact on accuracy.
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The vectors eb, eh, and all the astrom vectors, are with respect to BCRS axes.
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The geographical coordinates are with respect to the ERFA_WGS84 reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN CONVENTION: the longitude required by the present function is right-handed, i.e. east-positive, in accordance with geographical convention.
The adjusted longitude stored in the astrom array takes into account the TIO locator and polar motion.
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xp and yp are the coordinates (in radians) of the Celestial Intermediate Pole with respect to the International Terrestrial Reference System (see IERS Conventions), measured along the meridians 0 and 90 deg west respectively. sp is the TIO locator s', in radians, which positions the Terrestrial Intermediate Origin on the equator. For many applications, xp, yp and (especially) sp can be set to zero.
Internally, the polar motion is stored in a form rotated onto the local meridian.
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The refraction constants refa and refb are for use in a dZ = Atan(Z)+Btan^3(Z) model, where Z is the observed (i.e. refracted) zenith distance and dZ is the amount of refraction.
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It is advisable to take great care with units, as even unlikely values of the input parameters are accepted and processed in accordance with the models used.
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In cases where the caller does not wish to provide the Earth Ephemeris, the Earth rotation information and refraction constants, the function eraApco13 can be used instead of the present function. This starts from UTC and weather readings etc. and computes suitable values using other ERFA functions.
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This is one of several functions that inserts into the astrom structure star-independent parameters needed for the chain of astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.
The various functions support different classes of observer and portions of the transformation chain:
functions observer transformation
eraApcg eraApcg13 geocentric ICRS <-> GCRS
eraApci eraApci13 terrestrial ICRS <-> CIRS
eraApco eraApco13 terrestrial ICRS <-> observed
eraApcs eraApcs13 space ICRS <-> GCRS
eraAper eraAper13 terrestrial update Earth rotation
eraApio eraApio13 terrestrial CIRS <-> observed
Those with names ending in "13" use contemporary ERFA models to compute the various ephemerides. The others accept ephemerides supplied by the caller.
The transformation from ICRS to GCRS covers space motion, parallax, light deflection, and aberration. From GCRS to CIRS comprises frame bias and precession-nutation. From CIRS to observed takes account of Earth rotation, polar motion, diurnal aberration and parallax (unless subsumed into the ICRS <-> GCRS transformation), and atmospheric refraction.
- The context structure astrom produced by this function is used by eraAtioq, eraAtoiq, eraAtciq* and eraAticq*.
eraIr initialize r-matrix to identity
eraRz rotate around Z-axis
eraRy rotate around Y-axis
eraRx rotate around X-axis
eraAnpm normalize angle into range +/- pi
eraC2ixys celestial-to-intermediate matrix, given X,Y and s
eraPvtob position/velocity of terrestrial station
eraTrxpv product of transpose of r-matrix and pv-vector
eraApcs astrometry parameters, ICRS-GCRS, space observer
eraCr copy r-matrix
This revision: 2021 February 24
Copyright (C) 2013-2021, NumFOCUS Foundation. Derived, with permission, from the SOFA library.