11.2.1 Astronomical Coordinate Calculations

The frame bias matrix rb transforms vectors from Geocentric Celestial Reference System to the J2000.0 mean equator and equinox by applying frame bias. It does not depend on the date.

The precession matrix rp transforms vectors from the J2000.0 mean equator and equinox to the mean equator and equinox of the date by applying precession.

The bias-precession matrix rbp transforms vectors from Geocentric Celestial Reference System to the mean equator and equinox of the date by applying frame bias and then precession. rbp = rp # rb

The bias-precession-nutation matrix rbpn...

The Celestial Intermediate Pole coordinates x, y are components of the Celestial Intermediate Pole unit vector in the Geocentric Celestial Reference System.

The Celestial Intermediate Origin locator s positions the Celestial Intermediate Origin on the equator of the Celestial Intermediate Pole.

Given celestial coordinates crs (in the Geocentric Celestial Reference System), the celestial-to-intermediate-frame-of-date matrix rc2i, the polar motion matrix rpom, and Earth Rotation Angle era, the terrestrial coordinates trs (in the International Terrestrial Reference System) are found through

trs = rpom # R_3(era) # rc2i # crs

The celestial-to-terrestrial matrix rc2t translates coordinate from the Geocentric Celestial Reference System to the International Terrestrial Reference System:

trs = rc2t # crs

rc2t = rpom # R_3(era) # rc2i

Given celestial coordinates crs (in the Geocentric Celestial Reference System), the celestial-to-true matrix rbpn, the polar motion matrix rpom, and Greenwich apparent Sidereal Time gst, the terrestrial coordinates trs (in the International Terrestrial Reference System) are found through

trs = rpom # R_3(gst) # rbpn # crs

The celestial-to-terrestrial matrix rc2t translates coordinate from the Geocentric Celestial Reference System to the International Terrestrial Reference System:

trs = rc2t # crs

rc2t = rpom # R_3(gst) # rbpn