Transformations Between Celestial and Terrestrial Reference Frames

Abstract

The rotation of a Cartesian frame of reference due to general (lunisolar and planetary) precession and astronomic nutation between the epochs T₀ and T is given by the matrix formula

$${{\vec{e}}_{T}} = N{\mkern 1mu} P{{\vec{e}}_{M}}$$

(1)

where ${{\vec{e}}_{M}}$ and ${{\vec{e}}_{T}}$ denote unit vectors in the reference frame at the epoch T₀ (and affected by precession) and at the epoch T (and affected by precession and nutation) respectively. In the astronomical convention, the former is termed the ‘mean’ unit vector (at epoch T₀), while the latter is the ‘true’ unit vector (at epoch T). The terms mean and true are also used in the general sense, defining star positions, reference frames, celestial equator, equinox, pole positions, etc., depending on whether they are affected by precession only or also by nutation. Reference epoch designation must also follow. For the theory of precession and nutation, see Chapter 8.