Transformations Between Celestial and Terrestrial Reference Frames

  • Ivan I. Mueller
Part of the Astrophysics and Space Science Library book series (ASSL, volume 154)


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


Reference Frame Polar Motion Terrestrial Reference Frame Celestial Reference Frame Terrestrial Reference System 
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Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • Ivan I. Mueller
    • 1
  1. 1.Ohio State UniversityColumbusUSA

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