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Astronomical Applications Department, U.S. Naval Observatory - NOVAS 2004 Overview (Page 4)

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Astronomical Applications Department, U.S. Naval Observatory - NOVAS 2004 Overview
4
that the new nutation model has more than ten times the number of trigonometric terms than the pre-
vious model. Since evaluation of nutation has always been the most computationally intensive task in
NOVAS, you may notice an increase in execution time for some NOVAS applications (more on this
below).

A New Model for the Rotation of the Earth about its Axis

IAU resolutions passed in 2000 also dealt in a very fundamental way with how we describe the Earth's
spin around its axis. The conventional treatment is based on the equinox and sidereal time;
Greenwich (or local) sidereal time is just the Greenwich (or local) hour angle of the equinox of date.
However, the equinox is constantly moving due to precession, so that sidereal time combines two
angular motions, the Earth's rotation and the precession of its axis. (In the case of apparent sidereal
time, nutation is also mixed in.) One rotation of the Earth is about 0.008 second longer than one mean
sidereal day.

For about two decades, some of the people who routinely deal with the most precise measurements of
the Earth's rotation have been advocating for a change in the way it is described, and their ideas were
introduced in resolutions passed by the IAU in 2000. In this new paradigm, the reference point on the
moving celestial equator for the description of Earth rotation is called the celestial ephemeris origin
(CEO). Unlike the equinox, this point has no motion along the equator at all; as the orientation of the
equator changes in space due to precession and nutation, the CEO remains on the equator but its
instantaneous motion is always at right angles to it. Thus, loosely speaking, two transits of the CEO
across the local meridian define one rotation of the Earth. The CEO is a point on the celestial equator
near RA=0, and there is a corresponding point on the terrestrial equator near longitude=0 called the
terrestrial ephemeris origin (TEO). For all astronomical purposes, the TEO can be considered a point
fixed on the surface of the Earth at latitude and longitude zero.
1
In the new paradigm, the rotation of
the Earth is specified by the angle (in the instantaneous equatorial plane) between the TEO and the
CEO, which is a linear function of universal time (UT1). This angle is called the Earth rotation angle
and is designated by .

How are hour angles of celestial objects computed in the old and new paradigms? Assume that we are
considering Greenwich hour angles, that is, hour angles measured from the meridian of longitude zero,
and without polar motion. In the equinox-based scheme, we compute the topocentric apparent place of
the object of interest with respect to the true equator and equinox of date. Then we compute apparent
sidereal time and subtract the object's apparent right ascension to form the hour angle. In the CEO-
based scheme, we compute the object's topocentric apparent place with respect to the true equator and
CEO of date. To form the hour angle, we compute the Earth rotation angle and subtract the equatorial
angle measured eastward from the CEO to the object (essentially, the right ascension of the object
measured with respect to the CEO). Since hour angle is an observable quantity, the two results should
be identical. You might wonder, then, what the advantage of the new system is. In the equinox-based
scheme, precession and nutation appear in both the apparent place of the star and sidereal time. In the
CEO-based scheme, they appear only in the apparent place of the star. The CEO-based method also
does not depend on the equinox, and is thus independent of any model of the Earth's orbital motion.
1
The CEO and TEO are technically examples of non-rotating origins, and neither is fixed within its
respective coordinate system. However, the slow drift of the TEO, due to polar motion, with respect to
standard geodetic coordinates (the International Terrestrial Reference System, or, effectively, WGS84)
amounts to only 1.5 millimeters per century and is completely negligible for astronomical purposes.

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