Different Sorts of Mean Place

From d54fe7c1f704a63824c5bfa0ece65245572e9b27 Mon Sep 17 00:00:00 2001 From: Joseph Hunkeler Date: Wed, 4 Mar 2015 21:21:30 -0500 Subject: Initial commit --- src/slalib/sun67.htx/node210.html | 177 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 177 insertions(+) create mode 100644 src/slalib/sun67.htx/node210.html (limited to 'src/slalib/sun67.htx/node210.html') diff --git a/src/slalib/sun67.htx/node210.html b/src/slalib/sun67.htx/node210.html new file mode 100644 index 0000000..1a8e19e --- /dev/null +++ b/src/slalib/sun67.htx/node210.html @@ -0,0 +1,177 @@ + + + + +Different Sorts of Mean Place + + + + + + + + + + + + +

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+ Next: Mean Place Transformations +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Aberration +

+Different Sorts of Mean Place +

+A particularly confusing aspect of published mean places is that they +are sensitive to the precise way they were determined. A mean +place is not directly observable, even with fundamental +instruments such as transit circles, and to produce a mean +place will involve relying on some existing star catalogue, +for example the fundamental catalogues FK4 and FK5, +and applying given mathematical models of precession, nutation, +aberration and so on. +Note in particular that no star catalogue, +even a fundamental catalogue such as FK4 or +FK5, defines a coordinate system, strictly speaking; +it is merely a list of star positions and proper motions. +However, once the stars from a given catalogue +are used as position calibrators, e.g. for +transit-circle observations or for plate reductions, then a +broader sense of there being a coordinate grid naturally +arises, and such phrases as ``in the system of +the FK4'' can legitimately be employed. However, +there is no formal link between the +two concepts - no ``standard least squares fit'' between +reality and the inevitably flawed catalogues. All such +catalogues suffer at some level from systematic, zonal distortions +of both the star positions and of the proper motions, +and include measurement errors peculiar to individual +stars. +

+Many of these complications are of little significance except to +specialists. However, observational astronomers cannot +escape exposure to at least the two main varieties of +mean place, loosely called +FK4 and FK5, and should be aware of +certain pitfalls. For most practical purposes the more recent +system, FK5, is free of surprises and tolerates naive +use well. FK4, in contrast, contains two important traps: +

The FK4 system rotates at about +
$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$ per century relative to distant galaxies. + This is manifested as a systematic distortion in the + proper motions of all FK4-derived catalogues, which will + in turn pollute any astrometry done using those catalogues. + For example, FK4-based astrometry of a QSO using plates + taken decades apart will reveal a non-zero fictitious proper + motion, and any FK4 star which happens to have zero proper + motion is, in fact, slowly moving against the distant + background. The FK4 frame rotates because it was + established before the nature of the Milky Way, and hence the + existence of systematic motions of nearby stars, had been + recognized. +
Star positions in the FK4 system are part-corrected for + annual aberration (see above) and embody the so-called + E-terms of aberration. +

+The change from the old FK4-based system to FK5 +occurred at the beginning +of 1984 as part of a package of resolutions made by the IAU in 1976, +along with the adoption of J2000 as the reference epoch. Star +positions in the newer, FK5, system are free from the E-terms, and +the system is a much better approximation to an +inertial frame (about five times better). +

+It may occasionally be convenient to specify the FK4 fictitious proper +motion directly. In FK4, the centennial proper motion of (for example) +a QSO is: +

$\mu_\alpha=-$ $0^{\rm s}\hspace{-0.3em}.015869$ +(( $0^{\rm s}\hspace{-0.3em}.029032$ $~\sin \alpha + +$ $0^{\rm s}\hspace{-0.3em}.000340$ $~\cos \alpha ) \sin \delta + -$ $0^{\rm s}\hspace{-0.3em}.000105$ $~\cos \alpha + -$ $0^{\rm s}\hspace{-0.3em}.000083$ $~\sin \alpha ) \sec \delta$
+ $\mu_\delta\,=+$ $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.43549$ $~\cos \alpha + -$ $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00510$ $~\sin \alpha + + ($ $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00158$ $~\sin \alpha + -$ $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00125$ $~\cos \alpha ) \sin \delta + -$ $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00066$ $~\cos \delta$ +