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diff --git a/src/slalib/sun67.htx/node203.html b/src/slalib/sun67.htx/node203.html new file mode 100644 index 0000000..fd18b48 --- /dev/null +++ b/src/slalib/sun67.htx/node203.html @@ -0,0 +1,187 @@ +<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN"> +<!--Converted with LaTeX2HTML 97.1 (release) (July 13th, 1997) + by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds +* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan +* with significant contributions from: + Jens Lippman, Marek Rouchal, Martin Wilck and others --> +<HTML> +<HEAD> +<TITLE>Precession and Nutation</TITLE> +<META NAME="description" CONTENT="Precession and Nutation"> +<META NAME="keywords" CONTENT="sun67"> +<META NAME="resource-type" CONTENT="document"> +<META NAME="distribution" CONTENT="global"> +<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso_8859_1"> +<LINK REL="STYLESHEET" HREF="sun67.css"> +<LINK REL="next" HREF="node205.html"> +<LINK REL="previous" HREF="node202.html"> +<LINK REL="up" HREF="node197.html"> +<LINK REL="next" HREF="node204.html"> +</HEAD> +<BODY > +<BR> <HR> +<A NAME="tex2html2482" HREF="node204.html"> +<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next_motif.gif"></A> +<A NAME="tex2html2480" HREF="node197.html"> +<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up_motif.gif"></A> +<A NAME="tex2html2474" HREF="node202.html"> +<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="previous_motif.gif"></A> <A HREF="sun67.html#stardoccontents"><IMG ALIGN="BOTTOM" BORDER="0" + SRC="contents_motif.gif"></A> +<BR> +<B> Next:</B> <A NAME="tex2html2483" HREF="node204.html">SLALIB support for precession and nutation</A> +<BR> +<B>Up:</B> <A NAME="tex2html2481" HREF="node197.html">EXPLANATION AND EXAMPLES</A> +<BR> +<B> Previous:</B> <A NAME="tex2html2475" HREF="node202.html">Celestial Coordinate Systems</A> +<BR> <HR> <P> +<P><!--End of Navigation Panel--> +<H2><A NAME="SECTION00054000000000000000"> +Precession and Nutation</A> +</H2> +<I>Right ascension and declination</I>, (<IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img3.gif" + ALT="$[\,\alpha,\delta\,]$">), are the names +of the longitude and latitude in a spherical +polar coordinate system based on the Earth's axis of rotation. +The zero point of <IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img24.gif" + ALT="$\alpha$"> is the point of intersection of +the <I>celestial +equator</I> and the <I>ecliptic</I> (the apparent path of the Sun +through the year) where the Sun moves into the northern +hemisphere. This point is called the +<I>first point of Aries</I>, +the <I>vernal equinox</I> (with apologies to +southern-hemisphere readers) or simply the <I>equinox</I>.<A NAME="tex2html4" HREF="footnode.html#27833"><SUP><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]" SRC="foot_motif.gif"></SUP></A> +<P> +This simple picture is unfortunately +complicated by the difficulty of defining +a suitable equator and equinox. One problem is that the +Sun's apparent motion is not completely regular, due to the +ellipticity of the Earth's orbit and its continuous disturbance +by the Moon and planets. This is dealt with by +separating the motion into (i) a smooth and steady <I>mean Sun</I> +and (ii) a set of periodic corrections and perturbations; only the former +is involved in establishing reference frames and timescales. +A second, far larger problem, is that +the celestial equator and the ecliptic +are both moving with respect to the stars. +These motions arise because of the gravitational +interactions between the Earth and the other solar-system bodies. +<P> +By far the largest effect is the +so-called ``precession of the equinoxes'', where the Earth's +rotation axis sweeps out a cone centred on the ecliptic +pole, completing one revolution in about 26,000 years. The +cause of the motion is the torque exerted on the distorted and +spinning Earth by the Sun and the Moon. Consider the effect of the +Sun alone, at or near the northern summer solstice. The Sun +`sees' the top (north pole) of the Earth tilted towards it +(by about <IMG WIDTH="33" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img256.gif" + ALT="$23^{\circ} + \hspace{-0.37em}.\hspace{0.02em}5$">, the <I>obliquity of the +ecliptic</I>), +and sees the nearer part of the Earth's equatorial bulge +below centre and the further part above centre. +Although the Earth is in free fall, +the gravitational force on the nearer part of the +equatorial bulge is greater than that on the further part, and +so there is a net torque acting +as if to eliminate the tilt. Six months later the same thing +is happening in reverse, except that the torque is still +trying to eliminate the tilt. In between (at the equinoxes) the +torque shrinks to zero. A torque acting on a spinning body +is gyroscopically translated +into a precessional motion of the spin axis at right-angles to the torque, +and this happens to the Earth. +The motion varies during the +year, going through two maxima, but always acts in the +same direction. The Moon produces the same effect, +adding a contribution to the precession which peaks twice +per month. The Moon's proximity to the Earth more than compensates +for its smaller mass and gravitational attraction, so that it +in fact contributes most of the precessional effect. +<P> +The complex interactions between the three bodies produce a +precessional motion that is wobbly rather than completely smooth. +However, the main 26,000-year component is on such a grand scale that +it dwarfs the remaining terms, the biggest of +which has an amplitude of only <IMG WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" + SRC="img133.gif" + ALT="$17\hspace{-0.05em}^{'\hspace{-0.1em}'}$"> and a period of +about 18.6 years. This difference of scale makes it convenient to treat +these two components of the motion separately. The main 26,000-year +effect is called <I>luni-solar precession</I>; the smaller, +faster, periodic terms are called the <I>nutation</I>. +<P> +Note that precession and nutation are simply +different frequency components of the same physical effect. It is +a common misconception that precession is caused +by the Sun and nutation is caused by the Moon. In fact +the Moon is responsible for two-thirds of the precession, and, +while it is true that much of the complex detail of the nutation is +a reflection of the intricacies of the lunar orbit, there are +nonetheless important solar terms in the nutation. +<P> +In addition to and quite separate +from the precession/nutation effect, the orbit of the Earth-Moon system +is not fixed in orientation, a result of the attractions of the +planets. This slow (about + <IMG WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" + SRC="img83.gif" + ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$"> per year) +secular rotation of the ecliptic about a slowly-moving diameter is called, +confusingly, <I>planetary +precession</I> and, along with the luni-solar precession is +included in the <I>general precession</I>. The equator and +ecliptic as affected by general precession +are what define the various ``mean'' <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img3.gif" + ALT="$[\,\alpha,\delta\,]$"> reference frames. +<P> +The models for precession and nutation come from a combination +of observation and theory, and are subject to continuous +refinement. Nutation models in particular have reached a high +degree of sophistication, taking into account such things as +the non-rigidity of the Earth and the effects of +the planets; SLALIB's nutation +model (IAU 1980) involves 106 terms in each of <IMG WIDTH="14" HEIGHT="27" ALIGN="MIDDLE" BORDER="0" + SRC="img105.gif" + ALT="$\psi$"> (longitude) +and <IMG WIDTH="9" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img257.gif" + ALT="$\epsilon$"> (obliquity), some as small as + <IMG WIDTH="47" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" + SRC="img258.gif" + ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.0001$"> . +<P> +<BR><HR> +<!--Table of Child-Links--> +<A NAME="CHILD_LINKS"> </A> +<UL> +<LI><A NAME="tex2html2484" HREF="node204.html#SECTION00054100000000000000"> +SLALIB support for precession and nutation</A> +</UL> +<!--End of Table of Child-Links--> +<BR> <HR> +<A NAME="tex2html2482" HREF="node204.html"> +<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next_motif.gif"></A> +<A NAME="tex2html2480" HREF="node197.html"> +<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up_motif.gif"></A> +<A NAME="tex2html2474" HREF="node202.html"> +<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="previous_motif.gif"></A> <A HREF="sun67.html#stardoccontents"><IMG ALIGN="BOTTOM" BORDER="0" + SRC="contents_motif.gif"></A> +<BR> +<B> Next:</B> <A NAME="tex2html2483" HREF="node204.html">SLALIB support for precession and nutation</A> +<BR> +<B>Up:</B> <A NAME="tex2html2481" HREF="node197.html">EXPLANATION AND EXAMPLES</A> +<BR> +<B> Previous:</B> <A NAME="tex2html2475" HREF="node202.html">Celestial Coordinate Systems</A> +<BR> <HR> <P> +<P><!--End of Navigation Panel--> +<ADDRESS> +<I>SLALIB --- Positional Astronomy Library<BR>Starlink User Note 67<BR>P. T. Wallace<BR>12 October 1999<BR>E-mail:ptw@star.rl.ac.uk</I> +</ADDRESS> +</BODY> +</HTML> |