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0001 <sect1 id="ai-skycoords">
0002 <sect1info>
0003 <author>
0004 <firstname>Jason</firstname>
0005 <surname>Harris</surname>
0006 </author>
0007 </sect1info>
0008 <title>Celestial Coordinate Systems</title>
0009 <para>
0010 <indexterm><primary>Celestial Coordinate Systems</primary>
0011 <secondary>Overview</secondary></indexterm>
0012 A basic requirement for studying the heavens is determining where in the
0013 sky things are.  To specify sky positions, astronomers have developed
0014 several <firstterm>coordinate systems</firstterm>.  Each uses a coordinate grid
0015 projected on the <link linkend="ai-csphere">Celestial Sphere</link>, in
0016 analogy to the <link linkend="ai-geocoords">Geographic coordinate
0017 system</link> used on the surface of the Earth.  The coordinate systems
0018 differ only in their choice of the <firstterm>fundamental plane</firstterm>,
0019 which divides the sky into two equal hemispheres along a <link
0020 linkend="ai-greatcircle">great circle</link>. (the fundamental plane of the
0021 geographic system is the Earth's equator). Each coordinate system is named for
0022 its choice of fundamental plane.
0023 </para>
0025 <sect2 id="equatorial">
0026 <title>The Equatorial Coordinate System</title>
0027 <indexterm><primary>Celestial Coordinate Systems</primary>
0028 <secondary>Equatorial Coordinates</secondary>
0029 <seealso>Celestial Equator</seealso>
0030 <seealso>Celestial Poles</seealso>
0031 <seealso>Geographic Coordinate System</seealso>
0032 </indexterm>
0033 <indexterm><primary>Right Ascension</primary><see>Equatorial Coordinates</see></indexterm>
0034 <indexterm><primary>Declination</primary><see>Equatorial Coordinates</see></indexterm>
0036 <para>
0037 The <firstterm>Equatorial coordinate system</firstterm> is probably the most
0038 widely used celestial coordinate system.  It is also the most closely related
0039 to the <link linkend="ai-geocoords">Geographic coordinate system</link>, because
0040 they use the same fundamental plane, and the same poles.  The projection of the
0041 Earth's equator onto the celestial sphere is called the
0042 <link linkend="ai-cequator">Celestial Equator</link>.
0043 Similarly, projecting the geographic Poles onto the celestial sphere defines the
0044 North and South <link linkend="ai-cpoles">Celestial Poles</link>.
0045 </para><para>
0046 However, there is an important difference between the equatorial and
0047 geographic coordinate systems: the geographic system is fixed to the
0048 Earth; it rotates as the Earth does.  The Equatorial system is
0049 fixed to the stars<footnote id="fn-precess"><para>Actually, the equatorial
0050 coordinates are not quite fixed to the stars.  See <link
0051 linkend="ai-precession">precession</link>.  Also, if <link
0052 linkend="ai-hourangle">Hour Angle</link> is used in place of Right
0053 Ascension, then the Equatorial system is fixed to the Earth, not to the
0054 stars.</para></footnote>, so it appears to rotate across the sky with the stars,
0055 but of course it is really the Earth rotating under the fixed sky.
0056 </para><para>
0057 The <firstterm>latitudinal</firstterm> (latitude-like) angle of the Equatorial
0058 system is called <firstterm>Declination</firstterm> (Dec for short).  It
0059 measures the angle of an object above or below the Celestial Equator.  The
0060 <firstterm>longitudinal</firstterm> angle is called the <firstterm>Right
0061 Ascension</firstterm> (<acronym>RA</acronym> for short).  It measures the angle of an object East
0062 of the <link linkend="ai-equinox">Vernal Equinox</link>.  Unlike longitude,
0063 Right Ascension is usually measured in hours instead of degrees, because the
0064 apparent rotation of the Equatorial coordinate system is closely related to
0065 <link linkend="ai-sidereal">Sidereal Time</link> and <link
0066 linkend="ai-hourangle">Hour Angle</link>.  Since a full rotation of the sky
0067 takes 24 hours to complete, there are (360 degrees / 24 hours) = 15 degrees in
0068 one Hour of Right Ascension.
0069 </para>
0070 <para>
0071 The equatorial coordinates for deep-sky objects and stars do not vary
0072 appreciably over short durations of time, since they are not affected
0073 by the <firstterm>diurnal motion</firstterm> (the daily apparent
0074 rotation of the sky around the earth. However, note that this takes
0075 <link linkend="ai-sidereal">1 sidereal day</link>, as against 1 solar
0076 day). They are suitable coordinates for making catalogs of stars and
0077 deep-sky objects (note that <firstterm>Galactic
0078 Coordinates</firstterm> also work well, but are cumbersome to use from
0079 an earth point-of-view). However, there are effects that cause the RA
0080 and Dec of objects to vary over time,
0081 namely <link linkend="ai-precession">Precession</link>
0082 and <firstterm>nutation</firstterm>, and <firstterm>proper
0083 motion</firstterm>, the latter being even less important. Equatorial
0084 coordinates are thus generally specified with an
0085 appropriate <link linkend="ai-epoch">epoch</link>, to account for
0086 precession. Popular epochs include J2000.0
0087 (<link linkend="ai-julianday">Julian Year</link> 2000) and B1950.0
0088 (<firstterm>Besselian Year</firstterm> 1950).
0089 </para>
0090 </sect2>
0092 <sect2 id="horizontal">
0093 <title>The Horizontal Coordinate System</title>
0095 <indexterm><primary>Celestial Coordinate Systems</primary>
0096 <secondary>Horizontal Coordinates</secondary>
0097 <seealso>Horizon</seealso>
0098 <seealso>Zenith</seealso>
0099 </indexterm>
0100 <indexterm><primary>Azimuth</primary><see>Horizontal Coordinates</see></indexterm>
0101 <indexterm><primary>Altitude</primary><see>Horizontal Coordinates</see></indexterm>
0102 <para>
0103 The Horizontal coordinate system uses the observer's local <link
0104 linkend="ai-horizon">horizon</link> as the Fundamental Plane.  This conveniently
0105 divides the sky into the upper hemisphere that you can see, and the lower
0106 hemisphere that you can't (because the Earth is in the way).  The pole of the
0107 upper hemisphere is called the <link linkend="ai-zenith">Zenith</link>.  The
0108 pole of the lower hemisphere is called the <firstterm>nadir</firstterm>.  The
0109 angle of an object above or below the horizon is called the
0110 <firstterm>Altitude</firstterm> (Alt for short).  The angle of an object around
0111 the horizon (measured from the North point, toward the East) is called the
0112 <firstterm>Azimuth</firstterm>.  The Horizontal Coordinate System is sometimes
0113 also called the Alt/Az Coordinate System.
0114 </para><para>
0115 The Horizontal Coordinate System is fixed to the Earth, not the Stars.
0116 Therefore, the Altitude and Azimuth of an object changes with time, as the
0117 object appears to drift across the sky.  In addition, because the Horizontal
0118 system is defined by your local horizon, the same object viewed from different
0119 locations on Earth at the same time will have different values of Altitude and
0120 Azimuth.
0121 </para><para>
0122 Horizontal coordinates are very useful for determining the Rise and Set times of
0123 an object in the sky.  When an object has Altitude=0 degrees, it is either
0124 Rising (if its Azimuth is &lt; 180 degrees) or Setting (if its Azimuth is &gt;
0125 180 degrees).
0126 </para>
0127 </sect2>
0129 <sect2 id="ecliptic">
0130 <title>The Ecliptic Coordinate System</title>
0132 <indexterm><primary>Celestial Coordinate Systems</primary>
0133 <secondary>Ecliptic Coordinates</secondary>
0134 <seealso>Ecliptic</seealso>
0135 </indexterm>
0136 <para>
0137 The Ecliptic coordinate system uses the <link
0138 linkend="ai-ecliptic">Ecliptic</link> for its Fundamental Plane.  The
0139 Ecliptic is the path that the Sun appears to follow across the sky over
0140 the course of a year.  It is also the projection of the Earth's
0141 orbital plane onto the Celestial Sphere.  The latitudinal angle is
0142 called the <firstterm>Ecliptic Latitude</firstterm>, and the longitudinal angle
0143 is called the <firstterm>Ecliptic Longitude</firstterm>.  Like Right Ascension
0144 in the Equatorial system, the zeropoint of the Ecliptic Longitude is the <link
0145 linkend="ai-equinox">Vernal Equinox</link>.
0146 </para><para>
0147 What do you think such a coordinate system would be useful for?  If you
0148 guessed charting solar system objects, you are right!  Each of the
0149 planets (except Pluto) orbits the Sun in roughly the same plane, so they always
0150 appear to be somewhere near the Ecliptic (&ie;, they always have small ecliptic
0151 latitudes).
0152 </para>
0153 </sect2>
0155 <sect2 id="galactic">
0156 <title>The Galactic Coordinate System</title>
0158 <indexterm><primary>Celestial Coordinate Systems</primary>
0159 <secondary>Galactic Coordinates</secondary>
0160 </indexterm>
0161 <para>
0162 <indexterm><primary>Milky Way</primary></indexterm>
0163 The Galactic coordinate system uses the <firstterm>Milky Way</firstterm> as its
0164 Fundamental Plane.  The latitudinal angle is called the <firstterm>Galactic
0165 Latitude</firstterm>, and the longitudinal angle is called the
0166 <firstterm>Galactic Longitude</firstterm>.  This coordinate system is useful for
0167 studying the Galaxy itself.  For example, you might want to know how the density
0168 of stars changes as a function of Galactic Latitude, to how much the disk of the
0169 Milky Way is flattened.
0170 </para>
0171 </sect2>
0172 </sect1>