<sect1 id="ai-skycoords">
<sect1info>
<author>
<firstname>Jason</firstname>
<surname>Harris</surname>
</author>
</sect1info>
<title>Celestial Coordinate Systems</title>
<para>
<indexterm><primary>Celestial Coordinate Systems</primary>
<secondary>Overview</secondary></indexterm>
A basic requirement for studying the heavens is determining where in the
sky things are.  To specify sky positions, astronomers have developed
several <firstterm>coordinate systems</firstterm>.  Each uses a coordinate grid
projected on the <link linkend="ai-csphere">Celestial Sphere</link>, in
analogy to the <link linkend="ai-geocoords">Geographic coordinate
system</link> used on the surface of the Earth.  The coordinate systems
differ only in their choice of the <firstterm>fundamental plane</firstterm>,
which divides the sky into two equal hemispheres along a <link
linkend="ai-greatcircle">great circle</link>. (the fundamental plane of the
geographic system is the Earth's equator). Each coordinate system is named for
its choice of fundamental plane.
</para>

<sect2 id="equatorial">
<title>The Equatorial Coordinate System</title>
<indexterm><primary>Celestial Coordinate Systems</primary>
<secondary>Equatorial Coordinates</secondary>
<seealso>Celestial Equator</seealso>
<seealso>Celestial Poles</seealso>
<seealso>Geographic Coordinate System</seealso>
</indexterm>
<indexterm><primary>Right Ascension</primary><see>Equatorial Coordinates</see></indexterm>
<indexterm><primary>Declination</primary><see>Equatorial Coordinates</see></indexterm>

<para>
The <firstterm>Equatorial coordinate system</firstterm> is probably the most
widely used celestial coordinate system.  It is also the most closely related
to the <link linkend="ai-geocoords">Geographic coordinate system</link>, because
they use the same fundamental plane, and the same poles.  The projection of the
Earth's equator onto the celestial sphere is called the
<link linkend="ai-cequator">Celestial Equator</link>.
Similarly, projecting the geographic Poles onto the celestial sphere defines the
North and South <link linkend="ai-cpoles">Celestial Poles</link>.
</para><para>
However, there is an important difference between the equatorial and
geographic coordinate systems: the geographic system is fixed to the
Earth; it rotates as the Earth does.  The Equatorial system is
fixed to the stars<footnote id="fn-precess"><para>actually, the equatorial
coordinates are not quite fixed to the stars.  See <link
linkend="ai-precession">precession</link>.  Also, if <link
linkend="ai-hourangle">Hour Angle</link> is used in place of Right
Ascension, then the Equatorial system is fixed to the Earth, not to the
stars.</para></footnote>, so it appears to rotate across the sky with the stars,
but of course it is really the Earth rotating under the fixed sky.
</para><para>
The <firstterm>latitudinal</firstterm> (latitude-like) angle of the Equatorial
system is called <firstterm>Declination</firstterm> (Dec for short).  It
measures the angle of an object above or below the Celestial Equator.  The
<firstterm>longitudinal</firstterm> angle is called the <firstterm>Right
Ascension</firstterm> (<acronym>RA</acronym> for short).  It measures the angle of an object East
of the <link linkend="ai-equinox">Vernal Equinox</link>.  Unlike longitude,
Right Ascension is usually measured in hours instead of degrees, because the
apparent rotation of the Equatorial coordinate system is closely related to
<link linkend="ai-sidereal">Sidereal Time</link> and <link
linkend="ai-hourangle">Hour Angle</link>.  Since a full rotation of the sky
takes 24 hours to complete, there are (360 degrees / 24 hours) = 15 degrees in
one Hour of Right Ascension.
</para>
<para>
The equatorial coordinates for deep-sky objects and stars do not vary
appreciably over short durations of time, since they are not affected
by the <firstterm>diurnal motion</firstterm> (the daily apparent
rotation of the sky around the earth. However, note that this takes
<link linkend="ai-sidereal">1 sidereal day</link>, as against 1 solar
day). They are suitable coordinates for making catalogs of stars and
deep-sky objects (note that <firstterm>Galactic
Coordinates</firstterm> also work well, but are cumbersome to use from
an earth point-of-view). However, there are effects that cause the RA
and Dec of objects to vary over time,
namely <link linkend="ai-precession">Precession</link>
and <firstterm>nutation</firstterm>, and <firstterm>proper
motion</firstterm>, the latter being even less important. Equatorial
coordinates are thus generally specified with an
appropriate <link linkend="ai-epoch">epoch</link>, to account for
precession. Popular epochs include J2000.0
(<link linkend="ai-julianday">Julian Year</link> 2000) and B1950.0
(<firstterm>Besselian Year</firstterm> 1950).
</para>
</sect2>

<sect2 id="horizontal">
<title>The Horizontal Coordinate System</title>

<indexterm><primary>Celestial Coordinate Systems</primary>
<secondary>Horizontal Coordinates</secondary>
<seealso>Horizon</seealso>
<seealso>Zenith</seealso>
</indexterm>
<indexterm><primary>Azimuth</primary><see>Horizontal Coordinates</see></indexterm>
<indexterm><primary>Altitude</primary><see>Horizontal Coordinates</see></indexterm>
<para>
The Horizontal coordinate system uses the observer's local <link
linkend="ai-horizon">horizon</link> as the Fundamental Plane.  This conveniently
divides the sky into the upper hemisphere that you can see, and the lower
hemisphere that you can't (because the Earth is in the way).  The pole of the
upper hemisphere is called the <link linkend="ai-zenith">Zenith</link>.  The
pole of the lower hemisphere is called the <firstterm>nadir</firstterm>.  The
angle of an object above or below the horizon is called the
<firstterm>Altitude</firstterm> (Alt for short).  The angle of an object around
the horizon (measured from the North point, toward the East) is called the
<firstterm>Azimuth</firstterm>.  The Horizontal Coordinate System is sometimes
also called the Alt/Az Coordinate System.
</para><para>
The Horizontal Coordinate System is fixed to the Earth, not the Stars.
Therefore, the Altitude and Azimuth of an object changes with time, as the
object appears to drift across the sky.  In addition, because the Horizontal
system is defined by your local horizon, the same object viewed from different
locations on Earth at the same time will have different values of Altitude and
Azimuth.
</para><para>
Horizontal coordinates are very useful for determining the Rise and Set times of
an object in the sky.  When an object has Altitude=0 degrees, it is either
Rising (if its Azimuth is &lt; 180 degrees) or Setting (if its Azimuth is &gt;
180 degrees).
</para>
</sect2>

<sect2 id="ecliptic">
<title>The Ecliptic Coordinate System</title>

<indexterm><primary>Celestial Coordinate Systems</primary>
<secondary>Ecliptic Coordinates</secondary>
<seealso>Ecliptic</seealso>
</indexterm>
<para>
The Ecliptic coordinate system uses the <link
linkend="ai-ecliptic">Ecliptic</link> for its Fundamental Plane.  The
Ecliptic is the path that the Sun appears to follow across the sky over
the course of a year.  It is also the projection of the Earth's
orbital plane onto the Celestial Sphere.  The latitudinal angle is
called the <firstterm>Ecliptic Latitude</firstterm>, and the longitudinal angle
is called the <firstterm>Ecliptic Longitude</firstterm>.  Like Right Ascension
in the Equatorial system, the zeropoint of the Ecliptic Longitude is the <link
linkend="ai-equinox">Vernal Equinox</link>.
</para><para>
What do you think such a coordinate system would be useful for?  If you
guessed charting solar system objects, you are right!  Each of the
planets (except Pluto) orbits the Sun in roughly the same plane, so they always
appear to be somewhere near the Ecliptic (&ie;, they always have small ecliptic
latitudes).
</para>
</sect2>

<sect2 id="galactic">
<title>The Galactic Coordinate System</title>

<indexterm><primary>Celestial Coordinate Systems</primary>
<secondary>Galactic Coordinates</secondary>
</indexterm>
<para>
<indexterm><primary>Milky Way</primary></indexterm>
The Galactic coordinate system uses the <firstterm>Milky Way</firstterm> as its
Fundamental Plane.  The latitudinal angle is called the <firstterm>Galactic
Latitude</firstterm>, and the longitudinal angle is called the
<firstterm>Galactic Longitude</firstterm>.  This coordinate system is useful for
studying the Galaxy itself.  For example, you might want to know how the density
of stars changes as a function of Galactic Latitude, to how much the disk of the
Milky Way is flattened.
</para>
</sect2>
</sect1>
