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<sect1 id="ai-csphere">
<sect1info>
<author>
<firstname>Jason</firstname>
<surname>Harris</surname>
</author>
</sect1info>
<title>The Celestial Sphere</title>
<para>
The celestial sphere is an imaginary sphere of gigantic radius, centered
on the Earth. All objects which can be seen in the sky can be thought
of as lying on the surface of this sphere.
</para><para>
Of course, we know that the objects in the sky are not on the surface of
a sphere centered on the Earth, so why bother with such a construct?
Everything we see in the sky is so very far away, that their distances
are impossible to gauge just by looking at them. Since their distances
are indeterminate, you only need to know the <emphasis>direction</emphasis>
toward the object to locate it in the sky. In this sense, the celestial sphere
model is a very practical model for mapping the sky.
</para><para>
The directions toward various objects in the sky can be quantified by
constructing a <link linkend="ai-skycoords">Celestial Coordinate System</link>.
</para>
</sect1>
<sect1 id="ai-equinox">
<sect1info>
<author>
<firstname>Jason</firstname>
<surname>Harris</surname>
</author>
</sect1info>
<title>The Equinoxes</title>
<para>
Most people know the Vernal and Autumnal Equinoxes as
calendar dates, signifying the beginning of the Northern hemisphere's Spring
and Autumn, respectively. Did you know that the equinoxes are also positions in
the sky?
</para><para>
The <firstterm>Celestial Equator</firstterm> and the
<link linkend="ai-ecliptic">Ecliptic</link> are two
<link linkend="ai-greatcircle">Great Circles</link> on the
<link linkend="ai-csphere">Celestial Sphere</link>, set at an angle of 23.5
degrees. The two points where they intersect are called the
<firstterm>Equinoxes</firstterm>. The <firstterm>Vernal Equinox</firstterm> has
coordinates RA=0.0 hours, Dec=0.0 degrees. The <firstterm>Autumnal
Equinox</firstterm> has coordinates RA=12.0 hours, Dec=0.0 degrees.
</para><para>
The Equinoxes are important for marking the seasons. Because they are on
the <link linkend="ai-ecliptic">Ecliptic</link>, the Sun passes through each
equinox every year. When the Sun passes through the Vernal Equinox (usually on
March 21st), it crosses the Celestial Equator from South to North,
signifying the end of Winter for the Northern hemisphere. Similarly, when
the Sun passes through the Autumnal Equinox (usually on September 21st), it
crosses the Celestial Equator from North to South, signifying the
end of Winter for the Southern hemisphere.
</para>
</sect1>
<sect1 id="ai-geocoords">
<sect1info>
<author>
<firstname>Jason</firstname>
<surname>Harris</surname>
</author>
</sect1info>
<title>Geographic Coordinates</title>
<para>
Locations on Earth can be specified using a spherical coordinate system.
The geographic (<quote>earth-mapping</quote>) coordinate system is aligned
with the spin axis of the Earth. It defines two angles measured from
the center of the Earth. One angle, called the <firstterm>Latitude</firstterm>,
measures the angle between any point and the Equator. The other angle, called
the <firstterm>Longitude</firstterm>, measures the angle
<emphasis>along</emphasis> the Equator from an arbitrary point on the Earth
(Greenwich, England is the accepted zero-longitude point in most modern
societies).
</para><para>
By combining these two angles, any location on Earth can be specified.
For example, Baltimore, Maryland (USA) has a latitude of 39.3 degrees
North, and a longitude of 76.6 degrees West. So, a vector drawn from
the center of the Earth to a point 39.3 degrees above the Equator and
76.6 degrees west of Greenwich, England will pass through Baltimore.
</para><para>
The Equator is obviously an important part of this coordinate system, it
represents the <emphasis>zeropoint</emphasis> of the latitude angle, and the
halfway point between the poles. The Equator is the <firstterm>Fundamental
Plane</firstterm> of the geographic coordinate system. <link
linkend="ai-skycoords">All Spherical Coordinate Systems</link> define such a
Fundamental Plane.
</para><para>
Lines of constant Latitude are called <firstterm>Parallels</firstterm>. They
trace circles on the surface of the Earth, but the only parallel that is a <link
linkend="ai-greatcircle">Great Circle</link> is the Equator (Latitude=0
degrees). Lines of constant Longitude are called
<firstterm>Meridians</firstterm>. The Meridian passing through Greenwich is the
<firstterm>Prime Meridian</firstterm> (longitude=0 degrees). Unlike Parallels,
all Meridians are great cricles, and Meridians are not parallel: they intersect
at the north and south poles.
</para>
<tip>
<para>Exercise:</para>
<para>
What is the longitude of the North Pole? It's latitude
is 90 degrees North.
</para>
<para>
It is a trick question. The Longitude is meaningless at the north pole (and the
south pole too). It has all longitudes at the same time.
</para>
</tip>
</sect1>
<sect1 id="ai-greatcircle">
<sect1info>
<author>
<firstname>Jason</firstname>
<surname>Harris</surname>
</author>
</sect1info>
<title>Great Circles</title>
<para>
Consider a sphere, such as the Earth, or the <link
linkend="ai-csphere">Celestial Sphere</link>. The intersection of any plane
with the sphere will result in a circle on the surface of the sphere. If the
plane happens to contain the center of the sphere, the intersection circle is a
<firstterm>Great Circle</firstterm>. Great circles are the largest circles that
can be drawn on a sphere. Also, the shortest path between any two points on a
sphere is always along a great circle.
</para><para>
Some examples of great circles on the celestial sphere include: the
<link linkend="ai-horizon">Horizon</link>, the Celestial Equator, and the <link
linkend="ai-ecliptic">Ecliptic</link>.
</para>
</sect1>
<sect1 id="ai-horizon">
<sect1info>
<author>
<firstname>Jason</firstname>
<surname>Harris</surname>
</author>
</sect1info>
<title>The Horizon</title>
<para>
The <firstterm>Horizon</firstterm> is the line that separates Earth from Sky.
More precisely, it is the line that divides all of the directions you can
possibly look into two categories: those which intersect the Earth,
and those which do not. At many locations, the Horizon is
obscured by trees, buildings, mountains, etc. However, if you are on
a ship at sea, the Horizon is strikingly apparent.
</para><para>
The horizon is the <firstterm>Fundamental Plane</firstterm> of the <link
linkend="horizontal">Horizontal Coordinate System</link>. In other
words, it is the locus of points which have an <firstterm>Altitude</firstterm>
of zero degrees.
</para>
</sect1>
<sect1 id="ai-hourangle">
<sect1info>
<author>
<firstname>Jason</firstname>
<surname>Harris</surname>
</author>
</sect1info>
<title>Hour Angle</title>
<para>
As explained in the <link linkend="ai-sidereal">Sidereal Time</link> article,
the <firstterm>Right Ascension</firstterm> of an object indicates the Sidereal
Time at which it will transit across your <link linkend="ai-meridian">Local
Meridian</link>. An object's <firstterm>Hour Angle</firstterm> is
defined as the difference between the current Local Sidereal Time and the Right
Ascension of the object:
</para><para>
<abbrev>HA</abbrev><subscript>obj</subscript> =
<abbrev>LST</abbrev> - <abbrev>RA</abbrev><subscript>obj</subscript>
</para><para>
Thus, the object's Hour Angle indicates how much Sidereal Time has passed
since the object was on the Local Meridian. It is also the angular distance
between the object and the meridian, measured in hours (1 hour = 15 degrees).
For example, if an object has an hour angle of 2.5 hours, it transited across
the Local Meridian 2.5 hours ago, and is currently 37.5 degrees West of the
Meridian. Negative Hour Angles indicate the time until the
<emphasis>next</emphasis> transit across the Local Meridian. Of course, an Hour
Angle of zero means the object is currently on the Local Meridian.
</para>
</sect1>
<sect1 id="ai-julianday">
<sect1info>
<author>
<firstname>John</firstname>
<surname>Cirillo</surname>
</author>
</sect1info>
<title>Julian Day</title>
<para>
The Julian Calendar is a way of reckoning the current date by a simple count of
the number of days that have passed since some remote, arbitrary date. This
number of days is called the <firstterm>Julian Day</firstterm>,
abbreviated as <abbrev>JD</abbrev>. The starting point, <abbrev>JD=0</abbrev>,
is January 1, 4713 BC (or -4712 January 1, since there was no year '0'). Julian
Days are very useful because they make it easy to determine the number of days
between two events by simply subtracting their Julian Day numbers.
Such a calculation is difficult for the standard (Gregorian) calendar, because
days are grouped into months, which can contain a variable number of days, and
there is the added complication of <link linkend="ai-leapyear">Leap
Years</link>.
</para><para>
Converting from the standard (Gregorian) calendar to Julian Days and vice versa
is best left to a special program written to do this, and there are many to be
found on the web (and &kstars; does this too, of course!). However, for those
interested, here is a simple example of a Gregorian to Julian day converter:
</para><para>
<abbrev>JD</abbrev> = <abbrev>D</abbrev> - 32075 + 1461*( <abbrev>Y</abbrev> +
4800 * ( <abbrev>M</abbrev> - 14 ) / 12 ) / 4 + 367*( <abbrev>M</abbrev> - 2 -
( <abbrev>M</abbrev> - 14 ) / 12 * 12 ) / 12 - 3*( ( <abbrev>Y</abbrev> + 4900 +
( <abbrev>M</abbrev> - 14 ) / 12 ) / 100 ) / 4
</para><para>
where <abbrev>D</abbrev> is the day (1-31), <abbrev>M</abbrev> is the Month
(1-12), and <abbrev>Y</abbrev> is the year (1801-2099). Note that this formula
only works for dates between 1801 and 2099. More remote dates require a more
complicated transformation.
</para><para>
An example Julian Day is: <abbrev>JD</abbrev> 2440588, which corresponds to
1 Jan, 1970.
</para><para>
Julian Days can also be used to tell time; the time of day is expressed as a
fraction of a full day, with 12:00 noon (not midnight) as the zero point. So,
3:00 pm on 1 Jan 1970 is <abbrev>JD</abbrev> 2440588.125 (since 3:00 pm is 3
hours since noon, and 3/24 = 0.125 day). Note that the Julian Day is always
determined from <link linkend="ai-utime">Universal Time</link>, not Local Time.
</para><para>
Astronomers use certain Julian Day values as important reference points, called
<firstterm>Epochs</firstterm>. One widely-used epoch is called J2000; it is the
Julian Day for 1 Jan, 2000 at 12:00 noon = <abbrev>JD</abbrev> 2451545.0.
</para><para>
Much more information on Julian Days is availabel on the internet. A good
starting point is the <ulink
url="http://aa.usno.navy.mil/faq/docs/JD_Formula.html">U.S. Naval
Observatory</ulink>. If that site is not available when you read this, try
searching for <quote>Julian Day</quote> with your favorite search engine.
</para>
</sect1>
<sect1 id="ai-meridian">
<sect1info>
<author>
<firstname>Jason</firstname>
<surname>Harris</surname>
</author>
</sect1info>
<title>The Local Meridian</title>
<para>
The Meridian is an imaginary <link linkend="ai-greatcircle">Great Circle</link>
on the <link linkend="ai-csphere">Celestial Sphere</link> that is perpendicular
to the local <link linkend="ai-horizon">Horizon</link>. It passes through the
North point on the Horizon, through the <link linkend="ai-cpoles">Celestial
Pole</link>, up to the <link linkend="ai-zenith">Zenith</link>, and through the
South point on the Horizon.
</para><para>
Because it is fixed to the local Horizon, stars will appear to drift past
the Local Meridian as the Earth spins. You can use an object's <link
linkend="equatorial">Right Ascension</link> and the <link
linkend="ai-sidereal">Local Sidereal Time</link> to determine when it will
cross your Local Meridian (see <link linkend="ai-hourangle">Hour Angle</link>).
</para>
</sect1>
<sect1 id="ai-retrograde">
<sect1info>
<author>
<firstname>John</firstname>
<surname>Cirillo</surname>
</author>
</sect1info>
<title>Retrograde Motion</title>
<para>
<firstterm>Retrograde Motion</firstterm> is the orbital motion of a body in a
direction opposite that which is normal to spatial bodies within a given system.
</para><para>
When we observe the sky, we expect most objects to appear to move in a
particular direction with the passing of time. The apparent motion of
most bodies in the sky is from east to west. However it is possible to
observe a body moving west to east, such as an artificial satellite or
space shuttle that is orbiting eastward. This orbit is
considered Retrograde Motion.
</para><para>
Retrograde Motion is most often used in reference to the
motion of the outer planets (Mars, Jupiter, Saturn, and so forth).
Though these planets appear to move from east to west on a nightly
basis in response to the spin of the Earth, they are actually drifting
slowly eastward with respect to the stationary stars, which can be
observed by noting the position of these planets for several nights in a
row. This motion is normal for these planets, however, and not
considered Retrograde Motion. However, since the Earth completes its
orbit in a shorter period of time than these outer planets, we
occassionally overtake an outer planet, like a faster car on a
multiple-lane highway. When this occurs, the planet we are passing will
first appear to stop its eastward drift, and it will then
appear to drift back toward the west. This is Retrograde Motion, since
it is in a direction opposite that which is typical for planets. Finally
as the Earth swings past the the planet in its orbit, they appear to
resume their normal west-to-east drift on succesive nights.
</para><para>
This Retrograde Motion of the planets puzzled ancient Greek
astronomers, and was one reason why they named these bodies <quote>planets</quote>
which in Greek means <quote>wanderers</quote>.
</para>
</sect1>
<sect1 id="ai-skycoords">
<sect1info>
<author>
<firstname>Jason</firstname>
<surname>Harris</surname>
</author>
</sect1info>
<title>Celestial Coordinate Systems</title>
<para>
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>
<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 Celestial Equator.
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's 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> (RA 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>
</sect2>
<sect2 id="horizontal">
<title>The Horizontal Coordinate System</title>
<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>
<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're 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>
<para>
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>
<sect1 id="ai-timezones">
<sect1info>
<author>
<firstname>Jason</firstname>
<surname>Harris</surname>
</author>
</sect1info>
<title>Time Zones</title>
<para>
The Earth is round, and it is always half-illuminated by the Sun. However,
because the Earth is spinning, the half that is illuminated is always changing.
We experience this as the passing of days wherever we are on the Earth's
surface. At any given instant, there are places on the Earth passing from the
dark half into the illuminated half (which is seen as <emphasis>dawn</emphasis>
on the surface). At the same instant, on the opposite side of the Earth, points
are passing from the illuminated half into darkness (which is seen as
<emphasis>dusk</emphasis> at those locations). So, at any given time, different
places on Earth are experiencing different parts of the day. Thus, Solar time
is defined locally, so that the clock time at any location describes the part of
the day consistently.
</para><para>
This localization of time is accomplished by dividing the globe into 24 vertical
slices called <firstterm>Time Zones</firstterm>. The Local Time is the same
within any given zone, but the time in each zone is one Hour
<emphasis>earlier</emphasis> than the time in the neighboring Zone to the East.
Actually, this is a idealized simplification; real Time Zone boundaries are not
straight vertical lines, because they often follow national boundaries and other
political considerations.
</para><para>
Note that because the Local Time always increases by an hour when moving between
Zones to the East, by the time you move through all 24 Time Zones, you are a
full day ahead of where you started! We deal with this paradox by defining the
<firstterm>International Date Line</firstterm>, which is a Time Zone boundary in
the Pacific Ocean, between Asia and North America. Points just to the East of
this line are 24 hours behind the points just to the West of the line. This
leads to some interesting phenomena. A direct flight from Australia to
California arrives before it departs! Also, the islands of Fiji straddle the
International Date Line, so if you have a bad day on the West side of Fiji, you
can go over to the East side of Fiji and have a chance to live the same day all
over again!
</para>
</sect1>
<sect1 id="ai-utime">
<sect1info>
<author>
<firstname>Jason</firstname>
<surname>Harris</surname>
</author>
</sect1info>
<title>Universal Time</title>
<para>
The time on our clocks is essentially a measurement of the current position of
the Sun in the sky, which is different for places at different Longitudes
because the Earth is round (see <link linkend="ai-timezones">Time Zones</link>).
</para><para>
However, it is sometimes necessary to define a global time, one that is the same
for all places on Earth. One way to do this is to pick a place on the Earth,
and adopt the Local Time at that place as the <firstterm>Universal
Time</firstterm>, abbrteviated <abbrev>UT</abbrev>. (The name is a bit of a
misnomer, since Universal Time has little to do with the Universe. It would
perhaps be better to think of it as <emphasis>global time</emphasis>).
</para><para>
The geographic location chosen to represent Universal Time is Greenwich,
England. The choice is arbitrary and historical. Universal Time became an
important concept when European ships began to sail the wide open seas, far from
any known landmarks. A navigator could reckon the ship's longitude by comparing
the Local Time (as measured from the Sun's position) to the time back at the
home port (as kept by an accurate clock on board the ship). Greenwich was home
to England's Royal Observatory, which was charged with keeping time
very accurately, so that ships in port could re-calibrate their clocks before
setting sail.
</para>
<tip>
<para>Exercise:</para>
<para>
Set the geographic location to <quote>Greenwich, England</quote> using the
<guilabel>Set Location</guilabel> window
(<keycombo action="simul">&Ctrl;<keycap>G</keycap></keycombo>). Note that the
Local Time (<abbrev>LT</abbrev>)and the Universal Time (<abbrev>UT</abbrev>) are
now the same.
</para><para>
Further Reading: The history behind the construction of the first clock
that was accurate and stable enough to be used on ships to keep Universal Time
is a fascinating tale, and one told expertly in the book
<quote>Longitude</quote>, by Dava Sobel.
</para>
</tip>
</sect1>
<sect1 id="ai-zenith">
<sect1info>
<author>
<firstname>Jason</firstname>
<surname>Harris</surname>
</author>
</sect1info>
<title>The Zenith</title>
<para>
The Zenith is the point in the sky where you are looking when you look
<quote>straight up</quote> from the ground. More precisely, it is the point on
the sky with an <firstterm>Altitude</firstterm> of +90 Degrees; it is the Pole
of the <link linkend="horizontal">Horizontal Coordinate
System</link>. Geometrically, it is the point on the <link
linkend="ai-csphere">Celestial Sphere</link> intersected by a line drawn from
the center of the Earth through your location on the Earth's surface.
</para><para>
The Zenith is, by definition, a point along the <link
linkend="ai-meridian">Local Meridian</link>.
</para>
<tip>
<para>Exercise:</para>
<para>
You can point to the Zenith by pressing <keycap>Z</keycap> or by selecting
<guimenuitem>Zenith</guimenuitem> from the <guimenu>Location</guimenu> menu.
</para>
</tip>
</sect1>
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