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 <sect1 id="ai-cosmicdist">
 <sect1info>
 <author>
 <firstname>Akarsh</firstname>
 <surname>Simha</surname>
 </author>
 </sect1info>
 <title>Cosmic Distance Ladder</title>
 <indexterm><primary>Cosmic Distance Ladder</primary></indexterm>
 <para>
 The cosmic distance ladder refers to the succession of different
 methods that astronomers use to measure distances to objects in the
 sky. Some methods, like <link linkend="ai-parallax">parallax</link>,
 work well for only nearby objects. Other methods, like using the
 <firstterm>cosmological redshift</firstterm>, work only for very
 distance galaxies. Thus, there are several methods, each with its own
 limited validity, and hence the name.
 </para>
 <sect2>
 <title>Direct measurements</title>
 <para>
 The bottom of the ladder consists of objects whose distances can be
 directly measured, like the moon
 (see <ulink url="https://en.wikipedia.org/wiki/Lunar_Laser_Ranging_experiment">Lunar
 Laser Ranging</ulink>). The same technique, using radio waves, is
 applied to find distances to planets as well.
 </para>
 
 <para>
 For nearby stars, measuring the
 <link linkend="ai-parallax">parallax</link> is possible and yields the
 distance to the star.
 </para>
 </sect2>
 
 <sect2>
 <title>Standard candles</title>
 <para>
 "Standard candles" are objects whose intrinsic brightnesses we can
 know for sure. The
 apparent <link linkend="ai-magnitude">magnitude</link>, which is easy
 to measure, tells us how bright an object appears, not how bright it
 actually is. Distant objects appear less brighter, because their light
 gets spread out over a larger area.
 </para><para>
 In accordance with the <firstterm>inverse square law</firstterm> for
 light intensities, the amount of light we receive from an object drops
 with the distance squared. Thus, we may compute the distance to an
 object if we know both how bright it actually is (absolute magnitude; 'M')
 and how bright it appears to us on earth (apparent magnitude; 'm'). We may
 define the <firstterm>distance modulus</firstterm> as follows:
 </para><para>
 Distance Modulus = M - m = 5 log<subscript>10</subscript> d - 5
 </para><para>
 Here 'd' is the distance measured
 in <link linkend="ai-parallax">parsecs</link>.
 </para>
 <para>
 For these special standard candle objects, we have some other way of
 knowing their intrinsic brightness, and thereby can calculate their
 distance.
 </para>
 <para>
 Common "standard candles" used in astronomy are:
 
 <itemizedlist>
 
 <listitem><para>Cepheid Variables: A kind of periodic variable star, whose variation period
   is related to the luminosity</para></listitem>
 
 <listitem><para>RR Lyrae Variables: Another such periodic variable star with a
   well-known period-luminosity relationship</para></listitem>
 
 <listitem><para>Type-Ia supernovae: These supernovae have a very well-defined
   luminosity as a result of the physics that governs them and hence
   serve as standard-candles</para></listitem>
 
 </itemizedlist>
 </para>
 </sect2>
 
 <sect2>
 <title>Other methods</title>
 <para>
 There are many other methods. Some of them rely on the physics of
 stars, such as the relationship between luminosity and color for
 various types of stars (this is usually represented on
 a <firstterm>Hertzsprung-Russel Diagram</firstterm>). Some of them
 work for star clusters, such as the <firstterm>Moving cluster
 method</firstterm> and the <firstterm>main-sequence fitting
 method</firstterm>. The <firstterm>Tully-Fisher relation</firstterm>
 that relates the brightness of a spiral galaxy to its rotation can be
 used to find the distance modulus, since the rotation of a galaxy is
 easy to measure using <firstterm>Doppler shift</firstterm>. Distances
 to distant galaxies may be found by measuring
 the <firstterm>Cosmological redshift</firstterm>, which is the
 redshift of light from distance galaxies that results from the
 expansion of the universe.
 </para>
 <para>
 For further information,
 consult <ulink url="https://en.wikipedia.org/wiki/Cosmic_distance_ladder">Wikipedia
     on Cosmic Distance Ladder</ulink>
 </para>
 </sect2>
 </sect1>