<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>
