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      <hr>
      <h4><a name="uk.ac.starlink.ttools.func.Distances">10.5.4 Distances</a></h4>
      <p>Functions for converting between different measures of cosmological 
         distance.
      </p>
      <p>The following parameters are used:
         
         <ul>
            <li><strong>z</strong>: redshift
            </li>
            <li><strong>H0</strong>: Hubble constant in km/sec/Mpc
               (example value ~70)
            </li>
            <li><strong>omegaM</strong>: Density ratio of the universe
               (example value 0.3)
            </li>
            <li><strong>omegaLambda</strong>: Normalised cosmological constant
               (example value 0.7)
            </li>
         </ul>
      </p>
      <p>For a flat universe, <code>omegaM</code>+<code>omegaLambda</code>=1
      </p>
      <p>The terms and formulae used here are taken from the 
         paper by D.W.Hogg, <em>Distance measures in cosmology</em>,
         <a href="http://arxiv.org/abs/astro-ph/9905116">astro-ph/9905116</a> v4 
         (2000).
      </p>
      <p>
         <dl>
            <dt><strong><code>MpcToM( distMpc )</code></strong></dt>
            <dd>Converts from MegaParsecs to metres.
               <ul>
                  <li><code>distMpc</code> <em>(floating point)</em>: distance in Mpc
                  </li>
                  <li>return value <em>(floating point)</em>: distance in m
                  </li>
               </ul>
            </dd>
            <dt><strong><code>mToMpc( distM )</code></strong></dt>
            <dd>Converts from metres to MegaParsecs.
               <ul>
                  <li><code>distM</code> <em>(floating point)</em>: distance in m
                  </li>
                  <li>return value <em>(floating point)</em>: distance in Mpc
                  </li>
               </ul>
            </dd>
            <dt><strong><code>zToDist( z )</code></strong></dt>
            <dd>Quick and dirty function for converting from redshift to distance.
               <p><strong>Warning</strong>: this makes some reasonable
                  assumptions about the cosmology and returns the luminosity
                  distance.  It is only intended for approximate use.  If you care
                  about the details, use one of the more specific functions here.
                  <ul>
                     <li><code>z</code> <em>(floating point)</em>: redshift
                     </li>
                     <li>return value <em>(floating point)</em>: some distance measure in Mpc
                     </li>
                  </ul>
               </p>
            </dd>
            <dt><strong><code>zToAge( z )</code></strong></dt>
            <dd>Quick and dirty function for converting from redshift to time.
               <p><strong>Warning</strong>: this makes some reasonable
                  assumptions about the cosmology.  It is only intended for approximate
                  use.  If you care about the details use one of the more specific
                  functions here.
                  <ul>
                     <li><code>z</code> <em>(floating point)</em>: redshift
                     </li>
                     <li>return value <em>(floating point)</em>: 'age' of photons from redshift <code>z</code> in Gyr
                     </li>
                  </ul>
               </p>
            </dd>
            <dt><strong><code>comovingDistanceL( z, H0, omegaM, omegaLambda )</code></strong></dt>
            <dd>Line-of-sight comoving distance.
               <ul>
                  <li><code>z</code> <em>(floating point)</em>: redshift
                  </li>
                  <li><code>H0</code> <em>(floating point)</em>: Hubble constant in km/sec/Mpc
                  </li>
                  <li><code>omegaM</code> <em>(floating point)</em>: density ratio of the universe
                  </li>
                  <li><code>omegaLambda</code> <em>(floating point)</em>: normalised cosmological constant
                  </li>
                  <li>return value <em>(floating point)</em>: line-of-sight comoving distance in Mpc
                  </li>
               </ul>
            </dd>
            <dt><strong><code>comovingDistanceT( z, H0, omegaM, omegaLambda )</code></strong></dt>
            <dd>Transverse comoving distance.
               <ul>
                  <li><code>z</code> <em>(floating point)</em>: redshift
                  </li>
                  <li><code>H0</code> <em>(floating point)</em>: Hubble constant in km/sec/Mpc
                  </li>
                  <li><code>omegaM</code> <em>(floating point)</em>: density ratio of the universe
                  </li>
                  <li><code>omegaLambda</code> <em>(floating point)</em>: normalised cosmological constant
                  </li>
                  <li>return value <em>(floating point)</em>: transverse comoving distance in Mpc
                  </li>
               </ul>
            </dd>
            <dt><strong><code>angularDiameterDistance( z, H0, omegaM, omegaLambda )</code></strong></dt>
            <dd>Angular diameter distance.
               <ul>
                  <li><code>z</code> <em>(floating point)</em>: redshift
                  </li>
                  <li><code>H0</code> <em>(floating point)</em>: Hubble constant in km/sec/Mpc
                  </li>
                  <li><code>omegaM</code> <em>(floating point)</em>: density ratio of the universe
                  </li>
                  <li><code>omegaLambda</code> <em>(floating point)</em>: normalised cosmological constant
                  </li>
                  <li>return value <em>(floating point)</em>: angular diameter distance in Mpc
                  </li>
               </ul>
            </dd>
            <dt><strong><code>luminosityDistance( z, H0, omegaM, omegaLambda )</code></strong></dt>
            <dd>Luminosity distance.
               <ul>
                  <li><code>z</code> <em>(floating point)</em>: redshift
                  </li>
                  <li><code>H0</code> <em>(floating point)</em>: Hubble constant in km/sec/Mpc
                  </li>
                  <li><code>omegaM</code> <em>(floating point)</em>: density ratio of the universe
                  </li>
                  <li><code>omegaLambda</code> <em>(floating point)</em>: normalised cosmological constant
                  </li>
                  <li>return value <em>(floating point)</em>: luminosity distance in Mpc
                  </li>
               </ul>
            </dd>
            <dt><strong><code>lookbackTime( z, H0, omegaM, omegaLambda )</code></strong></dt>
            <dd>Lookback time.  This returns the difference between the age of
               the universe at time of observation (now) and the age of the
               universe at the time when photons of redshift <code>z</code>
               were emitted.
               <ul>
                  <li><code>z</code> <em>(floating point)</em>: redshift
                  </li>
                  <li><code>H0</code> <em>(floating point)</em>: Hubble constant in km/sec/Mpc
                  </li>
                  <li><code>omegaM</code> <em>(floating point)</em>: density ratio of the universe
                  </li>
                  <li><code>omegaLambda</code> <em>(floating point)</em>: normalised cosmological constant
                  </li>
                  <li>return value <em>(floating point)</em>: lookback time in Gyr
                  </li>
               </ul>
            </dd>
            <dt><strong><code>comovingVolume( z, H0, omegaM, omegaLambda )</code></strong></dt>
            <dd>Comoving volume.  This returns the all-sky total comoving
               volume out to a given redshift <code>z</code>.
               <ul>
                  <li><code>z</code> <em>(floating point)</em>: redshift
                  </li>
                  <li><code>H0</code> <em>(floating point)</em>: Hubble constant in km/sec/Mpc
                  </li>
                  <li><code>omegaM</code> <em>(floating point)</em>: density ratio of the universe
                  </li>
                  <li><code>omegaLambda</code> <em>(floating point)</em>: normalised cosmological constant
                  </li>
                  <li>return value <em>(floating point)</em>: comoving volume in Gpc<sup>3</sup></li>
               </ul>
            </dd>
            <dt><strong><code>SPEED_OF_LIGHT</code></strong></dt>
            <dd>Speed of light in m/s.
               <ul></ul>
            </dd>
            <dt><strong><code>METRE_PER_PARSEC</code></strong></dt>
            <dd>Number of metres in a parsec.
               <ul></ul>
            </dd>
            <dt><strong><code>SEC_PER_YEAR</code></strong></dt>
            <dd>Number of seconds in a year.
               <ul></ul>
            </dd>
         </dl>
      </p>
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