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<b class="current">The <tt class="ttfamily">ast</tt> module</b>
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<div><h2 id="a0000000246">2.1 The <tt class="ttfamily">ast</tt> module</h2>
<p>The <tt class="ttfamily">ast</tt> module contains specialist functions for astronomy and cosmology. </p><p>   <big class="large"><b class="bf">ast.Lcdm_­age(<img src="images/img-0463.png" alt="$H_0$" style="vertical-align:-2px; 
                                     width:22px; 
                                     height:14px" class="math gen" />,­<img src="images/img-0464.png" alt="$\Omega _\mathrm {M}$" style="vertical-align:-3px; 
                                     width:26px; 
                                     height:15px" class="math gen" />,­<img src="images/img-0465.png" alt="$\Omega _\Uplambda $" style="vertical-align:-3px; 
                                     width:24px; 
                                     height:15px" class="math gen" />)</b></big> <br />The ast.Lcdm_­age(<img src="images/img-0463.png" alt="$H_0$" style="vertical-align:-2px; 
                                     width:22px; 
                                     height:14px" class="math gen" />,­<img src="images/img-0464.png" alt="$\Omega _\mathrm {M}$" style="vertical-align:-3px; 
                                     width:26px; 
                                     height:15px" class="math gen" />,­<img src="images/img-0465.png" alt="$\Omega _\Uplambda $" style="vertical-align:-3px; 
                                     width:24px; 
                                     height:15px" class="math gen" />) function returns the current age of the Universe in a standard <img src="images/img-0709.png" alt="$\Uplambda _\mathrm {CDM}$" style="vertical-align:-3px; 
                                     width:48px; 
                                     height:17px" class="math gen" /> cosmology with specified values for Hubble’s constant, <img src="images/img-0464.png" alt="$\Omega _\mathrm {M}$" style="vertical-align:-3px; 
                                     width:26px; 
                                     height:15px" class="math gen" /> and <img src="images/img-0465.png" alt="$\Omega _\Uplambda $" style="vertical-align:-3px; 
                                     width:24px; 
                                     height:15px" class="math gen" />. Hubble’s constant should be specified either with physical units of recession velocity per unit distance, or as a dimensionless number, assumed to have implicit units of km/s/Mpc. Suitable input values for a standard cosmology are: <img src="images/img-0710.png" alt="$H_0=70$" style="vertical-align:-2px; 
                                     width:65px; 
                                     height:15px" class="math gen" />, <img src="images/img-0711.png" alt="$\Omega _\mathrm {M}=0.27$" style="vertical-align:-3px; 
                                     width:83px; 
                                     height:16px" class="math gen" /> and <img src="images/img-0712.png" alt="$\Omega _\Uplambda =0.73$" style="vertical-align:-3px; 
                                     width:80px; 
                                     height:16px" class="math gen" />. For more details, see David W. Hogg’s short article <i class="it">Distance measures in cosmology</i>, available online at:<br />http://arxiv.org/abs/astro-ph/9905116. <a name="a0000001549" id="a0000001549"></a>  </p><p>    <big class="large"><b class="bf">ast.Lcdm_­angscale(<img src="images/img-0110.png" alt="$z$" style="vertical-align:0px; 
                                     width:9px; 
                                     height:8px" class="math gen" />,­<img src="images/img-0463.png" alt="$H_0$" style="vertical-align:-2px; 
                                     width:22px; 
                                     height:14px" class="math gen" />,­<img src="images/img-0464.png" alt="$\Omega _\mathrm {M}$" style="vertical-align:-3px; 
                                     width:26px; 
                                     height:15px" class="math gen" />,­<img src="images/img-0465.png" alt="$\Omega _\Uplambda $" style="vertical-align:-3px; 
                                     width:24px; 
                                     height:15px" class="math gen" />)</b></big> <br />The ast.Lcdm_­angscale(<img src="images/img-0110.png" alt="$z$" style="vertical-align:0px; 
                                     width:9px; 
                                     height:8px" class="math gen" />,­<img src="images/img-0463.png" alt="$H_0$" style="vertical-align:-2px; 
                                     width:22px; 
                                     height:14px" class="math gen" />,­<img src="images/img-0464.png" alt="$\Omega _\mathrm {M}$" style="vertical-align:-3px; 
                                     width:26px; 
                                     height:15px" class="math gen" />,­<img src="images/img-0465.png" alt="$\Omega _\Uplambda $" style="vertical-align:-3px; 
                                     width:24px; 
                                     height:15px" class="math gen" />) function returns the angular scale of the sky at a redshift of <img src="images/img-0110.png" alt="$z$" style="vertical-align:0px; 
                                     width:9px; 
                                     height:8px" class="math gen" /> in a standard <img src="images/img-0709.png" alt="$\Uplambda _\mathrm {CDM}$" style="vertical-align:-3px; 
                                     width:48px; 
                                     height:17px" class="math gen" /> cosmology. For details, see the <tt class="tt">ast.Lcdm_age()</tt> function above. The returned value has dimensions of distance per unit angle. <a name="a0000001550" id="a0000001550"></a>  </p><p>    <big class="large"><b class="bf">ast.Lcdm_­DA(<img src="images/img-0110.png" alt="$z$" style="vertical-align:0px; 
                                     width:9px; 
                                     height:8px" class="math gen" />,­<img src="images/img-0463.png" alt="$H_0$" style="vertical-align:-2px; 
                                     width:22px; 
                                     height:14px" class="math gen" />,­<img src="images/img-0464.png" alt="$\Omega _\mathrm {M}$" style="vertical-align:-3px; 
                                     width:26px; 
                                     height:15px" class="math gen" />,­<img src="images/img-0465.png" alt="$\Omega _\Uplambda $" style="vertical-align:-3px; 
                                     width:24px; 
                                     height:15px" class="math gen" />)</b></big> <br />The ast.Lcdm_­DA(<img src="images/img-0110.png" alt="$z$" style="vertical-align:0px; 
                                     width:9px; 
                                     height:8px" class="math gen" />,­<img src="images/img-0463.png" alt="$H_0$" style="vertical-align:-2px; 
                                     width:22px; 
                                     height:14px" class="math gen" />,­<img src="images/img-0464.png" alt="$\Omega _\mathrm {M}$" style="vertical-align:-3px; 
                                     width:26px; 
                                     height:15px" class="math gen" />,­<img src="images/img-0465.png" alt="$\Omega _\Uplambda $" style="vertical-align:-3px; 
                                     width:24px; 
                                     height:15px" class="math gen" />) function returns the angular size distance of objects at a redshift of <img src="images/img-0110.png" alt="$z$" style="vertical-align:0px; 
                                     width:9px; 
                                     height:8px" class="math gen" /> in a standard <img src="images/img-0709.png" alt="$\Uplambda _\mathrm {CDM}$" style="vertical-align:-3px; 
                                     width:48px; 
                                     height:17px" class="math gen" /> cosmology. For details, see the <tt class="tt">ast.Lcdm_age()</tt> function above. The returned value has dimensions of distance. <a name="a0000001551" id="a0000001551"></a>  </p><p>    <big class="large"><b class="bf">ast.Lcdm_­DL(<img src="images/img-0110.png" alt="$z$" style="vertical-align:0px; 
                                     width:9px; 
                                     height:8px" class="math gen" />,­<img src="images/img-0463.png" alt="$H_0$" style="vertical-align:-2px; 
                                     width:22px; 
                                     height:14px" class="math gen" />,­<img src="images/img-0464.png" alt="$\Omega _\mathrm {M}$" style="vertical-align:-3px; 
                                     width:26px; 
                                     height:15px" class="math gen" />,­<img src="images/img-0465.png" alt="$\Omega _\Uplambda $" style="vertical-align:-3px; 
                                     width:24px; 
                                     height:15px" class="math gen" />)</b></big> <br />The ast.Lcdm_­DL(<img src="images/img-0110.png" alt="$z$" style="vertical-align:0px; 
                                     width:9px; 
                                     height:8px" class="math gen" />,­<img src="images/img-0463.png" alt="$H_0$" style="vertical-align:-2px; 
                                     width:22px; 
                                     height:14px" class="math gen" />,­<img src="images/img-0464.png" alt="$\Omega _\mathrm {M}$" style="vertical-align:-3px; 
                                     width:26px; 
                                     height:15px" class="math gen" />,­<img src="images/img-0465.png" alt="$\Omega _\Uplambda $" style="vertical-align:-3px; 
                                     width:24px; 
                                     height:15px" class="math gen" />) function returns the luminosity distance of objects at a redshift of <img src="images/img-0110.png" alt="$z$" style="vertical-align:0px; 
                                     width:9px; 
                                     height:8px" class="math gen" /> in a standard <img src="images/img-0709.png" alt="$\Uplambda _\mathrm {CDM}$" style="vertical-align:-3px; 
                                     width:48px; 
                                     height:17px" class="math gen" /> cosmology. For details, see the <tt class="tt">ast.Lcdm_age()</tt> function above. The returned value has dimensions of distance. <a name="a0000001552" id="a0000001552"></a>  </p><p>    <big class="large"><b class="bf">ast.Lcdm_­DM(<img src="images/img-0110.png" alt="$z$" style="vertical-align:0px; 
                                     width:9px; 
                                     height:8px" class="math gen" />,­<img src="images/img-0463.png" alt="$H_0$" style="vertical-align:-2px; 
                                     width:22px; 
                                     height:14px" class="math gen" />,­<img src="images/img-0464.png" alt="$\Omega _\mathrm {M}$" style="vertical-align:-3px; 
                                     width:26px; 
                                     height:15px" class="math gen" />,­<img src="images/img-0465.png" alt="$\Omega _\Uplambda $" style="vertical-align:-3px; 
                                     width:24px; 
                                     height:15px" class="math gen" />)</b></big> <br />The ast.Lcdm_­DM(<img src="images/img-0110.png" alt="$z$" style="vertical-align:0px; 
                                     width:9px; 
                                     height:8px" class="math gen" />,­<img src="images/img-0463.png" alt="$H_0$" style="vertical-align:-2px; 
                                     width:22px; 
                                     height:14px" class="math gen" />,­<img src="images/img-0464.png" alt="$\Omega _\mathrm {M}$" style="vertical-align:-3px; 
                                     width:26px; 
                                     height:15px" class="math gen" />,­<img src="images/img-0465.png" alt="$\Omega _\Uplambda $" style="vertical-align:-3px; 
                                     width:24px; 
                                     height:15px" class="math gen" />) function returns the proper motion distance of objects at a redshift of <img src="images/img-0110.png" alt="$z$" style="vertical-align:0px; 
                                     width:9px; 
                                     height:8px" class="math gen" /> in a standard <img src="images/img-0709.png" alt="$\Uplambda _\mathrm {CDM}$" style="vertical-align:-3px; 
                                     width:48px; 
                                     height:17px" class="math gen" /> cosmology. For details, see the <tt class="tt">ast.Lcdm_age()</tt> function above. The returned value has dimensions of distance. <a name="a0000001553" id="a0000001553"></a>  </p><p>    <big class="large"><b class="bf">ast.Lcdm_­t(<img src="images/img-0110.png" alt="$z$" style="vertical-align:0px; 
                                     width:9px; 
                                     height:8px" class="math gen" />,­<img src="images/img-0463.png" alt="$H_0$" style="vertical-align:-2px; 
                                     width:22px; 
                                     height:14px" class="math gen" />,­<img src="images/img-0464.png" alt="$\Omega _\mathrm {M}$" style="vertical-align:-3px; 
                                     width:26px; 
                                     height:15px" class="math gen" />,­<img src="images/img-0465.png" alt="$\Omega _\Uplambda $" style="vertical-align:-3px; 
                                     width:24px; 
                                     height:15px" class="math gen" />)</b></big> <br />The ast.Lcdm_­t(<img src="images/img-0110.png" alt="$z$" style="vertical-align:0px; 
                                     width:9px; 
                                     height:8px" class="math gen" />,­<img src="images/img-0463.png" alt="$H_0$" style="vertical-align:-2px; 
                                     width:22px; 
                                     height:14px" class="math gen" />,­<img src="images/img-0464.png" alt="$\Omega _\mathrm {M}$" style="vertical-align:-3px; 
                                     width:26px; 
                                     height:15px" class="math gen" />,­<img src="images/img-0465.png" alt="$\Omega _\Uplambda $" style="vertical-align:-3px; 
                                     width:24px; 
                                     height:15px" class="math gen" />) function returns the lookback time to objects at a redshift of <img src="images/img-0110.png" alt="$z$" style="vertical-align:0px; 
                                     width:9px; 
                                     height:8px" class="math gen" /> in a standard <img src="images/img-0709.png" alt="$\Uplambda _\mathrm {CDM}$" style="vertical-align:-3px; 
                                     width:48px; 
                                     height:17px" class="math gen" /> cosmology. For details, see the <tt class="tt">ast.Lcdm_age()</tt> function above. The returned value has dimensions of time. To find the age of the Universe at a redshift of <img src="images/img-0110.png" alt="$z$" style="vertical-align:0px; 
                                     width:9px; 
                                     height:8px" class="math gen" />, this value should be subtracted from the output of the <tt class="tt">ast.Lcdm_age()</tt> function. <a name="a0000001554" id="a0000001554"></a>  </p><p>    <big class="large"><b class="bf">ast.Lcdm_­z(<img src="images/img-0065.png" alt="$t$" style="vertical-align:0px; 
                                     width:6px; 
                                     height:12px" class="math gen" />,­<img src="images/img-0463.png" alt="$H_0$" style="vertical-align:-2px; 
                                     width:22px; 
                                     height:14px" class="math gen" />,­<img src="images/img-0464.png" alt="$\Omega _\mathrm {M}$" style="vertical-align:-3px; 
                                     width:26px; 
                                     height:15px" class="math gen" />,­<img src="images/img-0465.png" alt="$\Omega _\Uplambda $" style="vertical-align:-3px; 
                                     width:24px; 
                                     height:15px" class="math gen" />)</b></big> <br />The ast.Lcdm_­z(<img src="images/img-0065.png" alt="$t$" style="vertical-align:0px; 
                                     width:6px; 
                                     height:12px" class="math gen" />,­<img src="images/img-0463.png" alt="$H_0$" style="vertical-align:-2px; 
                                     width:22px; 
                                     height:14px" class="math gen" />,­<img src="images/img-0464.png" alt="$\Omega _\mathrm {M}$" style="vertical-align:-3px; 
                                     width:26px; 
                                     height:15px" class="math gen" />,­<img src="images/img-0465.png" alt="$\Omega _\Uplambda $" style="vertical-align:-3px; 
                                     width:24px; 
                                     height:15px" class="math gen" />) function returns the redshift corresponding to a lookback time of <img src="images/img-0065.png" alt="$t$" style="vertical-align:0px; 
                                     width:6px; 
                                     height:12px" class="math gen" /> in a standard <img src="images/img-0709.png" alt="$\Uplambda _\mathrm {CDM}$" style="vertical-align:-3px; 
                                     width:48px; 
                                     height:17px" class="math gen" /> cosmology. For details, see the <tt class="tt">ast.Lcdm_age()</tt> function above. The returned value is dimensionless. <a name="a0000001555" id="a0000001555"></a>  </p><p>    <big class="large"><b class="bf">ast.moonphase(<img src="images/img-0052.png" alt="$d$" style="vertical-align:0px; 
                                     width:10px; 
                                     height:13px" class="math gen" />)</b></big> <br />The ast.moonphase(<img src="images/img-0052.png" alt="$d$" style="vertical-align:0px; 
                                     width:10px; 
                                     height:13px" class="math gen" />) function returns the phase of the Moon, with dimensions of angle, at the time of the supplied date object <img src="images/img-0052.png" alt="$d$" style="vertical-align:0px; 
                                     width:10px; 
                                     height:13px" class="math gen" />. If <img src="images/img-0052.png" alt="$d$" style="vertical-align:0px; 
                                     width:10px; 
                                     height:13px" class="math gen" /> is numerical, it is assumed to be a Unix time. <a name="a0000001556" id="a0000001556"></a>  </p><p>    <big class="large"><b class="bf">ast.sidereal_­time(<img src="images/img-0052.png" alt="$d$" style="vertical-align:0px; 
                                     width:10px; 
                                     height:13px" class="math gen" />)</b></big> <br />The ast.sidereal_­time(<img src="images/img-0052.png" alt="$d$" style="vertical-align:0px; 
                                     width:10px; 
                                     height:13px" class="math gen" />) function returns the sidereal time at Greenwich, with dimensions of angle, at the time of the supplied date object <img src="images/img-0052.png" alt="$d$" style="vertical-align:0px; 
                                     width:10px; 
                                     height:13px" class="math gen" />. If <img src="images/img-0052.png" alt="$d$" style="vertical-align:0px; 
                                     width:10px; 
                                     height:13px" class="math gen" /> is numerical, it is assumed to be a Unix time. The returned sidereal time is equal to the right ascension of the stars which are transiting the Greenwich meridian at that time. This function uses the expression for sidereal time adopted in 1982 by the International Astronomical Union (IAU), and which is reproduced in Chapter 12 of Jean Meeus’ book <i class="it">Astronomical Algorithms</i> (1998). <a name="a0000001557" id="a0000001557"></a>  </p></div>





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