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<li><a href="index.html" accesskey="U">Astronomical Coordinate Systems (<tt class="docutils literal"><span class="pre">astropy.coordinates</span></tt>)</a> »</li>
<li>Distances and Cartesian Representations</li>
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<div class="section" id="distances-and-cartesian-representations">
<h1>Distances and Cartesian Representations<a class="headerlink" href="#distances-and-cartesian-representations" title="Permalink to this headline">ΒΆ</a></h1>
<p>Coordinates can also have line-of-sight distances. If these are provided, a
coordinate object becomes a full-fledged point in three-dimensional space. If
not (i.e., the <tt class="xref py py-obj docutils literal"><span class="pre">distance</span></tt> attribute of the coordinate object is <tt class="xref py py-obj docutils literal"><span class="pre">None</span></tt>), the
point is interpreted as lying on the (dimensionless) unit sphere.</p>
<p>The <a class="reference internal" href="../_generated/astropy.coordinates.distances.Distance.html#astropy.coordinates.distances.Distance" title="astropy.coordinates.distances.Distance"><tt class="xref py py-obj docutils literal"><span class="pre">Distance</span></tt></a> class is provided to represent a
line-of-sight distance for a coordinate. It must include a length unit to be
valid.:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">astropy.coordinates</span> <span class="kn">import</span> <span class="n">Distance</span>
<span class="gp">>>> </span><span class="n">d</span> <span class="o">=</span> <span class="n">Distance</span><span class="p">(</span><span class="mi">770</span><span class="p">)</span>
<span class="go">UnitsError: A unit must be provided for distance.</span>
<span class="gp">>>> </span><span class="n">d</span> <span class="o">=</span> <span class="n">Distance</span><span class="p">(</span><span class="mi">770</span><span class="p">,</span> <span class="n">u</span><span class="o">.</span><span class="n">kpc</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">c</span> <span class="o">=</span> <span class="n">ICRSCoordinates</span><span class="p">(</span><span class="s">'00h42m44.3s +41d16m9s'</span><span class="p">,</span> <span class="n">distance</span><span class="o">=</span><span class="n">d</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">c</span>
<span class="go"><ICRSCoordinates RA=10.68458 deg, Dec=41.26917 deg, Distance=7.7e+02 kpc></span>
</pre></div>
</div>
<p>If a distance is available, the coordinate can be converted into cartesian
coordinates using the <tt class="xref py py-obj docutils literal"><span class="pre">x</span></tt>/<tt class="xref py py-obj docutils literal"><span class="pre">y</span></tt>/<tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt> attributes:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">c</span><span class="o">.</span><span class="n">x</span>
<span class="go">568.7128882165681</span>
<span class="gp">>>> </span><span class="n">c</span><span class="o">.</span><span class="n">y</span>
<span class="go">107.3009359688103</span>
<span class="gp">>>> </span><span class="n">c</span><span class="o">.</span><span class="n">z</span>
<span class="go">507.8899092486349</span>
</pre></div>
</div>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">The location of the origin is different for different coordinate
systems, but for common celestial coordinate systems it is often
the Earth center (or for precision work, the Earth/Moon barycenter).</p>
</div>
<p>The cartesian coordinates can also be accessed via the
<tt class="xref py py-obj docutils literal"><span class="pre">CartesianCoordinates</span></tt> object, which has
additional capabilities like arithmetic operations:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">cp</span> <span class="o">=</span> <span class="n">c</span><span class="o">.</span><span class="n">cartesian</span>
<span class="gp">>>> </span><span class="n">cp</span>
<span class="go"><CartesianPoints (568.712888217, 107.300935969, 507.889909249) kpc></span>
<span class="gp">>>> </span><span class="n">cp</span><span class="o">.</span><span class="n">x</span>
<span class="go">568.7128882165681</span>
<span class="gp">>>> </span><span class="n">cp</span><span class="o">.</span><span class="n">y</span>
<span class="go">107.3009359688103</span>
<span class="gp">>>> </span><span class="n">cp</span><span class="o">.</span><span class="n">z</span>
<span class="go">507.8899092486349</span>
<span class="gp">>>> </span><span class="n">cp</span><span class="o">.</span><span class="n">unit</span>
<span class="go">Unit("kpc")</span>
<span class="gp">>>> </span><span class="n">cp</span> <span class="o">+</span> <span class="n">cp</span>
<span class="go"><CartesianPoints (1137.42577643, 214.601871938, 1015.7798185) kpc></span>
<span class="gp">>>> </span><span class="n">cp</span> <span class="o">-</span> <span class="n">cp</span>
<span class="go"><CartesianPoints (0.0, 0.0, 0.0) kpc></span>
</pre></div>
</div>
<p>This cartesian representation can also be used to create a new coordinate
object, either directly or through a <tt class="xref py py-obj docutils literal"><span class="pre">CartesianPoints</span></tt> object:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">ICRSCoordinates</span><span class="p">(</span><span class="n">x</span><span class="o">=</span><span class="mf">568.7129</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="mf">107.3009</span><span class="p">,</span> <span class="n">z</span><span class="o">=</span><span class="mf">507.8899</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="n">u</span><span class="o">.</span><span class="n">kpc</span><span class="p">)</span>
<span class="go"><ICRSCoordinates RA=10.68458 deg, Dec=41.26917 deg, Distance=7.7e+02 kpc></span>
<span class="gp">>>> </span><span class="n">cp</span> <span class="o">=</span> <span class="n">CartesianPoints</span><span class="p">(</span><span class="n">x</span><span class="o">=</span><span class="mf">568.7129</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="mf">107.3009</span><span class="p">,</span> <span class="n">z</span><span class="o">=</span><span class="mf">507.8899</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="n">u</span><span class="o">.</span><span class="n">kpc</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">ICRSCoordinates</span><span class="p">(</span><span class="n">cp</span><span class="p">)</span>
<span class="go"><ICRSCoordinates RA=10.68458 deg, Dec=41.26917 deg, Distance=7.7e+02 kpc></span>
</pre></div>
</div>
<p>Finally, two coordinates with distances can be used to derive a real-space
distance (i.e., non-projected separation):</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">c1</span> <span class="o">=</span> <span class="n">ICRSCoordinates</span><span class="p">(</span><span class="s">'5h23m34.5s -69d45m22s'</span><span class="p">,</span> <span class="n">distance</span><span class="o">=</span><span class="n">Distance</span><span class="p">(</span><span class="mi">49</span><span class="p">,</span> <span class="n">u</span><span class="o">.</span><span class="n">kpc</span><span class="p">))</span>
<span class="gp">>>> </span><span class="n">c2</span> <span class="o">=</span> <span class="n">ICRSCoordinates</span><span class="p">(</span><span class="s">'0h52m44.8s -72d49m43s'</span><span class="p">,</span> <span class="n">distance</span><span class="o">=</span><span class="n">Distance</span><span class="p">(</span><span class="mi">61</span><span class="p">,</span> <span class="n">u</span><span class="o">.</span><span class="n">kpc</span><span class="p">))</span>
<span class="gp">>>> </span><span class="n">sep3d</span> <span class="o">=</span> <span class="n">c1</span><span class="o">.</span><span class="n">separation_3d</span><span class="p">(</span><span class="n">c2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">sep3d</span>
<span class="go"><Distance 23.05685 kpc></span>
<span class="gp">>>> </span><span class="n">sep3d</span><span class="o">.</span><span class="n">kpc</span>
<span class="go">23.05684814695706</span>
<span class="gp">>>> </span><span class="n">sep3d</span><span class="o">.</span><span class="n">Mpc</span>
<span class="go">0.02305684814695706</span>
<span class="gp">>>> </span><span class="n">sep3d</span><span class="o">.</span><span class="n">au</span>
<span class="go">4755816315.663559</span>
</pre></div>
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