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diff --git a/.buildinfo b/.buildinfo
@@ -1,4 +1,4 @@
 # Sphinx build info version 1
 # This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
-config: 0941016d75bcc6c66813cdf40a97157f
+config: 60bb62437d27158275846ac1b5be2e2d
 tags: 645f666f9bcd5a90fca523b33c5a78b7
diff --git a/_static/documentation_options.js b/_static/documentation_options.js
@@ -1,6 +1,6 @@
 var DOCUMENTATION_OPTIONS = {
     URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'),
-    VERSION: '0.1.1',
+    VERSION: '0.1.2',
     LANGUAGE: 'en',
     COLLAPSE_INDEX: false,
     BUILDER: 'html',

diff --git a/api.html b/api.html
@@ -9,7 +9,7 @@
     <meta charset="utf-8" />
     <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="generator" content="Docutils 0.19: https://docutils.sourceforge.io/" />
 
-    <title>API &#8212; dsgp4 0.1.1 documentation</title>
+    <title>API &#8212; dsgp4 0.1.2 documentation</title>
 
 
 

diff --git a/capabilities.html b/capabilities.html
@@ -9,7 +9,7 @@
     <meta charset="utf-8" />
     <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="generator" content="Docutils 0.19: https://docutils.sourceforge.io/" />
 
-    <title>Capabilities &#8212; dsgp4 0.1.1 documentation</title>
+    <title>Capabilities &#8212; dsgp4 0.1.2 documentation</title>
 
 
 

diff --git a/credits.html b/credits.html
@@ -9,7 +9,7 @@
     <meta charset="utf-8" />
     <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="generator" content="Docutils 0.19: https://docutils.sourceforge.io/" />
 
-    <title>Credits &#8212; dsgp4 0.1.1 documentation</title>
+    <title>Credits &#8212; dsgp4 0.1.2 documentation</title>
 
 
 

diff --git a/genindex.html b/genindex.html
@@ -8,7 +8,7 @@
   <head>
     <meta charset="utf-8" />
     <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-    <title>Index &#8212; dsgp4 0.1.1 documentation</title>
+    <title>Index &#8212; dsgp4 0.1.2 documentation</title>
 
 
 

diff --git a/index.html b/index.html
@@ -9,7 +9,7 @@
     <meta charset="utf-8" />
     <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="generator" content="Docutils 0.19: https://docutils.sourceforge.io/" />
 
-    <title>\(\partial\textrm{SGP4}\) Documentation &#8212; dsgp4 0.1.1 documentation</title>
+    <title>\(\partial\textrm{SGP4}\) Documentation &#8212; dsgp4 0.1.2 documentation</title>
 
 
 

diff --git a/install.html b/install.html
@@ -9,7 +9,7 @@
     <meta charset="utf-8" />
     <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="generator" content="Docutils 0.19: https://docutils.sourceforge.io/" />
 
-    <title>Installation &#8212; dsgp4 0.1.1 documentation</title>
+    <title>Installation &#8212; dsgp4 0.1.2 documentation</title>
 
 
 

diff --git a/notebooks/covariance_propagation.html b/notebooks/covariance_propagation.html
@@ -9,7 +9,7 @@
     <meta charset="utf-8" />
     <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="generator" content="Docutils 0.19: https://docutils.sourceforge.io/" />
 
-    <title>Covariance Propagation &#8212; dsgp4 0.1.1 documentation</title>
+    <title>Covariance Propagation &#8212; dsgp4 0.1.2 documentation</title>
 
 
 
@@ -382,8 +382,8 @@ <h1>Covariance Propagation</h1>
   <section class="tex2jax_ignore mathjax_ignore" id="covariance-propagation">
 <h1>Covariance Propagation<a class="headerlink" href="#covariance-propagation" title="Permalink to this heading">#</a></h1>
 <p>In this notebook, we discuss how to use <code class="docutils literal notranslate"><span class="pre">dsgp4</span></code> to apply the first order approximation for propagating a covariance matrix:</p>
-<div class="amsmath math notranslate nohighlight" id="equation-7fbf6fda-9643-450e-851d-d34a2ef64f07">
-<span class="eqno">(1)<a class="headerlink" href="#equation-7fbf6fda-9643-450e-851d-d34a2ef64f07" title="Permalink to this equation">#</a></span>\[\begin{equation}
+<div class="amsmath math notranslate nohighlight" id="equation-57c54a31-d506-4c9d-96ec-dc086ca7d8df">
+<span class="eqno">(1)<a class="headerlink" href="#equation-57c54a31-d506-4c9d-96ec-dc086ca7d8df" title="Permalink to this equation">#</a></span>\[\begin{equation}
 P_{\pmb{x}_f}=\dfrac{\partial \pmb{x}}{\partial \textrm{TLE}_0}  P_{\textrm{TLE}_{0}}\dfrac{\partial \pmb{x}}{\partial \textrm{TLE}_0}^T\text{,}
 \end{equation}\]</div>
 <p>where <span class="math notranslate nohighlight">\(\textrm{TLE}_0\)</span> is the initial TLE, at time <span class="math notranslate nohighlight">\(t_0\)</span>, and <span class="math notranslate nohighlight">\(\pmb{x}\)</span> is the state vector in Cartesian TEME, at a certain propagation time <span class="math notranslate nohighlight">\(t_f\)</span>.</p>

diff --git a/notebooks/covariance_transformation.html b/notebooks/covariance_transformation.html
@@ -9,7 +9,7 @@
     <meta charset="utf-8" />
     <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="generator" content="Docutils 0.19: https://docutils.sourceforge.io/" />
 
-    <title>Similarity Transformation - from Cartesian to TLE Covariance &#8212; dsgp4 0.1.1 documentation</title>
+    <title>Similarity Transformation - from Cartesian to TLE Covariance &#8212; dsgp4 0.1.2 documentation</title>
 
 
 
@@ -410,13 +410,13 @@ <h2>Covariance Transformation<a class="headerlink" href="#covariance-transformat
 <li><p>first convert the RTN covariance into TEME</p></li>
 <li><p>then leverage <code class="docutils literal notranslate"><span class="pre">dsgp4</span></code> to transform the covariance matrix from position and velocity coordinates to TLE elements, leveraging the similarity transformation:</p></li>
 </ul>
-<div class="amsmath math notranslate nohighlight" id="equation-1eac0572-ec36-4443-9b25-01e65b1034b6">
-<span class="eqno">(1)<a class="headerlink" href="#equation-1eac0572-ec36-4443-9b25-01e65b1034b6" title="Permalink to this equation">#</a></span>\[\begin{equation}
+<div class="amsmath math notranslate nohighlight" id="equation-09952162-e5aa-44ee-831c-14a573926a71">
+<span class="eqno">(1)<a class="headerlink" href="#equation-09952162-e5aa-44ee-831c-14a573926a71" title="Permalink to this equation">#</a></span>\[\begin{equation}
 P_{y} = m P_x m^T\text{,}
 \end{equation}\]</div>
 <p>where:</p>
-<div class="amsmath math notranslate nohighlight" id="equation-4da32ab0-0c83-4397-ad0d-c7a05936f0d1">
-<span class="eqno">(2)<a class="headerlink" href="#equation-4da32ab0-0c83-4397-ad0d-c7a05936f0d1" title="Permalink to this equation">#</a></span>\[\begin{equation}
+<div class="amsmath math notranslate nohighlight" id="equation-e299798a-ec5d-4118-8484-350a9030d99a">
+<span class="eqno">(2)<a class="headerlink" href="#equation-e299798a-ec5d-4118-8484-350a9030d99a" title="Permalink to this equation">#</a></span>\[\begin{equation}
 m_{ij}=\dfrac{\partial y_i}{\partial x_j}
 \end{equation}\]</div>
 <ul class="simple">

diff --git a/notebooks/gradient_based_optimization.html b/notebooks/gradient_based_optimization.html
@@ -9,7 +9,7 @@
     <meta charset="utf-8" />
     <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="generator" content="Docutils 0.19: https://docutils.sourceforge.io/" />
 
-    <title>Gradient Based Optimization &#8212; dsgp4 0.1.1 documentation</title>
+    <title>Gradient Based Optimization &#8212; dsgp4 0.1.2 documentation</title>
 
 
 
@@ -395,26 +395,26 @@ <h1>Gradient Based Optimization<a class="headerlink" href="#gradient-based-optim
 <h2>Problem description:<a class="headerlink" href="#problem-description" title="Permalink to this heading">#</a></h2>
 <p>We have a TLE at a given time, which we call TLE<span class="math notranslate nohighlight">\(_{0}\)</span>, and we look for a TLE at a future observation time (<span class="math notranslate nohighlight">\(t_{obs}\)</span>): TLE<span class="math notranslate nohighlight">\(_{t}\)</span>.</p>
 <p>We can propagate the state from <span class="math notranslate nohighlight">\(t_0 \rightarrow t_{obs}\)</span>, and obtain the state at <span class="math notranslate nohighlight">\(t_{obs}\)</span>. In general, we define the state (i.e., position and velocity), as:</p>
-<div class="amsmath math notranslate nohighlight" id="equation-7caaf4a4-42b3-482d-a394-30ee50f496af">
-<span class="eqno">(1)<a class="headerlink" href="#equation-7caaf4a4-42b3-482d-a394-30ee50f496af" title="Permalink to this equation">#</a></span>\[\begin{equation}
+<div class="amsmath math notranslate nohighlight" id="equation-6a662a4d-f1aa-4d01-a50f-4d2095c3b402">
+<span class="eqno">(1)<a class="headerlink" href="#equation-6a662a4d-f1aa-4d01-a50f-4d2095c3b402" title="Permalink to this equation">#</a></span>\[\begin{equation}
 \vec{x}(t)=[x(t), y(t), z(t), \dot{x}(t), \dot{y}(t), \dot{z}(t)]^T
 \end{equation}\]</div>
 <p>We then have: TLE<span class="math notranslate nohighlight">\(_0\)</span>, <span class="math notranslate nohighlight">\(\vec{x}(t_0)\)</span>, and <span class="math notranslate nohighlight">\(\vec{x}(t_{obs})\)</span>, but we want to find TLE<span class="math notranslate nohighlight">\(_{obs}\)</span>. That is, the TLE at the observation time, that when propagated with SGP4 at its time, it corresponds to that <span class="math notranslate nohighlight">\(\vec{x}(t_{obs})\)</span>. In general, this means that we are able to invert from the state to the TLE, at any given time.</p>
 <p>In order to do this, we formulate the problem as looking for the minimum of a function of a free variables vector (i.e., <span class="math notranslate nohighlight">\(\vec{y}\)</span>) <span class="math notranslate nohighlight">\(F(\vec{y})\)</span>, where this function defines the difference between the given state propagated from TLE<span class="math notranslate nohighlight">\(_0\)</span> at <span class="math notranslate nohighlight">\(t_{obs}\)</span>, and the state generated from the free variables that make a TLE which is then propagated at its current time: TLE<span class="math notranslate nohighlight">\((\vec{y})(t_{0}\rightarrow t_{obs})\)</span>. So we can reformulate the problem as:</p>
-<div class="amsmath math notranslate nohighlight" id="equation-10b83634-0d94-4e2a-8a94-efadfc26c4fd">
-<span class="eqno">(2)<a class="headerlink" href="#equation-10b83634-0d94-4e2a-8a94-efadfc26c4fd" title="Permalink to this equation">#</a></span>\[\begin{align}
+<div class="amsmath math notranslate nohighlight" id="equation-c171c4aa-59e4-4f5c-b489-1d7a5e88ea32">
+<span class="eqno">(2)<a class="headerlink" href="#equation-c171c4aa-59e4-4f5c-b489-1d7a5e88ea32" title="Permalink to this equation">#</a></span>\[\begin{align}
 \textrm{given}: &amp; \ \textrm{TLE}_0, \vec{x}_0\\
 \textrm{find}: &amp; \ \vec{y}\\
 \textrm{that minimize}: &amp; F(\vec{y})=|SGP4(\textrm{TLE}(\vec{y}),t_{obs})-\vec{x}(t_{obs})| =|\vec{\tilde{x}}(t_{obs})-\vec{x}(t_{obs})|
 \end{align}\]</div>
 <p>We can do this via Newton method, by updating an initial guess <span class="math notranslate nohighlight">\(y_{0}\)</span> until convergence. Where the update is done as follows:</p>
-<div class="amsmath math notranslate nohighlight" id="equation-e772992a-d8a9-4b11-bd88-42e707f4ecf6">
-<span class="eqno">(3)<a class="headerlink" href="#equation-e772992a-d8a9-4b11-bd88-42e707f4ecf6" title="Permalink to this equation">#</a></span>\[\begin{equation}
+<div class="amsmath math notranslate nohighlight" id="equation-dbeae767-653e-4ebf-b86d-d15947022c28">
+<span class="eqno">(3)<a class="headerlink" href="#equation-dbeae767-653e-4ebf-b86d-d15947022c28" title="Permalink to this equation">#</a></span>\[\begin{equation}
 y_{k+1}=y_{k}-DF^{-1}(y_k)F(y_k)
 \end{equation}\]</div>
 <p>with <span class="math notranslate nohighlight">\(DF\)</span> the Jacobian of <span class="math notranslate nohighlight">\(F\)</span> with respect to <span class="math notranslate nohighlight">\(y_k\)</span>. We can easily see that this Jacobian is made of the following elements:</p>
-<div class="amsmath math notranslate nohighlight" id="equation-5660301e-2286-4b01-9562-a0cad538545a">
-<span class="eqno">(4)<a class="headerlink" href="#equation-5660301e-2286-4b01-9562-a0cad538545a" title="Permalink to this equation">#</a></span>\[\begin{equation}
+<div class="amsmath math notranslate nohighlight" id="equation-76af6216-0894-4a3a-a758-dfb2f49a8160">
+<span class="eqno">(4)<a class="headerlink" href="#equation-76af6216-0894-4a3a-a758-dfb2f49a8160" title="Permalink to this equation">#</a></span>\[\begin{equation}
 DF_{ij}=\dfrac{\partial \tilde{x}_{i}}{\partial y_{j}}|_{y_k}
 \end{equation}\]</div>
 <p>where <span class="math notranslate nohighlight">\(\tilde{x}_{i} \in [\tilde{x}_1,\tilde{x}_2,\tilde{x}_3,\tilde{x}_4,\tilde{x}_5,\tilde{x}_6]=[\tilde{x},\tilde{y},\tilde{z},\tilde{\dot{x}},\tilde{\dot{y}},\tilde{\dot{z}}]\)</span>; and <span class="math notranslate nohighlight">\(y_i \in [no_{kozai}, ecco, inclo, mo, argpo, nodeo, n_{dot},n_{ddot},B^*]\)</span>.</p>