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	<updated>2026-04-28T15:54:21Z</updated>
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		<id>https://gentleman.cnes.fr/index.php?title=Methods&amp;diff=90&amp;oldid=prev</id>
		<title>Admin le 7 septembre 2021 à 11:58</title>
		<link rel="alternate" type="text/html" href="https://gentleman.cnes.fr/index.php?title=Methods&amp;diff=90&amp;oldid=prev"/>
		<updated>2021-09-07T11:58:21Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Version précédente&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Version du 7 septembre 2021 à 11:58&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l7&quot;&gt;Ligne 7 :&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Ligne 7 :&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;2. TLE building:&amp;#039;&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;2. TLE building:&amp;#039;&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Once this trajectory has been computed, &amp;lt;font color=#556B2F&amp;gt;&#039;&#039;&#039;GENTLEMAN&#039;&#039;&#039;&amp;lt;/font&amp;gt; will generate one or several &amp;lt;font color=#FF8C00 title=&quot;Two Lines Elements&quot;&amp;gt;TLEs&amp;lt;/font&amp;gt;. The basic methods to build these &amp;lt;font color=#FF8C00 title=&quot;Two Lines Elements&quot;&amp;gt;TLEs&amp;lt;/font&amp;gt; are the ones proposed by [http://patrius.cnes.fr PATRIUS] (&#039;&#039;&#039;Differential&#039;&#039;&#039; or &#039;&#039;&#039;Levenberg Marquardt&#039;&#039;&#039; methods). But, &amp;lt;font color=#556B2F&amp;gt;&#039;&#039;&#039;GENTLEMAN&#039;&#039;&#039;&amp;lt;/font&amp;gt; adds a complementary functionality as it allows finding the best compromise on the amount of points to fit a &amp;lt;font color=#FF8C00 title=&quot;Two Lines &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Element&lt;/del&gt;&quot;&amp;gt;TLE&amp;lt;/font&amp;gt; thanks to the propagated trajectory.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Once this trajectory has been computed, &amp;lt;font color=#556B2F&amp;gt;&#039;&#039;&#039;GENTLEMAN&#039;&#039;&#039;&amp;lt;/font&amp;gt; will generate one or several &amp;lt;font color=#FF8C00 title=&quot;Two Lines Elements&quot;&amp;gt;TLEs&amp;lt;/font&amp;gt;. The basic methods to build these &amp;lt;font color=#FF8C00 title=&quot;Two Lines Elements&quot;&amp;gt;TLEs&amp;lt;/font&amp;gt; are the ones proposed by [http://patrius.cnes.fr PATRIUS] (&#039;&#039;&#039;Differential&#039;&#039;&#039; or &#039;&#039;&#039;Levenberg Marquardt&#039;&#039;&#039; methods). But, &amp;lt;font color=#556B2F&amp;gt;&#039;&#039;&#039;GENTLEMAN&#039;&#039;&#039;&amp;lt;/font&amp;gt; adds a complementary functionality as it allows finding the best compromise on the amount of points to fit a &amp;lt;font color=#FF8C00 title=&quot;Two Lines &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Elements&lt;/ins&gt;&quot;&amp;gt;TLE&amp;lt;/font&amp;gt; thanks to the propagated trajectory.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Let us give an example with a trajectory ephemeris (included in the [https://www.sqlite.org SQlite] file) composed of 50 output points.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Let us give an example with a trajectory ephemeris (included in the [https://www.sqlite.org SQlite] file) composed of 50 output points.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* A first possibility is to fit a &amp;lt;font color=#FF8C00 title=&quot;Two Lines &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Element&lt;/del&gt;&quot;&amp;gt;TLE&amp;lt;/font&amp;gt; by giving explicitly the amount of points to take into account: for example, the ten first ones.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* A first possibility is to fit a &amp;lt;font color=#FF8C00 title=&quot;Two Lines &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Elements&lt;/ins&gt;&quot;&amp;gt;TLE&amp;lt;/font&amp;gt; by giving explicitly the amount of points to take into account: for example, the ten first ones.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* A second possibility is to leave &amp;lt;font color=#556B2F&amp;gt;&#039;&#039;&#039;GENTLEMAN&#039;&#039;&#039;&amp;lt;/font&amp;gt; to find this amount of points for such a fitting. To do it, &amp;lt;font color=#556B2F&amp;gt;&#039;&#039;&#039;GENTLEMAN&#039;&#039;&#039;&amp;lt;/font&amp;gt; will compute different &amp;lt;font color=#FF8C00 title=&quot;Two Lines Elements&quot;&amp;gt;TLEs&amp;lt;/font&amp;gt; using 1, then 2, then 3, then up to 50 points (or less if the user entered a maximum number). Considering each of these  &amp;lt;font color=#FF8C00 title=&quot;Two Lines Elements&quot;&amp;gt;TLEs&amp;lt;/font&amp;gt;, &amp;lt;font color=#556B2F&amp;gt;&#039;&#039;&#039;GENTLEMAN&#039;&#039;&#039;&amp;lt;/font&amp;gt; will compute for each point of the trajectory (or less if the user entered another maximum number), the difference between the trajectory and the one propagated with the &amp;lt;font color=#FF8C00 title=&quot;Two Lines &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Element&lt;/del&gt;&quot;&amp;gt;TLE&amp;lt;/font&amp;gt; as initial condition and the model linked to it (&#039;&#039;&#039;SGP4&#039;&#039;&#039; for &amp;lt;font color=#FF8C00 title=&quot;Low Earth Orbit&quot;&amp;gt;LEO&amp;lt;/font&amp;gt; and &#039;&#039;&#039;DeepSDP4&#039;&#039;&#039; for &amp;lt;font color=#FF8C00 title=&quot;Geostationnary Earth Orbit&quot;&amp;gt;LEO&amp;lt;/font&amp;gt;). &amp;lt;font color=#556B2F&amp;gt;&#039;&#039;&#039;GENTLEMAN&#039;&#039;&#039;&amp;lt;/font&amp;gt; will then select the &amp;lt;font color=#FF8C00 title=&quot;Two Lines &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Element&lt;/del&gt;&quot;&amp;gt;TLE&amp;lt;/font&amp;gt; which will get the lowest value for the mean error in semi major axis.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* A second possibility is to leave &amp;lt;font color=#556B2F&amp;gt;&#039;&#039;&#039;GENTLEMAN&#039;&#039;&#039;&amp;lt;/font&amp;gt; to find this amount of points for such a fitting. To do it, &amp;lt;font color=#556B2F&amp;gt;&#039;&#039;&#039;GENTLEMAN&#039;&#039;&#039;&amp;lt;/font&amp;gt; will compute different &amp;lt;font color=#FF8C00 title=&quot;Two Lines Elements&quot;&amp;gt;TLEs&amp;lt;/font&amp;gt; using 1, then 2, then 3, then up to 50 points (or less if the user entered a maximum number). Considering each of these  &amp;lt;font color=#FF8C00 title=&quot;Two Lines Elements&quot;&amp;gt;TLEs&amp;lt;/font&amp;gt;, &amp;lt;font color=#556B2F&amp;gt;&#039;&#039;&#039;GENTLEMAN&#039;&#039;&#039;&amp;lt;/font&amp;gt; will compute for each point of the trajectory (or less if the user entered another maximum number), the difference between the trajectory and the one propagated with the &amp;lt;font color=#FF8C00 title=&quot;Two Lines &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Elements&lt;/ins&gt;&quot;&amp;gt;TLE&amp;lt;/font&amp;gt; as initial condition and the model linked to it (&#039;&#039;&#039;SGP4&#039;&#039;&#039; for &amp;lt;font color=#FF8C00 title=&quot;Low Earth Orbit&quot;&amp;gt;LEO&amp;lt;/font&amp;gt; and &#039;&#039;&#039;DeepSDP4&#039;&#039;&#039; for &amp;lt;font color=#FF8C00 title=&quot;Geostationnary Earth Orbit&quot;&amp;gt;LEO&amp;lt;/font&amp;gt;). &amp;lt;font color=#556B2F&amp;gt;&#039;&#039;&#039;GENTLEMAN&#039;&#039;&#039;&amp;lt;/font&amp;gt; will then select the &amp;lt;font color=#FF8C00 title=&quot;Two Lines &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Elements&lt;/ins&gt;&quot;&amp;gt;TLE&amp;lt;/font&amp;gt; which will get the lowest value for the mean error in semi major axis.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* In case of maneuvers to take into account or if the user decided to compute several &amp;lt;font color=#FF8C00 title=&quot;Two Lines Elements&quot;&amp;gt;TLEs&amp;lt;/font&amp;gt; (for example one &amp;lt;font color=#FF8C00 title=&quot;Two Lines &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Element&lt;/del&gt;&quot;&amp;gt;TLE&amp;lt;/font&amp;gt; by day), this process will be executed only in the interval between two &amp;lt;font color=#FF8C00 title=&quot;Two Lines Elements&quot;&amp;gt;TLEs&amp;lt;/font&amp;gt; (or one &amp;lt;font color=#FF8C00 title=&quot;Two Lines &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Element&lt;/del&gt;&quot;&amp;gt;TLE&amp;lt;/font&amp;gt; and the next maneuver).&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* In case of maneuvers to take into account or if the user decided to compute several &amp;lt;font color=#FF8C00 title=&quot;Two Lines Elements&quot;&amp;gt;TLEs&amp;lt;/font&amp;gt; (for example one &amp;lt;font color=#FF8C00 title=&quot;Two Lines &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Elements&lt;/ins&gt;&quot;&amp;gt;TLE&amp;lt;/font&amp;gt; by day), this process will be executed only in the interval between two &amp;lt;font color=#FF8C00 title=&quot;Two Lines Elements&quot;&amp;gt;TLEs&amp;lt;/font&amp;gt; (or one &amp;lt;font color=#FF8C00 title=&quot;Two Lines &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Elements&lt;/ins&gt;&quot;&amp;gt;TLE&amp;lt;/font&amp;gt; and the next maneuver).&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;

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		<author><name>Admin</name></author>
	</entry>
	<entry>
		<id>https://gentleman.cnes.fr/index.php?title=Methods&amp;diff=56&amp;oldid=prev</id>
		<title>Admin le 7 septembre 2021 à 08:40</title>
		<link rel="alternate" type="text/html" href="https://gentleman.cnes.fr/index.php?title=Methods&amp;diff=56&amp;oldid=prev"/>
		<updated>2021-09-07T08:40:36Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Version précédente&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Version du 7 septembre 2021 à 08:40&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l3&quot;&gt;Ligne 3 :&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Ligne 3 :&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;1. Propagation:&amp;#039;&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;1. Propagation:&amp;#039;&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:First it will propagate a trajectory thanks to [http://psimu.cnes.fr &#039;&#039;&#039;PSIMU&#039;&#039;&#039;] tool; all the possibilities linked to its use are available so, any kind of trajectories around the Earth are allowed (&amp;lt;font color=#FF8C00 title=&quot;Geostationnary Earth Orbit&quot;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;LEO&lt;/del&gt;&amp;lt;/font&amp;gt;, &amp;lt;font color=#FF8C00 title=&quot;Low Earth Orbit&quot;&amp;gt;LEO&amp;lt;/font&amp;gt;, even reentry !). This trajectory will be stored in a [https://www.sqlite.org SQlite] data base with an output step defined by the user.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:First it will propagate a trajectory thanks to [http://psimu.cnes.fr &#039;&#039;&#039;PSIMU&#039;&#039;&#039;] tool; all the possibilities linked to its use are available so, any kind of trajectories around the Earth are allowed (&amp;lt;font color=#FF8C00 title=&quot;Geostationnary Earth Orbit&quot;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;GEO&lt;/ins&gt;&amp;lt;/font&amp;gt;, &amp;lt;font color=#FF8C00 title=&quot;Low Earth Orbit&quot;&amp;gt;LEO&amp;lt;/font&amp;gt;, even reentry !). This trajectory will be stored in a [https://www.sqlite.org SQlite] data base with an output step defined by the user.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;2. TLE building:&amp;#039;&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;2. TLE building:&amp;#039;&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;

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&lt;/table&gt;</summary>
		<author><name>Admin</name></author>
	</entry>
	<entry>
		<id>https://gentleman.cnes.fr/index.php?title=Methods&amp;diff=31&amp;oldid=prev</id>
		<title>Admin le 7 septembre 2021 à 07:43</title>
		<link rel="alternate" type="text/html" href="https://gentleman.cnes.fr/index.php?title=Methods&amp;diff=31&amp;oldid=prev"/>
		<updated>2021-09-07T07:43:56Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;fr&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Version précédente&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Version du 7 septembre 2021 à 07:43&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l9&quot;&gt;Ligne 9 :&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Ligne 9 :&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Once this trajectory has been computed, &amp;lt;font color=#556B2F&amp;gt;&amp;#039;&amp;#039;&amp;#039;GENTLEMAN&amp;#039;&amp;#039;&amp;#039;&amp;lt;/font&amp;gt; will generate one or several &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Elements&amp;quot;&amp;gt;TLEs&amp;lt;/font&amp;gt;. The basic methods to build these &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Elements&amp;quot;&amp;gt;TLEs&amp;lt;/font&amp;gt; are the ones proposed by [http://patrius.cnes.fr PATRIUS] (&amp;#039;&amp;#039;&amp;#039;Differential&amp;#039;&amp;#039;&amp;#039; or &amp;#039;&amp;#039;&amp;#039;Levenberg Marquardt&amp;#039;&amp;#039;&amp;#039; methods). But, &amp;lt;font color=#556B2F&amp;gt;&amp;#039;&amp;#039;&amp;#039;GENTLEMAN&amp;#039;&amp;#039;&amp;#039;&amp;lt;/font&amp;gt; adds a complementary functionality as it allows finding the best compromise on the amount of points to fit a &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Element&amp;quot;&amp;gt;TLE&amp;lt;/font&amp;gt; thanks to the propagated trajectory.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Once this trajectory has been computed, &amp;lt;font color=#556B2F&amp;gt;&amp;#039;&amp;#039;&amp;#039;GENTLEMAN&amp;#039;&amp;#039;&amp;#039;&amp;lt;/font&amp;gt; will generate one or several &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Elements&amp;quot;&amp;gt;TLEs&amp;lt;/font&amp;gt;. The basic methods to build these &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Elements&amp;quot;&amp;gt;TLEs&amp;lt;/font&amp;gt; are the ones proposed by [http://patrius.cnes.fr PATRIUS] (&amp;#039;&amp;#039;&amp;#039;Differential&amp;#039;&amp;#039;&amp;#039; or &amp;#039;&amp;#039;&amp;#039;Levenberg Marquardt&amp;#039;&amp;#039;&amp;#039; methods). But, &amp;lt;font color=#556B2F&amp;gt;&amp;#039;&amp;#039;&amp;#039;GENTLEMAN&amp;#039;&amp;#039;&amp;#039;&amp;lt;/font&amp;gt; adds a complementary functionality as it allows finding the best compromise on the amount of points to fit a &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Element&amp;quot;&amp;gt;TLE&amp;lt;/font&amp;gt; thanks to the propagated trajectory.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Let us give an example with a trajectory ephemeris (included in the SQlite file) composed of 50 output points.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Let us give an example with a trajectory ephemeris (included in the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[https://www.sqlite.org &lt;/ins&gt;SQlite&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;] &lt;/ins&gt;file) composed of 50 output points.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* A first possibility is to fit a &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Element&amp;quot;&amp;gt;TLE&amp;lt;/font&amp;gt; by giving explicitly the amount of points to take into account: for example, the ten first ones.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* A first possibility is to fit a &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Element&amp;quot;&amp;gt;TLE&amp;lt;/font&amp;gt; by giving explicitly the amount of points to take into account: for example, the ten first ones.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* A second possibility is to leave &amp;lt;font color=#556B2F&amp;gt;&amp;#039;&amp;#039;&amp;#039;GENTLEMAN&amp;#039;&amp;#039;&amp;#039;&amp;lt;/font&amp;gt; to find this amount of points for such a fitting. To do it, &amp;lt;font color=#556B2F&amp;gt;&amp;#039;&amp;#039;&amp;#039;GENTLEMAN&amp;#039;&amp;#039;&amp;#039;&amp;lt;/font&amp;gt; will compute different &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Elements&amp;quot;&amp;gt;TLEs&amp;lt;/font&amp;gt; using 1, then 2, then 3, then up to 50 points (or less if the user entered a maximum number). Considering each of these  &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Elements&amp;quot;&amp;gt;TLEs&amp;lt;/font&amp;gt;, &amp;lt;font color=#556B2F&amp;gt;&amp;#039;&amp;#039;&amp;#039;GENTLEMAN&amp;#039;&amp;#039;&amp;#039;&amp;lt;/font&amp;gt; will compute for each point of the trajectory (or less if the user entered another maximum number), the difference between the trajectory and the one propagated with the &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Element&amp;quot;&amp;gt;TLE&amp;lt;/font&amp;gt; as initial condition and the model linked to it (&amp;#039;&amp;#039;&amp;#039;SGP4&amp;#039;&amp;#039;&amp;#039; for &amp;lt;font color=#FF8C00 title=&amp;quot;Low Earth Orbit&amp;quot;&amp;gt;LEO&amp;lt;/font&amp;gt; and &amp;#039;&amp;#039;&amp;#039;DeepSDP4&amp;#039;&amp;#039;&amp;#039; for &amp;lt;font color=#FF8C00 title=&amp;quot;Geostationnary Earth Orbit&amp;quot;&amp;gt;LEO&amp;lt;/font&amp;gt;). &amp;lt;font color=#556B2F&amp;gt;&amp;#039;&amp;#039;&amp;#039;GENTLEMAN&amp;#039;&amp;#039;&amp;#039;&amp;lt;/font&amp;gt; will then select the &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Element&amp;quot;&amp;gt;TLE&amp;lt;/font&amp;gt; which will get the lowest value for the mean error in semi major axis.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* A second possibility is to leave &amp;lt;font color=#556B2F&amp;gt;&amp;#039;&amp;#039;&amp;#039;GENTLEMAN&amp;#039;&amp;#039;&amp;#039;&amp;lt;/font&amp;gt; to find this amount of points for such a fitting. To do it, &amp;lt;font color=#556B2F&amp;gt;&amp;#039;&amp;#039;&amp;#039;GENTLEMAN&amp;#039;&amp;#039;&amp;#039;&amp;lt;/font&amp;gt; will compute different &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Elements&amp;quot;&amp;gt;TLEs&amp;lt;/font&amp;gt; using 1, then 2, then 3, then up to 50 points (or less if the user entered a maximum number). Considering each of these  &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Elements&amp;quot;&amp;gt;TLEs&amp;lt;/font&amp;gt;, &amp;lt;font color=#556B2F&amp;gt;&amp;#039;&amp;#039;&amp;#039;GENTLEMAN&amp;#039;&amp;#039;&amp;#039;&amp;lt;/font&amp;gt; will compute for each point of the trajectory (or less if the user entered another maximum number), the difference between the trajectory and the one propagated with the &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Element&amp;quot;&amp;gt;TLE&amp;lt;/font&amp;gt; as initial condition and the model linked to it (&amp;#039;&amp;#039;&amp;#039;SGP4&amp;#039;&amp;#039;&amp;#039; for &amp;lt;font color=#FF8C00 title=&amp;quot;Low Earth Orbit&amp;quot;&amp;gt;LEO&amp;lt;/font&amp;gt; and &amp;#039;&amp;#039;&amp;#039;DeepSDP4&amp;#039;&amp;#039;&amp;#039; for &amp;lt;font color=#FF8C00 title=&amp;quot;Geostationnary Earth Orbit&amp;quot;&amp;gt;LEO&amp;lt;/font&amp;gt;). &amp;lt;font color=#556B2F&amp;gt;&amp;#039;&amp;#039;&amp;#039;GENTLEMAN&amp;#039;&amp;#039;&amp;#039;&amp;lt;/font&amp;gt; will then select the &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Element&amp;quot;&amp;gt;TLE&amp;lt;/font&amp;gt; which will get the lowest value for the mean error in semi major axis.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* In case of maneuvers to take into account or if the user decided to compute several &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Elements&amp;quot;&amp;gt;TLEs&amp;lt;/font&amp;gt; (for example one &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Element&amp;quot;&amp;gt;TLE&amp;lt;/font&amp;gt; by day), this process will be executed only in the interval between two &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Elements&amp;quot;&amp;gt;TLEs&amp;lt;/font&amp;gt; (or one &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Element&amp;quot;&amp;gt;TLE&amp;lt;/font&amp;gt; and the next maneuver).&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* In case of maneuvers to take into account or if the user decided to compute several &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Elements&amp;quot;&amp;gt;TLEs&amp;lt;/font&amp;gt; (for example one &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Element&amp;quot;&amp;gt;TLE&amp;lt;/font&amp;gt; by day), this process will be executed only in the interval between two &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Elements&amp;quot;&amp;gt;TLEs&amp;lt;/font&amp;gt; (or one &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Element&amp;quot;&amp;gt;TLE&amp;lt;/font&amp;gt; and the next maneuver).&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;

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&lt;/table&gt;</summary>
		<author><name>Admin</name></author>
	</entry>
	<entry>
		<id>https://gentleman.cnes.fr/index.php?title=Methods&amp;diff=30&amp;oldid=prev</id>
		<title>Admin le 7 septembre 2021 à 07:43</title>
		<link rel="alternate" type="text/html" href="https://gentleman.cnes.fr/index.php?title=Methods&amp;diff=30&amp;oldid=prev"/>
		<updated>2021-09-07T07:43:08Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;fr&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Version précédente&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Version du 7 septembre 2021 à 07:43&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l3&quot;&gt;Ligne 3 :&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Ligne 3 :&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;1. Propagation:&amp;#039;&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;1. Propagation:&amp;#039;&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:First it will propagate a trajectory thanks to [http://psimu.cnes.fr &#039;&#039;&#039;PSIMU&#039;&#039;&#039;] tool; all the possibilities linked to its use are available so, any kind of trajectories around the Earth are allowed (&amp;lt;font color=#FF8C00 title=&quot;Geostationnary Earth Orbit&quot;&amp;gt;LEO&amp;lt;/font&amp;gt;, &amp;lt;font color=#FF8C00 title=&quot;Low Earth Orbit&quot;&amp;gt;LEO&amp;lt;/font&amp;gt;, even reentry !). This trajectory will be stored in a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;font color=#FF8C00&amp;gt;&lt;/del&gt;SQlite&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;/font&amp;gt; &lt;/del&gt;data base with an output step defined by the user.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:First it will propagate a trajectory thanks to [http://psimu.cnes.fr &#039;&#039;&#039;PSIMU&#039;&#039;&#039;] tool; all the possibilities linked to its use are available so, any kind of trajectories around the Earth are allowed (&amp;lt;font color=#FF8C00 title=&quot;Geostationnary Earth Orbit&quot;&amp;gt;LEO&amp;lt;/font&amp;gt;, &amp;lt;font color=#FF8C00 title=&quot;Low Earth Orbit&quot;&amp;gt;LEO&amp;lt;/font&amp;gt;, even reentry !). This trajectory will be stored in a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[https://www.sqlite.org &lt;/ins&gt;SQlite&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;] &lt;/ins&gt;data base with an output step defined by the user.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;2. TLE building:&amp;#039;&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;2. TLE building:&amp;#039;&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;

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&lt;/table&gt;</summary>
		<author><name>Admin</name></author>
	</entry>
	<entry>
		<id>https://gentleman.cnes.fr/index.php?title=Methods&amp;diff=29&amp;oldid=prev</id>
		<title>Admin le 7 septembre 2021 à 07:40</title>
		<link rel="alternate" type="text/html" href="https://gentleman.cnes.fr/index.php?title=Methods&amp;diff=29&amp;oldid=prev"/>
		<updated>2021-09-07T07:40:57Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;fr&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Version précédente&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Version du 7 septembre 2021 à 07:40&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Ligne 1 :&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Ligne 1 :&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;font color=#556B2F&amp;gt;&amp;#039;&amp;#039;&amp;#039;GENTLEMAN&amp;#039;&amp;#039;&amp;#039;&amp;lt;/font&amp;gt; is working in two steps.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;font color=#556B2F&amp;gt;&amp;#039;&amp;#039;&amp;#039;GENTLEMAN&amp;#039;&amp;#039;&amp;#039;&amp;lt;/font&amp;gt; is working in two steps.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;:&lt;/del&gt;&#039;&#039;&#039;1. Propagation:&#039;&#039;&#039;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&#039;&#039;&#039;1. Propagation:&#039;&#039;&#039;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:First it will propagate a trajectory thanks to [http://psimu.cnes.fr &amp;#039;&amp;#039;&amp;#039;PSIMU&amp;#039;&amp;#039;&amp;#039;] tool; all the possibilities linked to its use are available so, any kind of trajectories around the Earth are allowed (&amp;lt;font color=#FF8C00 title=&amp;quot;Geostationnary Earth Orbit&amp;quot;&amp;gt;LEO&amp;lt;/font&amp;gt;, &amp;lt;font color=#FF8C00 title=&amp;quot;Low Earth Orbit&amp;quot;&amp;gt;LEO&amp;lt;/font&amp;gt;, even reentry !). This trajectory will be stored in a &amp;lt;font color=#FF8C00&amp;gt;SQlite&amp;lt;/font&amp;gt; data base with an output step defined by the user.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:First it will propagate a trajectory thanks to [http://psimu.cnes.fr &amp;#039;&amp;#039;&amp;#039;PSIMU&amp;#039;&amp;#039;&amp;#039;] tool; all the possibilities linked to its use are available so, any kind of trajectories around the Earth are allowed (&amp;lt;font color=#FF8C00 title=&amp;quot;Geostationnary Earth Orbit&amp;quot;&amp;gt;LEO&amp;lt;/font&amp;gt;, &amp;lt;font color=#FF8C00 title=&amp;quot;Low Earth Orbit&amp;quot;&amp;gt;LEO&amp;lt;/font&amp;gt;, even reentry !). This trajectory will be stored in a &amp;lt;font color=#FF8C00&amp;gt;SQlite&amp;lt;/font&amp;gt; data base with an output step defined by the user.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;

&lt;!-- diff cache key w4?hgentleman?hprod:diff:1.41:old-28:rev-29:php=table --&gt;
&lt;/table&gt;</summary>
		<author><name>Admin</name></author>
	</entry>
	<entry>
		<id>https://gentleman.cnes.fr/index.php?title=Methods&amp;diff=28&amp;oldid=prev</id>
		<title>Admin le 7 septembre 2021 à 07:40</title>
		<link rel="alternate" type="text/html" href="https://gentleman.cnes.fr/index.php?title=Methods&amp;diff=28&amp;oldid=prev"/>
		<updated>2021-09-07T07:40:47Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;fr&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Version précédente&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Version du 7 septembre 2021 à 07:40&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Ligne 1 :&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Ligne 1 :&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;font color=#556B2F&amp;gt;&amp;#039;&amp;#039;&amp;#039;GENTLEMAN&amp;#039;&amp;#039;&amp;#039;&amp;lt;/font&amp;gt; is working in two steps.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;font color=#556B2F&amp;gt;&amp;#039;&amp;#039;&amp;#039;GENTLEMAN&amp;#039;&amp;#039;&amp;#039;&amp;lt;/font&amp;gt; is working in two steps.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;# &lt;/del&gt;Propagation&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;:&#039;&#039;&#039;1. &lt;/ins&gt;Propagation&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;:&#039;&#039;&#039;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:First it will propagate a trajectory thanks to [http://psimu.cnes.fr &amp;#039;&amp;#039;&amp;#039;PSIMU&amp;#039;&amp;#039;&amp;#039;] tool; all the possibilities linked to its use are available so, any kind of trajectories around the Earth are allowed (&amp;lt;font color=#FF8C00 title=&amp;quot;Geostationnary Earth Orbit&amp;quot;&amp;gt;LEO&amp;lt;/font&amp;gt;, &amp;lt;font color=#FF8C00 title=&amp;quot;Low Earth Orbit&amp;quot;&amp;gt;LEO&amp;lt;/font&amp;gt;, even reentry !). This trajectory will be stored in a &amp;lt;font color=#FF8C00&amp;gt;SQlite&amp;lt;/font&amp;gt; data base with an output step defined by the user.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:First it will propagate a trajectory thanks to [http://psimu.cnes.fr &amp;#039;&amp;#039;&amp;#039;PSIMU&amp;#039;&amp;#039;&amp;#039;] tool; all the possibilities linked to its use are available so, any kind of trajectories around the Earth are allowed (&amp;lt;font color=#FF8C00 title=&amp;quot;Geostationnary Earth Orbit&amp;quot;&amp;gt;LEO&amp;lt;/font&amp;gt;, &amp;lt;font color=#FF8C00 title=&amp;quot;Low Earth Orbit&amp;quot;&amp;gt;LEO&amp;lt;/font&amp;gt;, even reentry !). This trajectory will be stored in a &amp;lt;font color=#FF8C00&amp;gt;SQlite&amp;lt;/font&amp;gt; data base with an output step defined by the user.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;# &lt;/del&gt;TLE building&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;&#039;2. &lt;/ins&gt;TLE building&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;:&#039;&#039;&#039;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Once this trajectory has been computed, &amp;lt;font color=#556B2F&amp;gt;&amp;#039;&amp;#039;&amp;#039;GENTLEMAN&amp;#039;&amp;#039;&amp;#039;&amp;lt;/font&amp;gt; will generate one or several &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Elements&amp;quot;&amp;gt;TLEs&amp;lt;/font&amp;gt;. The basic methods to build these &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Elements&amp;quot;&amp;gt;TLEs&amp;lt;/font&amp;gt; are the ones proposed by [http://patrius.cnes.fr PATRIUS] (&amp;#039;&amp;#039;&amp;#039;Differential&amp;#039;&amp;#039;&amp;#039; or &amp;#039;&amp;#039;&amp;#039;Levenberg Marquardt&amp;#039;&amp;#039;&amp;#039; methods). But, &amp;lt;font color=#556B2F&amp;gt;&amp;#039;&amp;#039;&amp;#039;GENTLEMAN&amp;#039;&amp;#039;&amp;#039;&amp;lt;/font&amp;gt; adds a complementary functionality as it allows finding the best compromise on the amount of points to fit a &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Element&amp;quot;&amp;gt;TLE&amp;lt;/font&amp;gt; thanks to the propagated trajectory.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Once this trajectory has been computed, &amp;lt;font color=#556B2F&amp;gt;&amp;#039;&amp;#039;&amp;#039;GENTLEMAN&amp;#039;&amp;#039;&amp;#039;&amp;lt;/font&amp;gt; will generate one or several &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Elements&amp;quot;&amp;gt;TLEs&amp;lt;/font&amp;gt;. The basic methods to build these &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Elements&amp;quot;&amp;gt;TLEs&amp;lt;/font&amp;gt; are the ones proposed by [http://patrius.cnes.fr PATRIUS] (&amp;#039;&amp;#039;&amp;#039;Differential&amp;#039;&amp;#039;&amp;#039; or &amp;#039;&amp;#039;&amp;#039;Levenberg Marquardt&amp;#039;&amp;#039;&amp;#039; methods). But, &amp;lt;font color=#556B2F&amp;gt;&amp;#039;&amp;#039;&amp;#039;GENTLEMAN&amp;#039;&amp;#039;&amp;#039;&amp;lt;/font&amp;gt; adds a complementary functionality as it allows finding the best compromise on the amount of points to fit a &amp;lt;font color=#FF8C00 title=&amp;quot;Two Lines Element&amp;quot;&amp;gt;TLE&amp;lt;/font&amp;gt; thanks to the propagated trajectory.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;

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&lt;/table&gt;</summary>
		<author><name>Admin</name></author>
	</entry>
	<entry>
		<id>https://gentleman.cnes.fr/index.php?title=Methods&amp;diff=27&amp;oldid=prev</id>
		<title>Admin le 7 septembre 2021 à 07:37</title>
		<link rel="alternate" type="text/html" href="https://gentleman.cnes.fr/index.php?title=Methods&amp;diff=27&amp;oldid=prev"/>
		<updated>2021-09-07T07:37:56Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Version précédente&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Version du 7 septembre 2021 à 07:37&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Ligne 1 :&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Ligne 1 :&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;TBW &lt;/del&gt;...&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;font color=#556B2F&amp;gt;&#039;&#039;&#039;GENTLEMAN&#039;&#039;&#039;&amp;lt;/font&amp;gt; is working in two steps&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;# Propagation&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;:First it will propagate a trajectory thanks to [http://psimu&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;cnes.fr &#039;&#039;&#039;PSIMU&#039;&#039;&#039;] tool; all the possibilities linked to its use are available so, any kind of trajectories around the Earth are allowed (&amp;lt;font color=#FF8C00 title=&quot;Geostationnary Earth Orbit&quot;&amp;gt;LEO&amp;lt;/font&amp;gt;, &amp;lt;font color=#FF8C00 title=&quot;Low Earth Orbit&quot;&amp;gt;LEO&amp;lt;/font&amp;gt;, even reentry !). This trajectory will be stored in a &amp;lt;font color=#FF8C00&amp;gt;SQlite&amp;lt;/font&amp;gt; data base with an output step defined by the user.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;# TLE building&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;:Once this trajectory has been computed, &amp;lt;font color=#556B2F&amp;gt;&#039;&#039;&#039;GENTLEMAN&#039;&#039;&#039;&amp;lt;/font&amp;gt; will generate one or several &amp;lt;font color=#FF8C00 title=&quot;Two Lines Elements&quot;&amp;gt;TLEs&amp;lt;/font&amp;gt;. The basic methods to build these &amp;lt;font color=#FF8C00 title=&quot;Two Lines Elements&quot;&amp;gt;TLEs&amp;lt;/font&amp;gt; are the ones proposed by [http://patrius.cnes.fr PATRIUS] (&#039;&#039;&#039;Differential&#039;&#039;&#039; or &#039;&#039;&#039;Levenberg Marquardt&#039;&#039;&#039; methods). But, &amp;lt;font color=#556B2F&amp;gt;&#039;&#039;&#039;GENTLEMAN&#039;&#039;&#039;&amp;lt;/font&amp;gt; adds a complementary functionality as it allows finding the best compromise on the amount of points to fit a &amp;lt;font color=#FF8C00 title=&quot;Two Lines Element&quot;&amp;gt;TLE&amp;lt;/font&amp;gt; thanks to the propagated trajectory.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Let us give an example with a trajectory ephemeris (included in the SQlite file) composed of 50 output points.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* A first possibility is to fit a &amp;lt;font color=#FF8C00 title=&quot;Two Lines Element&quot;&amp;gt;TLE&amp;lt;/font&amp;gt; by giving explicitly the amount of points to take into account: for example, the ten first ones.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* A second possibility is to leave &amp;lt;font color=#556B2F&amp;gt;&#039;&#039;&#039;GENTLEMAN&#039;&#039;&#039;&amp;lt;/font&amp;gt; to find this amount of points for such a fitting. To do it, &amp;lt;font color=#556B2F&amp;gt;&#039;&#039;&#039;GENTLEMAN&#039;&#039;&#039;&amp;lt;/font&amp;gt; will compute different &amp;lt;font color=#FF8C00 title=&quot;Two Lines Elements&quot;&amp;gt;TLEs&amp;lt;/font&amp;gt; using 1, then 2, then 3, then up to 50 points (or less if the user entered a maximum number). Considering each of these  &amp;lt;font color=#FF8C00 title=&quot;Two Lines Elements&quot;&amp;gt;TLEs&amp;lt;/font&amp;gt;, &amp;lt;font color=#556B2F&amp;gt;&#039;&#039;&#039;GENTLEMAN&#039;&#039;&#039;&amp;lt;/font&amp;gt; will compute for each point of the trajectory (or less if the user entered another maximum number), the difference between the trajectory and the one propagated with the &amp;lt;font color=#FF8C00 title=&quot;Two Lines Element&quot;&amp;gt;TLE&amp;lt;/font&amp;gt; as initial condition and the model linked to it (&#039;&#039;&#039;SGP4&#039;&#039;&#039; for &amp;lt;font color=#FF8C00 title=&quot;Low Earth Orbit&quot;&amp;gt;LEO&amp;lt;/font&amp;gt; and &#039;&#039;&#039;DeepSDP4&#039;&#039;&#039; for &amp;lt;font color=#FF8C00 title=&quot;Geostationnary Earth Orbit&quot;&amp;gt;LEO&amp;lt;/font&amp;gt;). &amp;lt;font color=#556B2F&amp;gt;&#039;&#039;&#039;GENTLEMAN&#039;&#039;&#039;&amp;lt;/font&amp;gt; will then select the &amp;lt;font color=#FF8C00 title=&quot;Two Lines Element&quot;&amp;gt;TLE&amp;lt;/font&amp;gt; which will get the lowest value for the mean error in semi major axis.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* In case of maneuvers to take into account or if the user decided to compute several &amp;lt;font color=#FF8C00 title=&quot;Two Lines Elements&quot;&amp;gt;TLEs&amp;lt;/font&amp;gt; (for example one &amp;lt;font color=#FF8C00 title=&quot;Two Lines Element&quot;&amp;gt;TLE&amp;lt;/font&amp;gt; by day), this process will be executed only in the interval between two &amp;lt;font color=#FF8C00 title=&quot;Two Lines Elements&quot;&amp;gt;TLEs&amp;lt;/font&amp;gt; (or one &amp;lt;font color=#FF8C00 title=&quot;Two Lines Element&quot;&amp;gt;TLE&amp;lt;/font&amp;gt; and the next maneuver)&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;

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&lt;/table&gt;</summary>
		<author><name>Admin</name></author>
	</entry>
	<entry>
		<id>https://gentleman.cnes.fr/index.php?title=Methods&amp;diff=19&amp;oldid=prev</id>
		<title>Admin : Page créée avec « TBW ... »</title>
		<link rel="alternate" type="text/html" href="https://gentleman.cnes.fr/index.php?title=Methods&amp;diff=19&amp;oldid=prev"/>
		<updated>2021-09-07T07:09:46Z</updated>

		<summary type="html">&lt;p&gt;Page créée avec « TBW ... »&lt;/p&gt;
&lt;p&gt;&lt;b&gt;Nouvelle page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;TBW ...&lt;/div&gt;</summary>
		<author><name>Admin</name></author>
	</entry>
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