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	<id>https://en.formulasearchengine.com/index.php?action=history&amp;feed=atom&amp;title=Tilted_large_deviation_principle</id>
	<title>Tilted large deviation principle - Revision history</title>
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	<updated>2026-05-22T18:26:46Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://en.formulasearchengine.com/index.php?title=Tilted_large_deviation_principle&amp;diff=255801&amp;oldid=prev</id>
		<title>en&gt;Yobot: /* References */WP:CHECKWIKI error fixes using AWB (10093)</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/index.php?title=Tilted_large_deviation_principle&amp;diff=255801&amp;oldid=prev"/>
		<updated>2014-05-05T12:27:00Z</updated>

		<summary type="html">&lt;p&gt;&lt;span class=&quot;autocomment&quot;&gt;References: &lt;/span&gt;&lt;a href=&quot;/index.php?title=WP:CHECKWIKI&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;WP:CHECKWIKI (page does not exist)&quot;&gt;WP:CHECKWIKI&lt;/a&gt; error fixes using &lt;a href=&quot;/index.php?title=Testwiki:AWB&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;Testwiki:AWB (page does not exist)&quot;&gt;AWB&lt;/a&gt; (10093)&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;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 14:27, 5 May 2014&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;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 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;{{Orphan|date=February 2009}}&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;Hi there&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;I am Alyson Boon even though it &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;not &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;name on my birth certification&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Credit authorising is how he tends &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;make money&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Mississippi is where her home &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;but her husband desires them to move&lt;/ins&gt;. To &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;climb is some thing she &lt;/ins&gt;would &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;by no means give up&lt;/ins&gt;.&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Take a look at my web-site :&lt;/ins&gt;: &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;online psychic reading (&lt;/ins&gt;[http://&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;myfusionprofits&lt;/ins&gt;.com/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;groups&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;find-out-about-self-improvement-tips&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;here/ myfusionprofits&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;com&lt;/ins&gt;]&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;)&lt;/ins&gt;&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;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;&#039;Gate orbits&#039;&#039;&#039; are optimal circular departure orbits for transfer from one planet to another. At certain specific orbits around a cosmic body, the additional [[delta-v|delta-&#039;&#039;v&#039;&#039;]] required to go from orbital velocity to [[hyperbolic trajectory]] for an interplanetary transfer&lt;/del&gt;, is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;minimal. Gate orbits can therefore be very useful for minimising &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[delta-v budget|delta-&#039;&#039;v&#039;&#039; budget]] for an interplanetary trip&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;For example, the required delta-&#039;&#039;v&#039;&#039; for a [[Hohmann transfer orbit]] from the Earth &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Mars (considering Earth at 1 AU and Mars at 1&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;52 AU) &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2.94 km/s&lt;/del&gt;. To &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;reach 2.94 km/s at infinity from a [[low Earth orbit]] at, say 200 km altitude, requires a 3.61 km/s burn. If the vehicle were to leave the Earth&#039;s attraction from the 92,000 km high Mars gate orbit instead, required delta-&#039;&#039;v&#039;&#039; &lt;/del&gt;would &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;be only 2.08 km/s. At higher still orbits the required delta-&#039;&#039;v&#039;&#039; rises again. For example, at 150,000 km, required delta-v is now 2.17 km/s.&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;Reducing the delta-&#039;&#039;v&#039;&#039; from 3.61 to 2&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;08 km/s can reduce the total mass of the vehicle by as much as 38%, or increase the payload by 62%!&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;The radius of a given gate orbit can be calculated using the following equation:&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;r = {2\mu \over v_\infty^2}&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/del&gt;&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;where&lt;/del&gt;:&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;*&amp;lt;math&amp;gt;r\,&amp;lt;/math&amp;gt; is the distance between the [[orbiting body]] and the [[central body]], in km&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;*&amp;lt;math&amp;gt;\mu\,&amp;lt;/math&amp;gt; is the [[standard gravitational parameter]], in km&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;s&amp;lt;sup&amp;gt;−2&amp;lt;/sup&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;*&amp;lt;math&amp;gt;v_\infty\,&amp;lt;/math&amp;gt; is the required velocity at infinity, in km·s&amp;lt;sup&amp;gt;−1&amp;lt;/sup&amp;gt;. Remember &amp;lt;math&amp;gt;v_\infty^2&amp;lt;/math&amp;gt; is also known as &amp;lt;math&amp;gt;C3&amp;lt;/math&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;== External links ==&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;[http://&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;www.christov&lt;/del&gt;.com/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;space&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;IGO&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;5&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;pdf Interplanetary Gate Orbits by Marco Christov]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;[[Category:Spaceflight]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;[[Category:Orbital maneuvers]&lt;/del&gt;]&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>en&gt;Yobot</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/index.php?title=Tilted_large_deviation_principle&amp;diff=17980&amp;oldid=prev</id>
		<title>en&gt;Sodin: removed Category:Probability theory using HotCat</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/index.php?title=Tilted_large_deviation_principle&amp;diff=17980&amp;oldid=prev"/>
		<updated>2011-10-16T00:12:43Z</updated>

		<summary type="html">&lt;p&gt;removed &lt;a href=&quot;/index.php?title=Category:Probability_theory&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;Category:Probability theory (page does not exist)&quot;&gt;Category:Probability theory&lt;/a&gt; using &lt;a href=&quot;/index.php?title=WP:HC&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;WP:HC (page does not exist)&quot;&gt;HotCat&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{Orphan|date=February 2009}}&lt;br /&gt;
&amp;#039;&amp;#039;&amp;#039;Gate orbits&amp;#039;&amp;#039;&amp;#039; are optimal circular departure orbits for transfer from one planet to another. At certain specific orbits around a cosmic body, the additional [[delta-v|delta-&amp;#039;&amp;#039;v&amp;#039;&amp;#039;]] required to go from orbital velocity to [[hyperbolic trajectory]] for an interplanetary transfer, is minimal. Gate orbits can therefore be very useful for minimising the [[delta-v budget|delta-&amp;#039;&amp;#039;v&amp;#039;&amp;#039; budget]] for an interplanetary trip.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For example, the required delta-&amp;#039;&amp;#039;v&amp;#039;&amp;#039; for a [[Hohmann transfer orbit]] from the Earth to Mars (considering Earth at 1 AU and Mars at 1.52 AU) is 2.94 km/s. To reach 2.94 km/s at infinity from a [[low Earth orbit]] at, say 200 km altitude, requires a 3.61 km/s burn. If the vehicle were to leave the Earth&amp;#039;s attraction from the 92,000 km high Mars gate orbit instead, required delta-&amp;#039;&amp;#039;v&amp;#039;&amp;#039; would be only 2.08 km/s. At higher still orbits the required delta-&amp;#039;&amp;#039;v&amp;#039;&amp;#039; rises again. For example, at 150,000 km, required delta-v is now 2.17 km/s.&lt;br /&gt;
&lt;br /&gt;
Reducing the delta-&amp;#039;&amp;#039;v&amp;#039;&amp;#039; from 3.61 to 2.08 km/s can reduce the total mass of the vehicle by as much as 38%, or increase the payload by 62%!&lt;br /&gt;
&lt;br /&gt;
The radius of a given gate orbit can be calculated using the following equation:&lt;br /&gt;
:&amp;lt;math&amp;gt;r = {2\mu \over v_\infty^2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where:&lt;br /&gt;
*&amp;lt;math&amp;gt;r\,&amp;lt;/math&amp;gt; is the distance between the [[orbiting body]] and the [[central body]], in km&lt;br /&gt;
*&amp;lt;math&amp;gt;\mu\,&amp;lt;/math&amp;gt; is the [[standard gravitational parameter]], in km&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;s&amp;lt;sup&amp;gt;−2&amp;lt;/sup&amp;gt;&lt;br /&gt;
*&amp;lt;math&amp;gt;v_\infty\,&amp;lt;/math&amp;gt; is the required velocity at infinity, in km·s&amp;lt;sup&amp;gt;−1&amp;lt;/sup&amp;gt;. Remember &amp;lt;math&amp;gt;v_\infty^2&amp;lt;/math&amp;gt; is also known as &amp;lt;math&amp;gt;C3&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== External links ==&lt;br /&gt;
* [http://www.christov.com/space/IGO-5.pdf Interplanetary Gate Orbits by Marco Christov]&lt;br /&gt;
&lt;br /&gt;
[[Category:Spaceflight]]&lt;br /&gt;
[[Category:Orbital maneuvers]]&lt;/div&gt;</summary>
		<author><name>en&gt;Sodin</name></author>
	</entry>
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