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	<title>Comments on: Q&amp;BA: How does a gravity slingshot work?</title>
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	<link>http://blogs.discovermagazine.com/badastronomy/2012/02/17/qba-how-does-a-gravity-slingshot-work/</link>
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	<lastBuildDate>Wed, 21 Nov 2012 15:12:45 +0000</lastBuildDate>
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		<title>By: Stuff &#171; Econstudentlog</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2012/02/17/qba-how-does-a-gravity-slingshot-work/#comment-323750</link>
		<dc:creator>Stuff &#171; Econstudentlog</dc:creator>
		<pubDate>Mon, 30 Apr 2012 08:31:07 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/?p=44628#comment-323750</guid>
		<description>[...] ix. How does a gravity slingshot work? [...] </description>
		<content:encoded><![CDATA[<p>[...] ix. How does a gravity slingshot work? [...] </p>
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		<title>By: Matt B.</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2012/02/17/qba-how-does-a-gravity-slingshot-work/#comment-323749</link>
		<dc:creator>Matt B.</dc:creator>
		<pubDate>Thu, 29 Mar 2012 19:50:18 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/?p=44628#comment-323749</guid>
		<description>It&#039;s much easier to understand with vectors. Taking a hyperbolic orbit around a planet changes your direction, though not your speed, relative to the planet. However, the planet has a non-zero velocity relative to the sun, and you get to add twice the planet&#039;s velocity vector to your own, when looking at things from the reference frame of the sun. You just choose how close to pass the planet in order to choose your exit direction.</description>
		<content:encoded><![CDATA[<p>It&#8217;s much easier to understand with vectors. Taking a hyperbolic orbit around a planet changes your direction, though not your speed, relative to the planet. However, the planet has a non-zero velocity relative to the sun, and you get to add twice the planet&#8217;s velocity vector to your own, when looking at things from the reference frame of the sun. You just choose how close to pass the planet in order to choose your exit direction.</p>
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		<title>By: Alex</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2012/02/17/qba-how-does-a-gravity-slingshot-work/#comment-323748</link>
		<dc:creator>Alex</dc:creator>
		<pubDate>Tue, 20 Mar 2012 15:02:20 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/?p=44628#comment-323748</guid>
		<description>@kmw (#8),
You&#039;re right about moons experiencing this effect. When you get more than two bodies involved, the math gets pretty tricky. What usually happens is something called Orbital Resonance. If, say, the moons of Jupiter were all on arbitrary orbits, they would eventually tug eachother out of place, and the system would fly apart. If their orbits align, however - with their periods being a ratio of some small integers - they actually serve to stabilize eachother.
http://upload.wikimedia.org/wikipedia/commons/8/83/Galilean_moon_Laplace_resonance_animation.gif</description>
		<content:encoded><![CDATA[<p>@kmw (#8),<br />
You&#8217;re right about moons experiencing this effect. When you get more than two bodies involved, the math gets pretty tricky. What usually happens is something called Orbital Resonance. If, say, the moons of Jupiter were all on arbitrary orbits, they would eventually tug eachother out of place, and the system would fly apart. If their orbits align, however &#8211; with their periods being a ratio of some small integers &#8211; they actually serve to stabilize eachother.<br />
<a href="http://upload.wikimedia.org/wikipedia/commons/8/83/Galilean_moon_Laplace_resonance_animation.gif" rel="nofollow">http://upload.wikimedia.org/wikipedia/commons/8/83/Galilean_moon_Laplace_resonance_animation.gif</a></p>
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		<title>By: Dave</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2012/02/17/qba-how-does-a-gravity-slingshot-work/#comment-323747</link>
		<dc:creator>Dave</dc:creator>
		<pubDate>Wed, 22 Feb 2012 22:45:37 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/?p=44628#comment-323747</guid>
		<description>@CJ

Yeah, basically you throw a SuperBall at 60mph North, toward a truck that&#039;s heading 60mph South, and the SuperBall ends up going 180mph South (if you ignore air resistance — SuperBalls are quite efficient in their bounce).</description>
		<content:encoded><![CDATA[<p>@CJ</p>
<p>Yeah, basically you throw a SuperBall at 60mph North, toward a truck that&#8217;s heading 60mph South, and the SuperBall ends up going 180mph South (if you ignore air resistance — SuperBalls are quite efficient in their bounce).</p>
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		<title>By: CJ Nerd</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2012/02/17/qba-how-does-a-gravity-slingshot-work/#comment-323746</link>
		<dc:creator>CJ Nerd</dc:creator>
		<pubDate>Wed, 22 Feb 2012 22:16:31 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/?p=44628#comment-323746</guid>
		<description>@Dave
Sorry, I made a nonsense of my point by copying and pasting the wrong bit of shunt1&#039;s post at 35.

Where I put:
&gt; I’m not sure where you’re getting
&gt; “the lowest velocity has the highest orbit”-
&gt; who’s suggesting that?

I should have had:
&gt; I’m not sure where you’re getting
&gt; “The higher the orbit, the greater the velocity.”-
&gt; who’s suggesting that?

Turning to the truck analogy... ok, if it&#039;s a nearly-infinitely-massive truck and a neglibly-massive car, and a 100% efficient trampoline, I can see that it would work that way. I had  to force myself to make those assumptions before I could see it.</description>
		<content:encoded><![CDATA[<p>@Dave<br />
Sorry, I made a nonsense of my point by copying and pasting the wrong bit of shunt1&#8242;s post at 35.</p>
<p>Where I put:<br />
&gt; I’m not sure where you’re getting<br />
&gt; “the lowest velocity has the highest orbit”-<br />
&gt; who’s suggesting that?</p>
<p>I should have had:<br />
&gt; I’m not sure where you’re getting<br />
&gt; “The higher the orbit, the greater the velocity.”-<br />
&gt; who’s suggesting that?</p>
<p>Turning to the truck analogy&#8230; ok, if it&#8217;s a nearly-infinitely-massive truck and a neglibly-massive car, and a 100% efficient trampoline, I can see that it would work that way. I had  to force myself to make those assumptions before I could see it.</p>
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		<title>By: Dave</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2012/02/17/qba-how-does-a-gravity-slingshot-work/#comment-323745</link>
		<dc:creator>Dave</dc:creator>
		<pubDate>Wed, 22 Feb 2012 19:54:27 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/?p=44628#comment-323745</guid>
		<description>@CJ,

Did you see my reply about the truck?  The analogy works just fine, if you assume a (nearly) infinitely massive truck.

Also, you write, &quot;I’m not sure where you’re getting “the lowest velocity has the highest orbit”- who’s suggesting that?&quot;

Why do you say &quot;who&#039;s suggesting that?&quot;?  The numbers you just wrote show that the orbital speed goes inversely with orbital radius (actually goes as r^(-1/2), where r is the orbital separation), just as the claim &quot;the lowest velocity has the highest orbit&quot; suggests.</description>
		<content:encoded><![CDATA[<p>@CJ,</p>
<p>Did you see my reply about the truck?  The analogy works just fine, if you assume a (nearly) infinitely massive truck.</p>
<p>Also, you write, &#8220;I’m not sure where you’re getting “the lowest velocity has the highest orbit”- who’s suggesting that?&#8221;</p>
<p>Why do you say &#8220;who&#8217;s suggesting that?&#8221;?  The numbers you just wrote show that the orbital speed goes inversely with orbital radius (actually goes as r^(-1/2), where r is the orbital separation), just as the claim &#8220;the lowest velocity has the highest orbit&#8221; suggests.</p>
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		<title>By: CJ Nerd</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2012/02/17/qba-how-does-a-gravity-slingshot-work/#comment-323744</link>
		<dc:creator>CJ Nerd</dc:creator>
		<pubDate>Wed, 22 Feb 2012 13:36:08 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/?p=44628#comment-323744</guid>
		<description>@shunt1

Assuming your &quot;Does this actually need a reply?&quot; refers to my post 34... well, no-one *has* to reply, but surely sharing understanding with others is what this sort of thread is about? If I&#039;m wrong, I would hope that someone would be able to explain why.

&quot;The higher the orbit, the greater the velocity.
Please list the orbital velocity of each of the planets (or even satellites) and see if I am correct.&quot;

I&#039;m not sure if you&#039;re agreeing or disagreeing. But let&#039;s try it:
http://www.windows2universe.org/our_solar_system/planets_table.html
                                                             Merc     Ven   Earth  Mars  Jup       Sat    Ura     Nep
mean orbital velocity (km/sec) 47.89   35.03 29.79 24.13 13.06   9.64   6.81   5.43

Higher orbit seems to imply slower velocity, much as I thought.

I&#039;m not sure where you&#039;re getting &quot;the lowest velocity has the highest orbit&quot;- who&#039;s suggesting that?

&quot;Wikipedia is saying that a gravity assist adds the velocity of a space probe plus DOUBLE the velocity of the Planet?&quot;

Wikipedia is indeed saying that- see the first two paragraphs and the diagram under the heading &quot;Explanation&quot;. If Wikipedia is wrong, then it would be good if someone were to correct it.

The point of my lecturer&#039;s question is that the mass of the planet doesn&#039;t really matter- any planet is WAY big enough- but the speed does.

The Cassini graph in Wikipedia, near the bottom of the article, and here
http://en.wikipedia.org/wiki/File:Cassini%27s_speed_related_to_Sun.png
is attributed to JPL, and it shows Venus and Earth affecting the spacecraft&#039;s speed far more than Jupiter. Are you saying the graph is wrong?

I&#039;m not sure your analogy with trucks holds, as it doesn&#039;t appear to represent the kinetic energy that the spacecraft can gain by slowing the planet down.

Best
CJ Nerd.</description>
		<content:encoded><![CDATA[<p>@shunt1</p>
<p>Assuming your &#8220;Does this actually need a reply?&#8221; refers to my post 34&#8230; well, no-one *has* to reply, but surely sharing understanding with others is what this sort of thread is about? If I&#8217;m wrong, I would hope that someone would be able to explain why.</p>
<p>&#8220;The higher the orbit, the greater the velocity.<br />
Please list the orbital velocity of each of the planets (or even satellites) and see if I am correct.&#8221;</p>
<p>I&#8217;m not sure if you&#8217;re agreeing or disagreeing. But let&#8217;s try it:<br />
<a href="http://www.windows2universe.org/our_solar_system/planets_table.html" rel="nofollow">http://www.windows2universe.org/our_solar_system/planets_table.html</a><br />
                                                             Merc     Ven   Earth  Mars  Jup       Sat    Ura     Nep<br />
mean orbital velocity (km/sec) 47.89   35.03 29.79 24.13 13.06   9.64   6.81   5.43</p>
<p>Higher orbit seems to imply slower velocity, much as I thought.</p>
<p>I&#8217;m not sure where you&#8217;re getting &#8220;the lowest velocity has the highest orbit&#8221;- who&#8217;s suggesting that?</p>
<p>&#8220;Wikipedia is saying that a gravity assist adds the velocity of a space probe plus DOUBLE the velocity of the Planet?&#8221;</p>
<p>Wikipedia is indeed saying that- see the first two paragraphs and the diagram under the heading &#8220;Explanation&#8221;. If Wikipedia is wrong, then it would be good if someone were to correct it.</p>
<p>The point of my lecturer&#8217;s question is that the mass of the planet doesn&#8217;t really matter- any planet is WAY big enough- but the speed does.</p>
<p>The Cassini graph in Wikipedia, near the bottom of the article, and here<br />
<a href="http://en.wikipedia.org/wiki/File:Cassini%27s_speed_related_to_Sun.png" rel="nofollow">http://en.wikipedia.org/wiki/File:Cassini%27s_speed_related_to_Sun.png</a><br />
is attributed to JPL, and it shows Venus and Earth affecting the spacecraft&#8217;s speed far more than Jupiter. Are you saying the graph is wrong?</p>
<p>I&#8217;m not sure your analogy with trucks holds, as it doesn&#8217;t appear to represent the kinetic energy that the spacecraft can gain by slowing the planet down.</p>
<p>Best<br />
CJ Nerd.</p>
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		<title>By: Dave</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2012/02/17/qba-how-does-a-gravity-slingshot-work/#comment-323743</link>
		<dc:creator>Dave</dc:creator>
		<pubDate>Wed, 22 Feb 2012 03:14:44 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/?p=44628#comment-323743</guid>
		<description>@shunt1,

Yes, you would be going 180 mph!  Your relative velocity between you and the truck is 120mph.   Perhaps it&#039;s a bit easier to imagine if the truck has a giant trampoline attached to the grill, and you drive right into the trampoline.  You come in at 120mph relative to the trampoline, so you&#039;ll go back out (the opposite direction) at 120mph relative to the trampoline.  Since the trampoline is affixed to the truck and is traveling at 60mph relative to the ground, you&#039;ll be traveling at (60+120)mph or 180mph relative to the ground after the bounce.</description>
		<content:encoded><![CDATA[<p>@shunt1,</p>
<p>Yes, you would be going 180 mph!  Your relative velocity between you and the truck is 120mph.   Perhaps it&#8217;s a bit easier to imagine if the truck has a giant trampoline attached to the grill, and you drive right into the trampoline.  You come in at 120mph relative to the trampoline, so you&#8217;ll go back out (the opposite direction) at 120mph relative to the trampoline.  Since the trampoline is affixed to the truck and is traveling at 60mph relative to the ground, you&#8217;ll be traveling at (60+120)mph or 180mph relative to the ground after the bounce.</p>
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		<title>By: shunt1</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2012/02/17/qba-how-does-a-gravity-slingshot-work/#comment-323742</link>
		<dc:creator>shunt1</dc:creator>
		<pubDate>Wed, 22 Feb 2012 01:42:31 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/?p=44628#comment-323742</guid>
		<description>Does this actually need a reply?

The higher the orbit, the greater the velocity.

Please list the orbital velocity of each of the planets (or even satellites) and see if I am correct.

But to follow this logic, the lowest velocity has the highest orbit?  Then all we have to do to place a satellite in geosynchronous orbit would be to throw it into the air a couple of feet!

Wikipedia is saying that a gravity assist adds the velocity of a space probe plus DOUBLE the velocity of the Planet?

Giggle, I would love to see a demonstration of those physics!

Passing a heavy truck in the other lane where each has a speed of 60 mph and throwing out a grappling hook with a very strong cable.

After you spin around and are going in the same direction as the truck, your car would now be going 180 mph?

I DO NOT THINK SO!</description>
		<content:encoded><![CDATA[<p>Does this actually need a reply?</p>
<p>The higher the orbit, the greater the velocity.</p>
<p>Please list the orbital velocity of each of the planets (or even satellites) and see if I am correct.</p>
<p>But to follow this logic, the lowest velocity has the highest orbit?  Then all we have to do to place a satellite in geosynchronous orbit would be to throw it into the air a couple of feet!</p>
<p>Wikipedia is saying that a gravity assist adds the velocity of a space probe plus DOUBLE the velocity of the Planet?</p>
<p>Giggle, I would love to see a demonstration of those physics!</p>
<p>Passing a heavy truck in the other lane where each has a speed of 60 mph and throwing out a grappling hook with a very strong cable.</p>
<p>After you spin around and are going in the same direction as the truck, your car would now be going 180 mph?</p>
<p>I DO NOT THINK SO!</p>
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		<title>By: CJ Nerd</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2012/02/17/qba-how-does-a-gravity-slingshot-work/#comment-323741</link>
		<dc:creator>CJ Nerd</dc:creator>
		<pubDate>Tue, 21 Feb 2012 13:04:38 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/?p=44628#comment-323741</guid>
		<description>Hi Phil,
About 3:30 in the video, you refer to Jupiter being best for this sort of manouevre.

I recently attended a talk on this, where the lecturer started by asking the audience to guess if Venus, Jupiter or Saturn was best. Most plumped for Jupiter, a few for Venus.

The correct answer, the lecturer said, was Venus- because it moves faster than the other two, so more change in velocity is available.

In the Wikipedia article
http://en.wikipedia.org/wiki/Gravitational_slingshot
a graph shows that Cassini gained ~9km/sec from two passes of Venus, and just ~1.5km/sec from its one pass of Jupiter.

The total gain AFTER two passes of Venus and one of Earth is about 13km/sec- but that&#039;s AFTER those passes, not FROM them, because obviously falling towards the Sun accounts for quite a bit.

I&#039;d love to understand more about what&#039;s going on in that graph- especially on the first Venus pass. Could you possibly comment?</description>
		<content:encoded><![CDATA[<p>Hi Phil,<br />
About 3:30 in the video, you refer to Jupiter being best for this sort of manouevre.</p>
<p>I recently attended a talk on this, where the lecturer started by asking the audience to guess if Venus, Jupiter or Saturn was best. Most plumped for Jupiter, a few for Venus.</p>
<p>The correct answer, the lecturer said, was Venus- because it moves faster than the other two, so more change in velocity is available.</p>
<p>In the Wikipedia article<br />
<a href="http://en.wikipedia.org/wiki/Gravitational_slingshot" rel="nofollow">http://en.wikipedia.org/wiki/Gravitational_slingshot</a><br />
a graph shows that Cassini gained ~9km/sec from two passes of Venus, and just ~1.5km/sec from its one pass of Jupiter.</p>
<p>The total gain AFTER two passes of Venus and one of Earth is about 13km/sec- but that&#8217;s AFTER those passes, not FROM them, because obviously falling towards the Sun accounts for quite a bit.</p>
<p>I&#8217;d love to understand more about what&#8217;s going on in that graph- especially on the first Venus pass. Could you possibly comment?</p>
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