## Lagrange Points

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nIf you like physics and astronomy, check out my new improved\nwebpage on "Lagrange points" - those orbits where a small third\nbody can stay in equilibrium rotating along with two more massive\nones:\n\nhttp://math.ucr.edu/home/baez/langrange.html\n\nWatch a movie of Trojan asteroids, read about the rare Mars\nTrojans and the one known Neptune Trojan, see a movie of the\ncrazy horseshoe-shaped orbit of the asteroid 3753 Cruithne,\nread about the search for alien spacecraft at the earth-moon\nLagrange points, and learn what was *found* at these Lagrange\npoints! Read about the mysterious missing extra moons of the\nEarth: Lilith and Kleinchen! There\'s some nice math here, too:\nNeil Cornish\'s proof that orbits at L4 and L5 are stable.\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>If you like physics and astronomy, check out my new improved
webpage on "Lagrange points" - those orbits where a small third
body can stay in equilibrium rotating along with two more massive
ones:

http://math.ucr.edu/home/baez/langrange.html

Trojans and the one known Neptune Trojan, see a movie of the
crazy horseshoe-shaped orbit of the asteroid 3753 Cruithne,
Lagrange points, and learn what was *found* at these Lagrange
Earth: Lilith and Kleinchen! There's some nice math here, too:
Neil Cornish's proof that orbits at L4 and L5 are stable.

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In article , John Baez wrote: That's http://math.ucr.edu/home/baez/lagrange.html of course. $$-Ted$$ -- [E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]



John Baez wrote: > > If you like physics and astronomy, check out my new improved > webpage on "Lagrange points" - those orbits where a small third > body can stay in equilibrium rotating along with two more massive > ones: > > http://math.ucr.edu/home/baez/langrange.html > > Watch a movie of Trojan asteroids, read about the rare Mars > Trojans and the one known Neptune Trojan, see a movie of the > crazy horseshoe-shaped orbit of the asteroid 3753 Cruithne, > read about the search for alien spacecraft at the earth-moon > Lagrange points, and learn what was *found* at these Lagrange > points! Read about the mysterious missing extra moons of the > Earth: Lilith and Kleinchen! There's some nice math here, too: > Neil Cornish's proof that orbits at L4 and L5 are stable. As noted elsewhere, John got hit by an ohnosecond. The correct URL is http://math.ucr.edu/home/baez/lagrange.html and it's a lovely page. -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf

## Lagrange Points

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>John Baez &lt;baez@galaxy.ucr.edu&gt; wrote:\n\n&gt; If you like physics and astronomy, check out my new improved\n&gt; webpage on "Lagrange points" - those orbits where a small third\n&gt; body can stay in equilibrium rotating along with two more massive\n&gt; ones:\n&gt;\n&gt; http://math.ucr.edu/home/baez/lagrange.html\n&gt;\n&gt; Watch a movie of Trojan asteroids, read about the rare Mars\n&gt; Trojans and the one known Neptune Trojan, see a movie of the\n&gt; crazy horseshoe-shaped orbit of the asteroid 3753 Cruithne,\n&gt; read about the search for alien spacecraft at the earth-moon\n&gt; Lagrange points, and learn what was *found* at these Lagrange\n&gt; points! Read about the mysterious missing extra moons of the\n&gt; Earth: Lilith and Kleinchen! There\'s some nice math here, too:\n&gt; Neil Cornish\'s proof that orbits at L4 and L5 are stable.\n\nAs you say there:\n&gt; But in these cases, the Coriolis force also plays a crucial role!\n\nA remark on the Coriolis force in problems like these:\nyou can see immediately that it must play a crucial role\nby considering the motion a stationary point in an inertial frame,\nas seen from a rotating frame.\nIn the rotating frame the motion is uniformly circular.\n\nActing on it in the rotating frame is at first sight\nonly the centrifugal force, so it might seem a mystery\nthat it would stay in it\'s circular orbit.\nOf course the coriolis force comes to the rescue\n(notice the essential factor two!)\nto provide the needed centripetal force.\n\nBest,\n\nJan\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>John Baez <baez@galaxy.ucr.edu> wrote:

> If you like physics and astronomy, check out my new improved
> webpage on "Lagrange points" - those orbits where a small third
> body can stay in equilibrium rotating along with two more massive
> ones:
>
> http://math.ucr.edu/home/baez/lagrange.html
>
> Watch a movie of Trojan asteroids, read about the rare Mars
> Trojans and the one known Neptune Trojan, see a movie of the
> crazy horseshoe-shaped orbit of the asteroid 3753 Cruithne,
> Lagrange points, and learn what was *found* at these Lagrange
> Earth: Lilith and Kleinchen! There's some nice math here, too:
> Neil Cornish's proof that orbits at L4 and L5 are stable.

As you say there:
> But in these cases, the Coriolis force also plays a crucial role!

A remark on the Coriolis force in problems like these:
you can see immediately that it must play a crucial role
by considering the motion a stationary point in an inertial frame,
as seen from a rotating frame.
In the rotating frame the motion is uniformly circular.

Acting on it in the rotating frame is at first sight
only the centrifugal force, so it might seem a mystery
that it would stay in it's circular orbit.
Of course the coriolis force comes to the rescue
(notice the essential factor two!)
to provide the needed centripetal force.

Best,

Jan


In article , John Baez wrote: >If you like physics and astronomy, check out my new improved >webpage on "Lagrange points" - those orbits where a small third >body can stay in equilibrium rotating along with two more massive >ones: > >http://math.ucr.edu/home/baez/langrange.html Or even better: http://math.ucr.edu/home/baez/lagrange.html I know physics but I can't speell.



John Baez wrote: > If you like physics and astronomy, check out my new improved > webpage on "Lagrange points" - those orbits where a small third > body can stay in equilibrium rotating along with two more massive > ones: > > http://math.ucr.edu/home/baez/lagrange.html > > Watch a movie of Trojan asteroids, read about the rare Mars > Trojans and the one known Neptune Trojan, see a movie of the > crazy horseshoe-shaped orbit of the asteroid 3753 Cruithne, > read about the search for alien spacecraft at the earth-moon > Lagrange points, and learn what was *found* at these Lagrange > points! Read about the mysterious missing extra moons of the > Earth: Lilith and Kleinchen! There's some nice math here, too: > Neil Cornish's proof that orbits at L4 and L5 are stable. As you say there: > But in these cases, the Coriolis force also plays a crucial role! A remark on the Coriolis force in problems like these: you can see immediately that it must play a crucial role by considering the motion a stationary point in an inertial frame, as seen from a rotating frame. In the rotating frame the motion is uniformly circular. Acting on it in the rotating frame is at first sight only the centrifugal force, so it might seem a mystery that it would stay in it's circular orbit. Of course the coriolis force comes to the rescue (notice the essential factor two!) to provide the needed centripetal force. Best, Jan

 Recognitions: Gold Member Science Advisor Its also important to realise that the Lagrange points are forced oscillations, the 'trojan' is kept in check by the parent body. This is significant when extra-solar planetary systems with 'hot Jupiters' are concerned. If these planets have migrated from their place of origin they would have taken their 'trojans' with them. So planets that themselves are unsuitable for life because they are gas giants, but are in the biological zone of their parent star, could not only have life bearing satellites but also life bearing 'trojan' companions.


While, me too, was very much in awe of the concepts of Lagrange Points, thought I would share one of my thoughts when I first learned about this math (and thats what I would consider it, math). Our present most advance theories limit our velocities to that of the speed of light. If I am a physics, and someone ask me if I think we will able break the speed of light barrier (the so-called 'warp'), my answer would be we don't know how, but someday, we will. If you don't have faith that its possible, why continue to study, everythings already known. So, thanks for those have have preceeded, to show the light to those that follow, but if the study physics is what drives your heart, don't use Lagrange points as a panacea. Subject: Lagrange Points From: baez@galaxy.ucr.edu (John Baez) Date: $10/25/04 5:09 AM$ Pacific Standard Time Message-id: If you like physics and astronomy, check out my new improved webpage on "Lagrange points" - those orbits where a small third body can stay in equilibrium rotating along with two more massive ones: http://math.ucr.edu/home/baez/langrange.html Watch a movie of Trojan asteroids, read about the rare Mars Trojans and the one known Neptune Trojan, see a movie of the crazy horseshoe-shaped orbit of the asteroid 3753 Cruithne, read about the search for alien spacecraft at the earth-moon Lagrange points, and learn what was *found* at these Lagrange points! Read about the mysterious missing extra moons of the Earth: Lilith and Kleinchen! There's some nice math here, too:Neil Cornish's proof that orbits at L4 and L5 are stable.