Lagrange Points

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.

In article , John Baez wrote:

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

That's

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

of course.

-Ted


--
[E-mail me at , as opposed to .]

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

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 the
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 the
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

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.



It may interest you and others in the group that the "Gallica" site of
the French national library has the paper by Lagrange "Essai sur le
probl=E8me des trois corps" available for free download.
Go to http://gallica.bnf.fr/Metacata.htm and write Lagrange as the
author. Select the 6th volume of the collected works: "Oeuvres / Joseph
Louis de Lagrange. 6 / publ. par les soins de J.-A. Serret" and then go
to page 229.
Beside, Gallica has many other vintage astronomy books and papers
available for download.
Paolo